Datasets:

unigram

/

FOL-nli

like 1

Barbara is the only person in the room. If “Barbara is an expert in identifying and foraging wild edible plants” then “Barbara collects antique jewelry”. If “it is not the case that “Barbara collects foreign coins”” then “Barbara collects foreign coins and is a coffee connoisseur”. If “Barbara uses contact lenses” then “Barbara is an expert in identifying and foraging wild edible plants”. Barbara enjoys watercolor painting and collects vintage stamps. Barbara regularly goes on multi-day backpacking trips in national parks.

Barbara collects antique clocks.

neutral

room(barbara)&(![X]:(room(X)=>(X='barbara')))& ((is_an_expert_in_identifying_and_foraging_wild_edible_plants(barbara))=>(collects_antique_jewelry(barbara)))& ((~(collects_foreign_coins(barbara)))=>(((collects_foreign_coins(barbara))&(is_a_coffee_connoisseur(barbara)))))& ((uses_contact_lenses(barbara))=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(barbara)))& (((enjoys_watercolor_painting(barbara))&(collects_vintage_stamps(barbara))))& (regularly_goes_on_multi-day_backpacking_trips_in_national_parks(barbara))& (?[X]:(room(X)&(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))& (is_a_craft_beer_aficionado(barbara))& (is_a_coffee_connoisseur(barbara))& (is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(barbara))& (streams_on_Twitch(barbara))& (?[X]:(room(X)&(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))& ((![X]:((is_a_professional_photographer_specializing_in_portrait_photography(X))<=>(mentors_a_youth_basketball_team_on_weekends(X)))))& (~((writes_and_illustrates_their_own_graphic_novels(barbara))|(collects_rare_and_antique_scientific_instruments(barbara))))& (uses_contact_lenses(barbara))& (collects_foreign_coins(barbara))& (~(?[X]:(~room(X)&(collects_antique_clocks(X)))))& (enjoys_watercolor_painting(barbara))& (~(mentors_a_youth_basketball_team_on_weekends(barbara)))& (is_a_culinary_enthusiast_who_experiments_with_international_cuisines(barbara))& (collects_vintage_stamps(barbara))& (practices_and_performs_acrobatic_dance_routines(barbara))

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

Amber, Lena are the only persons in the room. Everyone in the room is funny only if Lena is the oldest in the room. Everyone in the room neither is a tall person nor is curious. Not everyone in the room neither is a quiet person nor is wise. Lena and Amber are old persons. If someone is tall then he/she neither is a strong person nor is strong. Everyone in the room is generous. All generous persons are patient. Lena either is a funny person or is generous but not both. Everyone outside the room is a quiet person. Everyone anywhere is a quiet person. Everyone in the room is a strong person. All wise persons are brave. Everyone in the room is kind. Lena is a tall person, is kind or is generous. Everyone in the room is a humble person, is curious or is generous. Lena is a patient person, is happy or is a brave person. All calm persons are brave. Amber is generous. Only one person outside the room is curious. Everyone in the room is strong. Lena is the oldest in the room. Everyone in the room is patient.

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.

contradiction

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

room(amber)&room(lena)&(![X]:(room(X)=>(X='amber'|X='lena')))& ~(~(~((?[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))))))

% SZS status Unsatisfiable for 6969956456215280849442226 % SZS output start Proof for 6969956456215280849442226 5. ! [X0] : anywhere(X0) [input b4] 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 48. person(mary) & old(mary) & person(paul) & old(paul) [input p4] 49. ! [X0] : (tall(X0) => ~(strong(X0) | (person(X0) & strong(X0)))) [input p5] 54. ! [X0] : (anywhere(X0) => (person(X0) & quiet(X0))) [input p10] 55. ! [X0] : (room(X0) => (person(X0) & strong(X0))) [input p11] 57. ! [X0] : (room(X0) => kind(X0)) [input p13] 67. ~~~? [X0,X1] : (X0 != X1 & person(X1) & old(X1) & person(X1) & kind(X1) & ~tall(X1) & person(X0) & old(X0) & person(X0) & kind(X0) & ~tall(X0) & room(X1) & room(X0)) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 70. ~~~? [X0,X1] : (X0 != X1 & person(X1) & old(X1) & person(X1) & kind(X1) & ~tall(X1) & person(X0) & old(X0) & person(X0) & kind(X0) & ~tall(X0) & room(X1) & room(X0)) & ! [X2] : (room(X2) => (paul = X2 | mary = X2)) & room(paul) & room(mary) [rectify 67] 71. ~? [X0,X1] : (X0 != X1 & person(X1) & old(X1) & person(X1) & kind(X1) & ~tall(X1) & person(X0) & old(X0) & person(X0) & kind(X0) & ~tall(X0) & room(X1) & room(X0)) & ! [X2] : (room(X2) => (paul = X2 | mary = X2)) & room(paul) & room(mary) [flattening 70] 150. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 151. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 150] 156. ! [X0] : ((~strong(X0) & (~person(X0) | ~strong(X0))) | ~tall(X0)) [ennf transformation 49] 159. ! [X0] : ((person(X0) & quiet(X0)) | ~anywhere(X0)) [ennf transformation 54] 160. ! [X0] : ((person(X0) & strong(X0)) | ~room(X0)) [ennf transformation 55] 161. ! [X0] : (kind(X0) | ~room(X0)) [ennf transformation 57] 169. ! [X0,X1] : (X0 = X1 | ~person(X1) | ~old(X1) | ~person(X1) | ~kind(X1) | tall(X1) | ~person(X0) | ~old(X0) | ~person(X0) | ~kind(X0) | tall(X0) | ~room(X1) | ~room(X0)) & ! [X2] : ((paul = X2 | mary = X2) | ~room(X2)) & room(paul) & room(mary) [ennf transformation 71] 170. ! [X0,X1] : (X0 = X1 | ~person(X1) | ~old(X1) | ~person(X1) | ~kind(X1) | tall(X1) | ~person(X0) | ~old(X0) | ~person(X0) | ~kind(X0) | tall(X0) | ~room(X1) | ~room(X0)) & ! [X2] : (paul = X2 | mary = X2 | ~room(X2)) & room(paul) & room(mary) [flattening 169] 181. anywhere(X0) [cnf transformation 5] 226. mary != paul [cnf transformation 43] 262. room(mary) [cnf transformation 151] 263. room(paul) [cnf transformation 151] 270. old(paul) [cnf transformation 48] 272. old(mary) [cnf transformation 48] 275. ~strong(X0) | ~tall(X0) [cnf transformation 156] 283. person(X0) | ~anywhere(X0) [cnf transformation 159] 284. ~room(X0) | strong(X0) [cnf transformation 160] 286. ~room(X0) | kind(X0) [cnf transformation 161] 299. X0 = X1 | ~person(X1) | ~old(X1) | ~person(X1) | ~kind(X1) | tall(X1) | ~person(X0) | ~old(X0) | ~person(X0) | ~kind(X0) | tall(X0) | ~room(X1) | ~room(X0) [cnf transformation 170] 300. X0 = X1 | ~person(X1) | ~old(X1) | ~kind(X1) | tall(X1) | ~person(X0) | ~old(X0) | ~kind(X0) | tall(X0) | ~room(X1) | ~room(X0) [duplicate literal removal 299] 325. person(X0) [subsumption resolution 283,181] 328. 6 <=> tall(paul) [avatar definition] 329. ~tall(paul) <- (~6) [avatar component clause 328] 339. X0 = X1 | ~old(X1) | ~kind(X1) | tall(X1) | ~person(X0) | ~old(X0) | ~kind(X0) | tall(X0) | ~room(X1) | ~room(X0) [subsumption resolution 300,325] 340. X0 = X1 | ~old(X1) | ~kind(X1) | tall(X1) | ~old(X0) | ~kind(X0) | tall(X0) | ~room(X1) | ~room(X0) [subsumption resolution 339,325] 341. X0 = X1 | ~old(X1) | tall(X1) | ~old(X0) | ~kind(X0) | tall(X0) | ~room(X1) | ~room(X0) [subsumption resolution 340,286] 342. ~room(X1) | ~old(X1) | tall(X1) | ~old(X0) | tall(X0) | X0 = X1 | ~room(X0) [subsumption resolution 341,286] 353. strong(mary) [resolution 284,262] 354. strong(paul) [resolution 284,263] 356. ~tall(mary) [resolution 353,275] 363. ~tall(paul) [resolution 354,275] 364. ~6 [avatar split clause 363,328] 453. ~old(mary) | tall(mary) | ~old(X4) | tall(X4) | mary = X4 | ~room(X4) [resolution 342,262] 455. tall(mary) | ~old(X4) | tall(X4) | mary = X4 | ~room(X4) [subsumption resolution 453,272] 456. ~room(X4) | tall(X4) | mary = X4 | ~old(X4) [subsumption resolution 455,356] 462. tall(paul) | mary = paul | ~old(paul) [resolution 456,263] 463. mary = paul | ~old(paul) <- (~6) [subsumption resolution 462,329] 464. ~old(paul) <- (~6) [subsumption resolution 463,226] 465. $false <- (~6) [subsumption resolution 464,270] 466. 6 [avatar contradiction clause 465] 467. $false [avatar sat refutation 364,466] % SZS output end Proof for 6969956456215280849442226 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Laura, Vernon, Madeline, Franchesca are the only persons in the room. Someone in the room does not practice kickboxing. Everyone in the room does not practice kickboxing. Vernon does not play the violin. It is true that “not everyone in the room does not enjoy mountain biking or does not own a 3D printer or both”. Everyone anywhere does not play the violin and does not have completed a triathlon. Madeline does not have completed a triathlon and does not play the violin. Laura does not have completed a triathlon and does not own a 3D printer. More than one person in the room does not play the violin. Madeline does not have completed a triathlon.

Laura plays the violin.

contradiction

room(laura)&room(vernon)&room(madeline)&room(franchesca)&(![X]:(room(X)=>(X='laura'|X='vernon'|X='madeline'|X='franchesca')))& (?[X]:(room(X)&(does_not_practice_kickboxing(X))))& (![X]:(room(X)=>(does_not_practice_kickboxing(X))))& (does_not_play_the_violin(vernon))& (~![X]:(room(X)=>(((does_not_enjoy_mountain_biking(X))|(does_not_own_a_3D_printer(X))))))& (![X]:(anywhere(X)=>(((does_not_play_the_violin(X))&(does_not_have_completed_a_triathlon(X))))))& (((does_not_have_completed_a_triathlon(madeline))&(does_not_play_the_violin(madeline))))& (((does_not_have_completed_a_triathlon(laura))&(does_not_own_a_3D_printer(laura))))& ((?[X,Y]:(room(X)&room(Y)&(does_not_play_the_violin(X)&does_not_play_the_violin(Y))&(X!=Y))))& (does_not_have_completed_a_triathlon(madeline))

room(laura)&room(vernon)&room(madeline)&room(franchesca)&(![X]:(room(X)=>(X='laura'|X='vernon'|X='madeline'|X='franchesca')))& plays_the_violin(laura)

% SZS status Unsatisfiable for 4601520198932162940181246 % SZS output start Proof for 4601520198932162940181246 5. ! [X0] : anywhere(X0) [input b4] 49. ! [X0] : (anywhere(X0) => (~preda(X0) & ~predb(X0))) [input p5] 54. predb(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 57. ! [X0] : (anywhere(X0) => ~predb(X0)) [pure predicate removal 49] 136. ! [X0] : (~predb(X0) | ~anywhere(X0)) [ennf transformation 57] 137. predb(mary) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 54] 138. predb(mary) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 137] 146. anywhere(X0) [cnf transformation 5] 236. ~predb(X0) | ~anywhere(X0) [cnf transformation 136] 249. predb(mary) [cnf transformation 138] 250. ~predb(X0) [subsumption resolution 236,146] 251. $false [subsumption resolution 249,250] % SZS output end Proof for 4601520198932162940181246 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.034 s % ------------------------------ % ------------------------------

Lisa, Ronald, Kimberly are the only persons in the room. “Ronald is not a certified yoga instructor teaching classes weekly” if “Lisa practices calligraphy” and vice versa. Ronald is not a certified yoga instructor teaching classes weekly. Everyone in the room owns a 3D printer. Ronald owns a 3D printer. Ronald enjoys kayaking and exploring remote waterways. Everyone in the room neither enjoys kayaking and exploring remote waterways nor does enjoy mountain biking if they enjoys macrame. It is true that “Lisa plays the drums”. Everyone in the room enjoys kayaking and exploring remote waterways or owns a microscope or both if they enjoys kayaking and exploring remote waterways. Lisa either owns a 3D printer or enjoys macrame but not both. Everyone in the room either owns a 3D printer or collects vintage stamps but not both if they owns a 3D printer. Lisa is allergic to anything. Lisa practices calligraphy.

Lisa practices calligraphy.

entailment

room(lisa)&room(ronald)&room(kimberly)&(![X]:(room(X)=>(X='lisa'|X='ronald'|X='kimberly')))& ((practices_calligraphy(lisa))<=>(is_not_a_certified_yoga_instructor_teaching_classes_weekly(ronald)))& (is_not_a_certified_yoga_instructor_teaching_classes_weekly(ronald))& (![X]:(room(X)=>(owns_a_3D_printer(X))))& (owns_a_3D_printer(ronald))& (enjoys_kayaking_and_exploring_remote_waterways(ronald))& (![X]:(room(X)=>(((enjoys_macrame(X))=>(~((enjoys_kayaking_and_exploring_remote_waterways(X))|(does_enjoy_mountain_biking(X))))))))& (plays_the_drums(lisa))& (![X]:(room(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))=>(((enjoys_kayaking_and_exploring_remote_waterways(X))|(owns_a_microscope(X))))))))& (((owns_a_3D_printer(lisa))<~>(enjoys_macrame(lisa))))& (![X]:(room(X)=>(((owns_a_3D_printer(X))=>(((owns_a_3D_printer(X))<~>(collects_vintage_stamps(X))))))))& (is_allergic_to_anything(lisa))& (practices_calligraphy(lisa))& (~![X]:(room(X)=>(((plays_the_drums(X))&(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& (enjoys_kayaking_and_exploring_remote_waterways(lisa))

room(lisa)&room(ronald)&room(kimberly)&(![X]:(room(X)=>(X='lisa'|X='ronald'|X='kimberly')))& practices_calligraphy(lisa)

% SZS status Unsatisfiable for 2680997457823631311151013 % SZS output start Proof for 2680997457823631311151013 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 56. predj(mary) [input p12] 59. ~(predj(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 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] 143. ~predj(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 59] 144. ~predj(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 143] 151. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) [choice axiom] 152. ~predj(mary) | (fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 144,151] 233. room(mary) [cnf transformation 136] 234. room(paul) [cnf transformation 136] 235. room(fred) [cnf transformation 136] 236. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 136] 249. predj(mary) [cnf transformation 56] 253. ~predj(mary) | room(sK1) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 152] 254. ~predj(mary) | mary != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 152] 255. ~predj(mary) | paul != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 152] 256. ~predj(mary) | fred != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 152] 263. 2 <=> predj(mary) [avatar definition] 280. 2 [avatar split clause 249,263] 290. ~predj(mary) | fred != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 256,235] 291. ~predj(mary) | fred != sK1 | ~room(mary) [subsumption resolution 290,234] 292. ~predj(mary) | fred != sK1 [subsumption resolution 291,233] 294. 7 <=> fred = sK1 [avatar definition] 296. fred != sK1 <- (~7) [avatar component clause 294] 297. ~7 | ~2 [avatar split clause 292,263,294] 298. ~predj(mary) | paul != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 255,235] 299. ~predj(mary) | paul != sK1 | ~room(mary) [subsumption resolution 298,234] 300. ~predj(mary) | paul != sK1 [subsumption resolution 299,233] 302. 8 <=> paul = sK1 [avatar definition] 304. paul != sK1 <- (~8) [avatar component clause 302] 305. ~8 | ~2 [avatar split clause 300,263,302] 306. ~predj(mary) | mary != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 254,235] 307. ~predj(mary) | mary != sK1 | ~room(mary) [subsumption resolution 306,234] 308. ~predj(mary) | mary != sK1 [subsumption resolution 307,233] 310. 9 <=> mary = sK1 [avatar definition] 312. mary != sK1 <- (~9) [avatar component clause 310] 313. ~9 | ~2 [avatar split clause 308,263,310] 314. ~predj(mary) | room(sK1) | ~room(paul) | ~room(mary) [subsumption resolution 253,235] 315. ~predj(mary) | room(sK1) | ~room(mary) [subsumption resolution 314,234] 316. ~predj(mary) | room(sK1) [subsumption resolution 315,233] 318. 10 <=> room(sK1) [avatar definition] 320. room(sK1) <- (10) [avatar component clause 318] 321. 10 | ~2 [avatar split clause 316,263,318] 376. paul = sK1 | mary = sK1 | fred = sK1 <- (10) [resolution 236,320] 390. mary = sK1 | fred = sK1 <- (~8, 10) [subsumption resolution 376,304] 391. fred = sK1 <- (~8, ~9, 10) [subsumption resolution 390,312] 392. $false <- (~7, ~8, ~9, 10) [subsumption resolution 391,296] 393. 7 | 8 | 9 | ~10 [avatar contradiction clause 392] 394. $false [avatar sat refutation 280,297,305,313,321,393] % SZS output end Proof for 2680997457823631311151013 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 is the only person in the room. “Everyone in the room does not regularly goes on multi-day backpacking trips in national parks or uses contact lenses” if “Linda owns a high-end gaming PC with custom-built components” and vice versa. If someone collects luxury watches then he/she has completed a triathlon, collects classic novels and does not regularly goes on multi-day backpacking trips in national parks. Linda who uses contact lenses is a coffee connoisseur. Someone in the room enjoys bird watching. Linda uses contact lenses. Linda enjoys bird watching. Everyone in the room does not regularly goes on multi-day backpacking trips in national parks or uses contact lenses. Linda who has a specialized collection of handmade artisan pottery collects classic novels. Linda either enjoys kayaking and exploring remote waterways or owns a high-end gaming PC with custom-built components but not both. At least one person anywhere neither regularly goes on multi-day backpacking trips in national parks nor enjoys bird watching.

Linda enjoys kayaking and exploring remote waterways.

contradiction

room(linda)&(![X]:(room(X)=>(X='linda')))& ((owns_a_high-end_gaming_PC_with_custom-built_components(linda))<=>(![X]:(room(X)=>(((uses_contact_lenses(X))|(does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X)))))))& ((![X]:((collects_luxury_watches(X))=>(((has_completed_a_triathlon(X))&(collects_classic_novels(X))&(does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X)))))))& ((uses_contact_lenses(linda))&(is_a_coffee_connoisseur(linda)))& (?[X]:(room(X)&(enjoys_bird_watching(X))))& (uses_contact_lenses(linda))& (enjoys_bird_watching(linda))& (![X]:(room(X)=>(((uses_contact_lenses(X))|(does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))& ((has_a_specialized_collection_of_handmade_artisan_pottery(linda))&(collects_classic_novels(linda)))& (((enjoys_kayaking_and_exploring_remote_waterways(linda))<~>(owns_a_high-end_gaming_PC_with_custom-built_components(linda))))& (((?[X]:(anywhere(X)&~((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))|(enjoys_bird_watching(X)))))))

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

% SZS status Unsatisfiable for 32541870806694585793762 % SZS output start Proof for 32541870806694585793762 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 45. predg(mary) <=> ! [X0] : (room(X0) => (~predh(X0) | preda(X0))) [input p1] 47. predi(mary) & preda(mary) [input p3] 53. predc(mary) <~> predg(mary) [input p9] 55. predc(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 57. preda(mary) [pure predicate removal 47] 135. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 136. predg(mary) <=> ! [X0] : ((~predh(X0) | preda(X0)) | ~room(X0)) [ennf transformation 45] 137. predg(mary) <=> ! [X0] : (~predh(X0) | preda(X0) | ~room(X0)) [flattening 136] 141. predc(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 55] 143. (predg(mary) | ? [X0] : (predh(X0) & ~preda(X0) & room(X0))) & (! [X0] : (~predh(X0) | preda(X0) | ~room(X0)) | ~predg(mary)) [nnf transformation 137] 144. (predg(mary) | ? [X0] : (predh(X0) & ~preda(X0) & room(X0))) & (! [X1] : (~predh(X1) | preda(X1) | ~room(X1)) | ~predg(mary)) [rectify 143] 145. ? [X0] : (predh(X0) & ~preda(X0) & room(X0)) => (predh(sK0) & ~preda(sK0) & room(sK0)) [choice axiom] 146. (predg(mary) | (predh(sK0) & ~preda(sK0) & room(sK0))) & (! [X1] : (~predh(X1) | preda(X1) | ~room(X1)) | ~predg(mary)) [skolemisation 144,145] 149. (~predg(mary) | ~predc(mary)) & (predg(mary) | predc(mary)) [nnf transformation 53] 233. ~room(X0) | mary = X0 [cnf transformation 135] 235. predg(mary) | room(sK0) [cnf transformation 146] 236. predg(mary) | ~preda(sK0) [cnf transformation 146] 238. preda(mary) [cnf transformation 57] 245. ~predg(mary) | ~predc(mary) [cnf transformation 149] 250. predc(mary) [cnf transformation 141] 256. 2 <=> predg(mary) [avatar definition] 261. 3 <=> preda(sK0) [avatar definition] 263. ~preda(sK0) <- (~3) [avatar component clause 261] 264. ~3 | 2 [avatar split clause 236,256,261] 266. 4 <=> room(sK0) [avatar definition] 268. room(sK0) <- (4) [avatar component clause 266] 269. 4 | 2 [avatar split clause 235,256,266] 276. 6 <=> predc(mary) [avatar definition] 279. ~6 | ~2 [avatar split clause 245,256,276] 281. 6 [avatar split clause 250,276] 284. mary = sK0 <- (4) [resolution 233,268] 288. ~preda(mary) <- (~3, 4) [backward demodulation 263,284] 290. $false <- (~3, 4) [subsumption resolution 288,238] 291. 3 | ~4 [avatar contradiction clause 290] 292. $false [avatar sat refutation 264,269,279,281,291] % SZS output end Proof for 32541870806694585793762 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.021 s % ------------------------------ % ------------------------------

Chance is the only person in the room. If 'no one anywhere does not practice kickboxing or is a patient kind person' then 'everyone outside the room is not a member of a local theater group specializing in improv or does not maintain a personal blog focused on cybersecurity tips'. 'Everyone in the room who is louder than Antonia collects comic books' if 'Chance and Herbert hate each other'. Either 'Chance is not quiet, not generous' or 'everyone in the room does not write a travel blog or is a wise person' but not both. Either 'Nina and Chance hate each other' or 'everyone in the room is not a quiet person or does not enjoy coding in Python' but not both. Antonia is a client of Chance. Everyone in the room collects vintage stamps if they is not a wise tourist and is a strong creative person. Chance and Herbert hate each other. Chance is a wise person. Chance composes and performs experimental electronic music. Everyone in the room is a certified scuba diver with advanced underwater photography skills only if they does not make homemade pastries. Everyone in the room is louder than Micah if they plays the drums and vice versa. Everyone in the room collects limited-edition art prints from contemporary artists if they plays the drums.

Chance is humble.

neutral

room(chance)&(![X]:(room(X)=>(X='chance')))& ((~?[X]:(anywhere(X)=>(((patient(X)&kind(X)&person(X))|(does_not_practice_kickboxing(X))))))=>(![X]:(~room(X)=>(((does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))|(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X)))))))& (((hate(chance,herbert) & hate(herbert,chance)))=>(![X]:(room(X)=>(((louder(antonia,X))=>(collects_comic_books(X)))))))& ((~quiet(chance)&~generous(chance))<~>(![X]:(room(X)=>(((wise(X)&person(X))|(does_not_write_a_travel_blog(X)))))))& (((hate(nina,chance) & hate(chance,nina)))<~>(![X]:(room(X)=>(((does_not_enjoy_coding_in_Python(X))|(~(quiet(X)&person(X))))))))& (client(chance,antonia))& (![X]:(room(X)=>(((((~(wise(X)&tourist(X)))&(strong(X)&creative(X)&person(X))))=>(collects_vintage_stamps(X))))))& ((hate(chance,herbert) & hate(herbert,chance)))& (wise(chance)&person(chance))& (composes_and_performs_experimental_electronic_music(chance))& (![X]:(room(X)=>(((does_not_make_homemade_pastries(X))<=(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))& (![X]:(room(X)=>(((louder(micah,X))<=>(plays_the_drums(X))))))& (![X]:(room(X)=>(((plays_the_drums(X))=>(collects_limited-edition_art_prints_from_contemporary_artists(X))))))& (~(curious(chance)&tourist(chance)))& (sibling(nina,chance))& (![X]:(happy(X)=>strong(X)))& (![X]:(room(X)=>(sibling(nina,X))))& (![X]:(tall(X)=>humble(X)))& (client(chance,micah))& ((![X]:((does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))=>(trains_for_and_competes_in_international_triathlons(X)))))& (![X]:(room(X)=>(((collects_comic_books(X))=>(kind(X)&person(X))))))& (collects_limited-edition_art_prints_from_contemporary_artists(chance))& (?[X]:(room(X)&(has_lived_in_exactly_three_countries(X))))& ((![X]:((trains_for_and_competes_in_international_triathlons(X))=>(is_a_night_owl(X)))))

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

Linda, Donald, Pam, Eusebio are the only persons in the room. Everyone in the room does not own an extensive assortment of vintage comic book memorabilia or enjoys stand-up paddleboarding. Pam who collects vintage stamps owns an extensive assortment of vintage comic book memorabilia. If someone enjoys stand-up paddleboarding then he/she either designs and sews custom cosplay costumes for conventions or has a specialized collection of handmade artisan pottery but not both. Pam designs and sews custom cosplay costumes for conventions.

Pam has a specialized collection of handmade artisan pottery.

contradiction

room(linda)&room(donald)&room(pam)&room(eusebio)&(![X]:(room(X)=>(X='linda'|X='donald'|X='pam'|X='eusebio')))& (![X]:(room(X)=>(((collects_vintage_stamps(X))|(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))))))& (designs_and_sews_custom_cosplay_costumes_for_conventions(donald))& (![X]:(room(X)=>(((enjoys_stand-up_paddleboarding(X))|(does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))))& (is_passionate_about_collecting_and_restoring_classic_cars(linda))& (?[X]:(room(X)&(frequently_participates_in_hackathons_and_coding_competitions(X))))& ((collects_vintage_stamps(pam))&(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(pam)))& (![X]:(room(X)=>(((does_not_build_model_airplanes(X))=>(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))& (?[X]:(room(X)&(can_play_the_guitar(X))))& (![X]:(room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))=>(((enjoys_spelunking(X))&(collects_rare_minerals(X))&(can_play_the_guitar(X))))))))& (![X]:(room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))|(cannot_play_the_guitar(X))))))& (?[X]:(room(X)&(((frequently_participates_in_hackathons_and_coding_competitions(X))|(enjoys_stand-up_paddleboarding(X))|(enjoys_spelunking(X))))))& ((![X]:((enjoys_stand-up_paddleboarding(X))=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))<~>(has_a_specialized_collection_of_handmade_artisan_pottery(X)))))))& ((collects_vintage_stamps(donald))&(can_play_the_piano(donald)))& (enjoys_spelunking(pam))& (designs_and_sews_custom_cosplay_costumes_for_conventions(pam))& (![X]:(room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))<=>(((writes_and_illustrates_their_own_graphic_novels(X))<~>(does_not_frequently_participates_in_hackathons_and_coding_competitions(X))))))))& (designs_and_sews_custom_cosplay_costumes_for_conventions(linda))& (![X]:(room(X)=>(((collects_vintage_stamps(X))=>(((frequently_participates_in_hackathons_and_coding_competitions(X))&(enjoys_stand-up_paddleboarding(X))&(can_play_the_piano(X))))))))& (![X]:(room(X)=>(((((frequently_participates_in_hackathons_and_coding_competitions(X))&(enjoys_stand-up_paddleboarding(X))&(can_play_the_piano(X))))<=>(collects_vintage_stamps(X))))))& (?[X]:(room(X)&(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))& (![X]:(room(X)=>(((can_play_the_guitar(X))|(is_not_passionate_about_collecting_and_restoring_classic_cars(X))))))& (![X]:(room(X)=>(((collects_rare_minerals(X))|(does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))))& (![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))=>(frequently_participates_in_hackathons_and_coding_competitions(X))))))& (![X]:(room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))=>(builds_model_airplanes(X))))))

room(linda)&room(donald)&room(pam)&room(eusebio)&(![X]:(room(X)=>(X='linda'|X='donald'|X='pam'|X='eusebio')))& has_a_specialized_collection_of_handmade_artisan_pottery(pam)

% SZS status Unsatisfiable for 1322117125298626301603561 % SZS output start Proof for 1322117125298626301603561 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 47. ! [X0] : (room(X0) => (~predf(X0) | predj(X0))) [input p3] 50. predf(fred) & predd(fred) [input p6] 56. ! [X0] : (predj(X0) => (predb(X0) <~> predk(X0))) [input p12] 59. predb(fred) [input p15] 69. predk(fred) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 150. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 151. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 150] 154. ! [X0] : ((~predf(X0) | predj(X0)) | ~room(X0)) [ennf transformation 47] 155. ! [X0] : (~predf(X0) | predj(X0) | ~room(X0)) [flattening 154] 160. ! [X0] : ((predb(X0) <~> predk(X0)) | ~predj(X0)) [ennf transformation 56] 167. predk(fred) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 69] 168. predk(fred) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 167] 176. ! [X0] : (((~predk(X0) | ~predb(X0)) & (predk(X0) | predb(X0))) | ~predj(X0)) [nnf transformation 160] 264. room(fred) [cnf transformation 151] 269. ~predf(X0) | predj(X0) | ~room(X0) [cnf transformation 155] 274. predf(fred) [cnf transformation 50] 281. ~predj(X0) | ~predb(X0) | ~predk(X0) [cnf transformation 176] 284. predb(fred) [cnf transformation 59] 305. predk(fred) [cnf transformation 168] 318. predj(fred) | ~room(fred) [resolution 269,274] 319. predj(fred) [subsumption resolution 318,264] 334. ~predb(fred) | ~predk(fred) [resolution 319,281] 336. ~predk(fred) [subsumption resolution 334,284] 337. $false [subsumption resolution 336,305] % SZS output end Proof for 1322117125298626301603561 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Darren is the only person in the room. Either Darren enjoys kayaking or Darren enjoys origami but not both. If everyone in the room does not use contact lenses or is a client of LVMH then everyone in the room is a client of LVMH if and only if they enjoys landscape photography or watches fantasy movies or both. Darren who enjoys cross-country skiing owns a smart tv, cannot play the guitar or writes in-depth travel guides for off-the-beaten-path destinations. Darren is a client of LVMH. Darren has a specialized collection of handmade artisan pottery. Everyone in the room uses an ios phone if they does not write in-depth travel guides for off-the-beaten-path destinations and vice versa. Everyone in the room uses contact lenses, is a client of Costco and watches fantasy movies. Everyone in the room owns a smart tv if they hosts regular game nights featuring complex strategy games. Everyone outside the room enjoys fishing if they owns a smart tv. Darren enjoys landscape photography. Everyone in the room is a client of LVMH if and only if they enjoys landscape photography or watches fantasy movies or both.

Darren enjoys origami.

neutral

room(darren)&(![X]:(room(X)=>(X='darren')))& ((enjoys_kayaking(darren))<~>(enjoys_origami(darren)))& ((![X]:(room(X)=>(((is_a_client_of_LVMH(X))|(does_not_use_contact_lenses(X))))))=>(![X]:(room(X)=>(((is_a_client_of_LVMH(X))<=>(((enjoys_landscape_photography(X))|(watches_fantasy_movies(X)))))))))& ((enjoys_cross-country_skiing(darren))&(((owns_a_smart_tv(darren))|(cannot_play_the_guitar(darren))|(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(darren)))))& (is_a_client_of_LVMH(darren))& (has_a_specialized_collection_of_handmade_artisan_pottery(darren))& (![X]:(room(X)=>(((uses_an_ios_phone(X))<=>(does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))& (![X]:(room(X)=>(((uses_contact_lenses(X))&(is_a_client_of_Costco(X))&(watches_fantasy_movies(X))))))& (![X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(owns_a_smart_tv(X))))))& (![X]:(~room(X)=>(((owns_a_smart_tv(X))=>(enjoys_fishing(X))))))& (enjoys_landscape_photography(darren))& (![X]:(room(X)=>(((is_a_client_of_LVMH(X))<=>(((enjoys_landscape_photography(X))|(watches_fantasy_movies(X))))))))

room(darren)&(![X]:(room(X)=>(X='darren')))& enjoys_origami(darren)

Tracy, Jeffrey, Monika, Tim are the only persons in the room. “Tim neither is not a tea enthusiast nor creates large-scale murals for public art installations” if “everyone in the room owns a microscope”. If “everyone in the room hosts a YouTube channel dedicated to art tutorials or does not have a curated collection of mid-century modern furniture” then “Tim enjoys fishing and writes and illustrates their own graphic novels”. “Tracy does not have a curated collection of mid-century modern furniture” if “it is not the case that “at least one person in the room does not write and illustrates their own graphic novels”” and vice versa. If “Tim neither enjoys windsurfing nor has a curated collection of mid-century modern furniture” then “someone in the room writes and illustrates their own graphic novels”. “Jeffrey plays the violin, enjoys salsa dancing and is an enthusiastic bird watcher who travels for rare sightings” unless “Jeffrey is a certified scuba diver with advanced underwater photography skills”. “Everyone in the room owns a microscope” if “Jeffrey designs and sews custom cosplay costumes for conventions” and vice versa. “Monika does not host themed dinner parties featuring gourmet home-cooked meals” if “Tracy practices calligraphy” and vice versa. “Tracy hosts regular workshops on creative writing” if “Monika either does not collect rare minerals or collects rare minerals but not both”. Either “Tim uses contact lenses” or “Tracy does not host regular workshops on creative writing or does not collect rare minerals or both” but not both. Tracy knows morse code. Tracy who does not have a curated collection of mid-century modern furniture knows morse code. Everyone in the room owns a microscope. Tracy who hosts a popular podcast about emerging technologies or does not write and illustrates their own graphic novels or both enjoys salsa dancing. At least one person in the room collects rare minerals. Monika does not host themed dinner parties featuring gourmet home-cooked meals.

Tim writes and illustrates their own graphic novels.

entailment

room(tracy)&room(jeffrey)&room(monika)&room(tim)&(![X]:(room(X)=>(X='tracy'|X='jeffrey'|X='monika'|X='tim')))& ((![X]:(room(X)=>(owns_a_microscope(X))))=>(~((is_not_a_tea_enthusiast(tim))|(creates_large-scale_murals_for_public_art_installations(tim)))))& ((![X]:(room(X)=>(((does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))|(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))=>(((enjoys_fishing(tim))&(writes_and_illustrates_their_own_graphic_novels(tim)))))& ((~(((?[X]:(room(X)&does_not_write_and_illustrates_their_own_graphic_novels(X))))))<=>(does_not_have_a_curated_collection_of_mid-century_modern_furniture(tracy)))& ((~((enjoys_windsurfing(tim))|(has_a_curated_collection_of_mid-century_modern_furniture(tim))))=>(?[X]:(room(X)&(writes_and_illustrates_their_own_graphic_novels(X)))))& (~(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(jeffrey))=>(((plays_the_violin(jeffrey))&(enjoys_salsa_dancing(jeffrey))&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(jeffrey)))))& ((designs_and_sews_custom_cosplay_costumes_for_conventions(jeffrey))<=>(![X]:(room(X)=>(owns_a_microscope(X)))))& ((practices_calligraphy(tracy))<=>(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(monika)))& ((((does_not_collect_rare_minerals(monika))<~>(collects_rare_minerals(monika))))=>(hosts_regular_workshops_on_creative_writing(tracy)))& ((uses_contact_lenses(tim))<~>(((does_not_host_regular_workshops_on_creative_writing(tracy))|(does_not_collect_rare_minerals(tracy)))))& (knows_morse_code(tracy))& ((does_not_have_a_curated_collection_of_mid-century_modern_furniture(tracy))&(knows_morse_code(tracy)))& (![X]:(room(X)=>(owns_a_microscope(X))))& ((((hosts_a_popular_podcast_about_emerging_technologies(tracy))|(does_not_write_and_illustrates_their_own_graphic_novels(tracy))))&(enjoys_salsa_dancing(tracy)))& (((?[X]:(room(X)&collects_rare_minerals(X)))))& (does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(monika))& (does_not_use_an_ios_phone(tim))& (![X]:(~room(X)=>(((enjoys_salsa_dancing(X))=>(((uses_an_ios_phone(X))|(is_a_tea_enthusiast(X))))))))& (![X]:(room(X)=>(((uses_an_ios_phone(X))=>(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))& ((![X]:((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))<=>(((is_a_tea_enthusiast(X))|(is_not_allergic_to_anything(X)))))))& (enjoys_fishing(tim))& (collects_historical_artifacts_related_to_ancient_civilizations(tracy))& (((does_not_host_regular_workshops_on_creative_writing(tracy))|(does_not_collect_rare_minerals(tracy))))& (owns_a_microscope(tim))& ((![X]:((((does_not_play_the_violin(X))&(uses_contact_lenses(X))&(plays_the_violin(X))))=>(enjoys_windsurfing(X)))))& (designs_and_sews_custom_cosplay_costumes_for_conventions(tracy))& (plays_the_violin(jeffrey))& ((hosts_regular_workshops_on_creative_writing(monika))&(does_not_host_a_popular_podcast_about_emerging_technologies(monika)))

room(tracy)&room(jeffrey)&room(monika)&room(tim)&(![X]:(room(X)=>(X='tracy'|X='jeffrey'|X='monika'|X='tim')))& writes_and_illustrates_their_own_graphic_novels(tim)

% SZS status Unsatisfiable for 687504629454915952233873 % SZS output start Proof for 687504629454915952233873 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 47. ~? [X0] : (~predv(X0) & room(X0)) <=> ~predx(mary) [input p3] 55. predw(mary) & ~predx(mary) [input p11] 72. ~(predv(alice) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 83. ~predx(mary) [pure predicate removal 55] 163. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 164. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 163] 166. ! [X0] : (predv(X0) | ~room(X0)) <=> ~predx(mary) [ennf transformation 47] 170. ~predv(alice) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 72] 171. ~predv(alice) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 170] 175. (! [X0] : (predv(X0) | ~room(X0)) | predx(mary)) & (~predx(mary) | ? [X0] : (~predv(X0) & room(X0))) [nnf transformation 166] 176. (! [X0] : (predv(X0) | ~room(X0)) | predx(mary)) & (~predx(mary) | ? [X1] : (~predv(X1) & room(X1))) [rectify 175] 177. ? [X1] : (~predv(X1) & room(X1)) => (~predv(sK1) & room(sK1)) [choice axiom] 178. (! [X0] : (predv(X0) | ~room(X0)) | predx(mary)) & (~predx(mary) | (~predv(sK1) & room(sK1))) [skolemisation 176,177] 189. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK4 & fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) [choice axiom] 190. ~predv(alice) | (alice != sK4 & fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 171,189] 271. room(mary) [cnf transformation 164] 272. room(paul) [cnf transformation 164] 273. room(fred) [cnf transformation 164] 274. room(alice) [cnf transformation 164] 275. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 164] 280. predv(X0) | ~room(X0) | predx(mary) [cnf transformation 178] 291. ~predx(mary) [cnf transformation 83] 302. ~predv(alice) | room(sK4) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 190] 303. ~predv(alice) | mary != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 190] 304. ~predv(alice) | paul != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 190] 305. ~predv(alice) | fred != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 190] 306. ~predv(alice) | alice != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 190] 314. 2 <=> predv(alice) [avatar definition] 324. 4 <=> predx(mary) [avatar definition] 328. 5 <=> ! [X0] : (predv(X0) | ~room(X0)) [avatar definition] 329. ~room(X0) | predv(X0) <- (5) [avatar component clause 328] 330. 4 | 5 [avatar split clause 280,328,324] 390. ~4 [avatar split clause 291,324] 403. ~predv(alice) | alice != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 306,274] 404. ~predv(alice) | alice != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 403,273] 405. ~predv(alice) | alice != sK4 | ~room(mary) [subsumption resolution 404,272] 406. ~predv(alice) | alice != sK4 [subsumption resolution 405,271] 408. 20 <=> alice = sK4 [avatar definition] 410. alice != sK4 <- (~20) [avatar component clause 408] 411. ~20 | ~2 [avatar split clause 406,314,408] 412. ~predv(alice) | fred != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 305,274] 413. ~predv(alice) | fred != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 412,273] 414. ~predv(alice) | fred != sK4 | ~room(mary) [subsumption resolution 413,272] 415. ~predv(alice) | fred != sK4 [subsumption resolution 414,271] 417. 21 <=> fred = sK4 [avatar definition] 420. ~21 | ~2 [avatar split clause 415,314,417] 421. ~predv(alice) | paul != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 304,274] 422. ~predv(alice) | paul != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 421,273] 423. ~predv(alice) | paul != sK4 | ~room(mary) [subsumption resolution 422,272] 424. ~predv(alice) | paul != sK4 [subsumption resolution 423,271] 426. 22 <=> paul = sK4 [avatar definition] 428. paul != sK4 <- (~22) [avatar component clause 426] 429. ~22 | ~2 [avatar split clause 424,314,426] 430. ~predv(alice) | mary != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 303,274] 431. ~predv(alice) | mary != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 430,273] 432. ~predv(alice) | mary != sK4 | ~room(mary) [subsumption resolution 431,272] 433. ~predv(alice) | mary != sK4 [subsumption resolution 432,271] 435. 23 <=> mary = sK4 [avatar definition] 437. mary != sK4 <- (~23) [avatar component clause 435] 438. ~23 | ~2 [avatar split clause 433,314,435] 439. ~predv(alice) | room(sK4) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 302,274] 440. ~predv(alice) | room(sK4) | ~room(paul) | ~room(mary) [subsumption resolution 439,273] 441. ~predv(alice) | room(sK4) | ~room(mary) [subsumption resolution 440,272] 442. ~predv(alice) | room(sK4) [subsumption resolution 441,271] 444. 24 <=> room(sK4) [avatar definition] 446. room(sK4) <- (24) [avatar component clause 444] 447. 24 | ~2 [avatar split clause 442,314,444] 451. predv(alice) <- (5) [resolution 329,274] 510. fred = sK4 | paul = sK4 | mary = sK4 | alice = sK4 <- (24) [resolution 275,446] 533. 2 | ~5 [avatar split clause 451,328,314] 534. fred = sK4 | mary = sK4 | alice = sK4 <- (~22, 24) [subsumption resolution 510,428] 535. fred = sK4 | alice = sK4 <- (~22, ~23, 24) [subsumption resolution 534,437] 536. fred = sK4 <- (~20, ~22, ~23, 24) [subsumption resolution 535,410] 537. 21 | 20 | 22 | 23 | ~24 [avatar split clause 536,444,435,426,408,417] 547. $false [avatar sat refutation 330,390,411,420,429,438,447,533,537] % SZS output end Proof for 687504629454915952233873 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.039 s % ------------------------------ % ------------------------------

There is a room. If someone enjoys cross-country skiing then he/she is a wine connoisseur with a private cellar of vintage wines. Everyone in the room is a wine connoisseur with a private cellar of vintage wines if they neither is a tea enthusiast nor enjoys rooftop gardening. Someone outside the room practices and performs acrobatic dance routines. Everyone anywhere enjoys cross-country skiing if they is a wine connoisseur with a private cellar of vintage wines. Everyone in the room does not practice and performs acrobatic dance routines. Everyone in the room who enjoys cross-country skiing practices and performs acrobatic dance routines. Everyone in the room practices and performs acrobatic dance routines if they enjoys rooftop gardening or is a tea enthusiast or both and vice versa. Everyone in the room is a wine connoisseur with a private cellar of vintage wines if they enjoys rooftop gardening or is a tea enthusiast or both. Everyone in the room does not enjoy rooftop gardening if they is a wine connoisseur with a private cellar of vintage wines. Everyone in the room is not a wine connoisseur with a private cellar of vintage wines if they does not enjoy rooftop gardening.

Everyone outside the room enjoys cross-country skiing.

neutral

(there_is_a_room)& ((![X]:((enjoys_cross-country_skiing(X))=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X)))))& (![X]:(room(X)=>(((~((is_a_tea_enthusiast(X))|(enjoys_rooftop_gardening(X))))=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))& (?[X]:(~room(X)&(practices_and_performs_acrobatic_dance_routines(X))))& (![X]:(anywhere(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(enjoys_cross-country_skiing(X))))))& (![X]:(room(X)=>(does_not_practice_and_performs_acrobatic_dance_routines(X))))& (![X]:(room(X)=>(((enjoys_cross-country_skiing(X))=>(practices_and_performs_acrobatic_dance_routines(X))))))& (![X]:(room(X)=>(((practices_and_performs_acrobatic_dance_routines(X))<=>(((enjoys_rooftop_gardening(X))|(is_a_tea_enthusiast(X))))))))& (![X]:(room(X)=>(((((enjoys_rooftop_gardening(X))|(is_a_tea_enthusiast(X))))=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))& (![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(does_not_enjoy_rooftop_gardening(X))))))& (![X]:(room(X)=>(((does_not_enjoy_rooftop_gardening(X))=>(is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))

(there_is_a_room)& ![X]:(~room(X)=>(enjoys_cross-country_skiing(X)))

Jose, Enrique are the only persons in the room. Enrique who is a brave person is not a tall person. Someone who is creative and is tall is a client of someone who either is not a wise person or is a wise person but not both. It is true that 'all creative persons are brave'. Someone who is not a creative person is a client of someone who is a wise person. Jose who is not a wise person is not a brave person. All wise persons are brave. Only one person outside the room is tall.

Jose is tall.

neutral

room(jose)&room(enrique)&(![X]:(room(X)=>(X='jose'|X='enrique')))& ((brave(enrique)&person(enrique))&(~(tall(enrique)&person(enrique))))& (?[X,Y]:((((creative(X))&(tall(X))))&(((~(wise(Y)&person(Y)))<~>(wise(Y)&person(Y))))&(client(X,Y))))& (![X]:(creative(X)=>brave(X)))& (?[X,Y]:((~(creative(X)&person(X)))&(wise(Y)&person(Y))&(client(X,Y))))& ((~(wise(jose)&person(jose)))&(~(brave(jose)&person(jose))))& (![X]:(wise(X)=>brave(X)))& (((?[X]:(~room(X)&tall(X)))&(![X,Y]:((~room(X)&~room(Y)&(tall(X))&(tall(Y)))=>(X=Y)))))& (![X]:(brave(X)=>wise(X)))& (![X]:(brave(X)=>creative(X)))& (?[X,Y]:((~(brave(X)&person(X)))&(((tall(Y)&person(Y))&(creative(Y)&person(Y))))&(client(X,Y))))& (?[X,Y]:((creative(X)&person(X))&(wise(Y)&person(Y))&(client(X,Y))))& (![X]:(wise(X)=>creative(X)))

room(jose)&room(enrique)&(![X]:(room(X)=>(X='jose'|X='enrique')))& tall(jose)

There is a room. “Everyone in the room does not play the drums and is an avid mountain climber who has scaled several peaks if they does not host themed dinner parties featuring gourmet home-cooked meals, does enjoy mountain biking or does not practice archery” if “everyone in the room is a dedicated advocate for digital privacy and encryption”. “If someone does not enjoy coding in Python then he/she owns a smartwatch and vice versa” if “everyone in the room enjoys bird watching or is not a dedicated advocate for digital privacy and encryption”. “Everyone in the room does not enjoy mountain biking or does not practice archery” only if “everyone outside the room who does not enjoy mountain biking either enjoys bird watching or owns a smartwatch but not both”. “Everyone in the room is not a certified yoga instructor teaching classes weekly if they does not host themed dinner parties featuring gourmet home-cooked meals” if “everyone in the room does not host themed dinner parties featuring gourmet home-cooked meals or does not use a Windows laptop”. “Everyone in the room who writes and illustrates their own graphic novels practices archery” unless “everyone in the room does not enjoy mountain biking or collects limited-edition art prints from contemporary artists”. If “no one in the room is not an expert in identifying and foraging wild edible plants or collects limited-edition art prints from contemporary artists” then “everyone in the room is not a certified yoga instructor teaching classes weekly or is not an avid mountain climber who has scaled several peaks”.

Everyone in the room does not enjoy bird watching.

contradiction

(there_is_a_room)& ((![X]:(room(X)=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))=>(![X]:(room(X)=>(((((does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))|(does_enjoy_mountain_biking(X))|(does_not_practice_archery(X))))=>(((does_not_play_the_drums(X))&(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X)))))))))& ((![X]:(room(X)=>(((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(enjoys_bird_watching(X))))))=>((![X]:((does_not_enjoy_coding_in_Python(X))<=>(owns_a_smartwatch(X))))))& ((![X]:(room(X)=>(((does_not_practice_archery(X))|(does_not_enjoy_mountain_biking(X))))))=>(![X]:(~room(X)=>(((does_not_enjoy_mountain_biking(X))=>(((enjoys_bird_watching(X))<~>(owns_a_smartwatch(X)))))))))& ((![X]:(room(X)=>(((does_not_use_a_Windows_laptop(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))=>(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X)))))))& (~(![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))|(does_not_enjoy_mountain_biking(X))))))=>(![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))=>(practices_archery(X)))))))& (((~?[X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))|(is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))=>(![X]:(room(X)=>(((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X)))))))& ((![X]:(room(X)=>(((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))))))=>(![X]:(room(X)=>(((((is_a_certified_yoga_instructor_teaching_classes_weekly(X))&(owns_a_high-end_gaming_PC_with_custom-built_components(X))))<=(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))))& (![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))<=>(((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))&(volunteers_for_local_environmental_conservation_projects(X))&(regularly_contributes_to_tech_forums_and_online_communities(X))))))))& (~?[X]:(room(X)=>(((does_not_enjoy_coding_in_Python(X))&(enjoys_coding_in_Python(X))))))& (![X]:(room(X)=>(((enjoys_coding_in_Python(X))<=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(does_not_enjoy_coding_in_Python(X))|(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))))& (![X]:(~room(X)=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))& (![X]:(~room(X)=>(((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))<=(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))& (![X]:(anywhere(X)=>(((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))=>(practices_archery(X))))))& ((![X]:((collects_limited-edition_art_prints_from_contemporary_artists(X))<=>(practices_archery(X)))))& (~![X]:(anywhere(X)=>(((((does_not_enjoy_mountain_biking(X))&(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))=>(((practices_archery(X))<~>(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))))))))& (![X]:(room(X)=>(((((is_a_certified_yoga_instructor_teaching_classes_weekly(X))&(owns_a_high-end_gaming_PC_with_custom-built_components(X))))<=(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))& (![X]:(room(X)=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))& (![X]:(room(X)=>(((does_not_volunteer_for_local_environmental_conservation_projects(X))<~>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))& ((linda_dream=>(![X]:(room(X)=>(((((is_a_certified_yoga_instructor_teaching_classes_weekly(X))&(does_not_write_and_illustrates_their_own_graphic_novels(X))))=>(((plays_the_drums(X))&(does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))))))))))& (![X]:(room(X)=>(is_right-handed(X))))& (![X]:(room(X)=>(does_not_practice_archery(X))))& (![X]:(room(X)=>(((((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(plays_the_drums(X))))=>(((does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(is_right-handed(X))|(does_enjoy_mountain_biking(X))))))))& (![X]:(anywhere(X)=>(uses_a_Windows_laptop(X))))& (~?[X]:(room(X)=>(((does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))|(plays_video_games(X))))))& (![X]:(room(X)=>(((((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))&(does_not_enjoy_coding_in_Python(X))))=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))& (![X]:(room(X)=>(((enjoys_bird_watching(X))&(enjoys_coding_in_Python(X))&(does_not_play_video_games(X))))))& (![X]:(room(X)=>(((does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))=>(((enjoys_coding_in_Python(X))&(is_a_certified_yoga_instructor_teaching_classes_weekly(X))&(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))))

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

% SZS status Unsatisfiable for 2088794862768579566674504 % SZS output start Proof for 2088794862768579566674504 44. ! [X0] : (room(X0) => (~predj(X0) => (~predj(X0) & predn(X0) & predt(X0)))) & ! [X0] : (room(X0) => (~predo(X0) & predt(X0) & predm(X0))) & ! [X0] : (room(X0) => ((~predt(X0) & predj(X0)) => predd(X0))) & ~? [X0] : (room(X0) => (predo(X0) | ~predj(X0))) & ! [X0] : (anywhere(X0) => predh(X0)) & ! [X0] : (room(X0) => ((predq(X0) | ~predr(X0)) => (preda(X0) | predg(X0) | ~predi(X0)))) & ! [X0] : (room(X0) => ~predc(X0)) & ! [X0] : (room(X0) => predg(X0)) & (mary_dream => ! [X0] : (room(X0) => ((~predk(X0) & predn(X0)) => (~predp(X0) & predq(X0))))) & ! [X0] : (room(X0) => (~preds(X0) <~> predf(X0))) & ! [X0] : (room(X0) => predd(X0)) & ! [X0] : (room(X0) => (predl(X0) => (predp(X0) & predn(X0)))) & ~! [X0] : (anywhere(X0) => ((predj(X0) & ~preda(X0)) => (predc(X0) <~> ~predn(X0)))) & ! [X0] : (prede(X0) <=> predc(X0)) & ! [X0] : (anywhere(X0) => (~predd(X0) => predc(X0))) & ! [X0] : (~room(X0) => (predj(X0) => ~predd(X0))) & ! [X0] : (~room(X0) => predi(X0)) & ! [X0] : (room(X0) => (predt(X0) <=> (predn(X0) | ~predt(X0) | predr(X0)))) & ~? [X0] : (room(X0) => (predt(X0) & ~predt(X0))) & ! [X0] : (room(X0) => (prede(X0) <=> (predu(X0) & preds(X0) & ~predr(X0)))) & (! [X0] : (room(X0) => (~predn(X0) | ~predr(X0))) => ! [X0] : (room(X0) => (predl(X0) => (predp(X0) & predn(X0))))) & (~? [X0] : (room(X0) => (~predl(X0) | prede(X0))) => ! [X0] : (room(X0) => (~predn(X0) | ~predr(X0)))) & (~! [X0] : (room(X0) => (~preda(X0) | prede(X0))) => ! [X0] : (room(X0) => (predk(X0) => predc(X0)))) & (! [X0] : (room(X0) => (~predf(X0) | ~predh(X0))) => ! [X0] : (room(X0) => (~predf(X0) => ~predn(X0)))) & (! [X0] : (room(X0) => (~preda(X0) | ~predc(X0))) => ! [X0] : (~room(X0) => (~preda(X0) => (predm(X0) <~> predb(X0))))) & (! [X0] : (room(X0) => (predm(X0) | ~predd(X0))) => ! [X0] : (~predt(X0) <=> predb(X0))) & (! [X0] : (room(X0) => predd(X0)) => ! [X0] : (room(X0) => ((~predc(X0) | preda(X0) | ~predf(X0)) => (predr(X0) & ~predq(X0))))) & there_is_a_room [input p0] 45. ! [X0] : (room(X0) => ~predm(X0)) & there_is_a_room [input hypothesis] 46. ! [X0] : (room(X0) => (~predj(X0) => (~predj(X0) & predn(X0) & predt(X0)))) & ! [X1] : (room(X1) => (~predo(X1) & predt(X1) & predm(X1))) & ! [X2] : (room(X2) => ((~predt(X2) & predj(X2)) => predd(X2))) & ~? [X3] : (room(X3) => (predo(X3) | ~predj(X3))) & ! [X4] : (anywhere(X4) => predh(X4)) & ! [X5] : (room(X5) => ((predq(X5) | ~predr(X5)) => (preda(X5) | predg(X5) | ~predi(X5)))) & ! [X6] : (room(X6) => ~predc(X6)) & ! [X7] : (room(X7) => predg(X7)) & (mary_dream => ! [X8] : (room(X8) => ((~predk(X8) & predn(X8)) => (~predp(X8) & predq(X8))))) & ! [X9] : (room(X9) => (~preds(X9) <~> predf(X9))) & ! [X10] : (room(X10) => predd(X10)) & ! [X11] : (room(X11) => (predl(X11) => (predp(X11) & predn(X11)))) & ~! [X12] : (anywhere(X12) => ((predj(X12) & ~preda(X12)) => (predc(X12) <~> ~predn(X12)))) & ! [X13] : (prede(X13) <=> predc(X13)) & ! [X14] : (anywhere(X14) => (~predd(X14) => predc(X14))) & ! [X15] : (~room(X15) => (predj(X15) => ~predd(X15))) & ! [X16] : (~room(X16) => predi(X16)) & ! [X17] : (room(X17) => (predt(X17) <=> (predn(X17) | ~predt(X17) | predr(X17)))) & ~? [X18] : (room(X18) => (predt(X18) & ~predt(X18))) & ! [X19] : (room(X19) => (prede(X19) <=> (predu(X19) & preds(X19) & ~predr(X19)))) & (! [X20] : (room(X20) => (~predn(X20) | ~predr(X20))) => ! [X21] : (room(X21) => (predl(X21) => (predp(X21) & predn(X21))))) & (~? [X22] : (room(X22) => (~predl(X22) | prede(X22))) => ! [X23] : (room(X23) => (~predn(X23) | ~predr(X23)))) & (~! [X24] : (room(X24) => (~preda(X24) | prede(X24))) => ! [X25] : (room(X25) => (predk(X25) => predc(X25)))) & (! [X26] : (room(X26) => (~predf(X26) | ~predh(X26))) => ! [X27] : (room(X27) => (~predf(X27) => ~predn(X27)))) & (! [X28] : (room(X28) => (~preda(X28) | ~predc(X28))) => ! [X29] : (~room(X29) => (~preda(X29) => (predm(X29) <~> predb(X29))))) & (! [X30] : (room(X30) => (predm(X30) | ~predd(X30))) => ! [X31] : (~predt(X31) <=> predb(X31))) & (! [X32] : (room(X32) => predd(X32)) => ! [X33] : (room(X33) => ((~predc(X33) | preda(X33) | ~predf(X33)) => (predr(X33) & ~predq(X33))))) & there_is_a_room [rectify 44] 47. ! [X0] : (room(X0) => (~predj(X0) => (~predj(X0) & predn(X0) & predt(X0)))) & ! [X1] : (room(X1) => (predt(X1) & predm(X1))) & ! [X2] : (room(X2) => ((~predt(X2) & predj(X2)) => predd(X2))) & ~? [X3] : (room(X3) => ~predj(X3)) & ! [X4] : (anywhere(X4) => predh(X4)) & ! [X5] : (room(X5) => ((predq(X5) | ~predr(X5)) => (preda(X5) | predg(X5) | ~predi(X5)))) & ! [X6] : (room(X6) => ~predc(X6)) & ! [X7] : (room(X7) => predg(X7)) & (mary_dream => ! [X8] : (room(X8) => ((~predk(X8) & predn(X8)) => (~predp(X8) & predq(X8))))) & ! [X9] : (room(X9) => (~preds(X9) <~> predf(X9))) & ! [X10] : (room(X10) => predd(X10)) & ! [X11] : (room(X11) => (predl(X11) => (predp(X11) & predn(X11)))) & ~! [X12] : (anywhere(X12) => ((predj(X12) & ~preda(X12)) => (predc(X12) <~> ~predn(X12)))) & ! [X13] : (prede(X13) <=> predc(X13)) & ! [X14] : (anywhere(X14) => (~predd(X14) => predc(X14))) & ! [X15] : (~room(X15) => (predj(X15) => ~predd(X15))) & ! [X16] : (~room(X16) => predi(X16)) & ! [X17] : (room(X17) => (predt(X17) <=> (predn(X17) | ~predt(X17) | predr(X17)))) & ~? [X18] : (room(X18) => (predt(X18) & ~predt(X18))) & ! [X19] : (room(X19) => (prede(X19) <=> (predu(X19) & preds(X19) & ~predr(X19)))) & (! [X20] : (room(X20) => (~predn(X20) | ~predr(X20))) => ! [X21] : (room(X21) => (predl(X21) => (predp(X21) & predn(X21))))) & (~? [X22] : (room(X22) => (~predl(X22) | prede(X22))) => ! [X23] : (room(X23) => (~predn(X23) | ~predr(X23)))) & (~! [X24] : (room(X24) => (~preda(X24) | prede(X24))) => ! [X25] : (room(X25) => (predk(X25) => predc(X25)))) & (! [X26] : (room(X26) => (~predf(X26) | ~predh(X26))) => ! [X27] : (room(X27) => (~predf(X27) => ~predn(X27)))) & (! [X28] : (room(X28) => (~preda(X28) | ~predc(X28))) => ! [X29] : (~room(X29) => (~preda(X29) => (predm(X29) <~> predb(X29))))) & (! [X30] : (room(X30) => (predm(X30) | ~predd(X30))) => ! [X31] : (~predt(X31) <=> predb(X31))) & (! [X32] : (room(X32) => predd(X32)) => ! [X33] : (room(X33) => ((~predc(X33) | preda(X33) | ~predf(X33)) => (predr(X33) & ~predq(X33))))) & there_is_a_room [pure predicate removal 46] 48. ! [X0] : (room(X0) => (~predj(X0) => (~predj(X0) & predn(X0) & predt(X0)))) & ! [X1] : (room(X1) => (predt(X1) & predm(X1))) & ! [X2] : (room(X2) => ((~predt(X2) & predj(X2)) => predd(X2))) & ~? [X3] : (room(X3) => ~predj(X3)) & ! [X4] : (anywhere(X4) => predh(X4)) & ! [X6] : (room(X6) => ~predc(X6)) & (mary_dream => ! [X8] : (room(X8) => ((~predk(X8) & predn(X8)) => (~predp(X8) & predq(X8))))) & ! [X9] : (room(X9) => (~preds(X9) <~> predf(X9))) & ! [X10] : (room(X10) => predd(X10)) & ! [X11] : (room(X11) => (predl(X11) => (predp(X11) & predn(X11)))) & ~! [X12] : (anywhere(X12) => ((predj(X12) & ~preda(X12)) => (predc(X12) <~> ~predn(X12)))) & ! [X13] : (prede(X13) <=> predc(X13)) & ! [X14] : (anywhere(X14) => (~predd(X14) => predc(X14))) & ! [X15] : (~room(X15) => (predj(X15) => ~predd(X15))) & ! [X16] : (~room(X16) => predi(X16)) & ! [X17] : (room(X17) => (predt(X17) <=> (predn(X17) | ~predt(X17) | predr(X17)))) & ~? [X18] : (room(X18) => (predt(X18) & ~predt(X18))) & ! [X19] : (room(X19) => (prede(X19) <=> (predu(X19) & preds(X19) & ~predr(X19)))) & (! [X20] : (room(X20) => (~predn(X20) | ~predr(X20))) => ! [X21] : (room(X21) => (predl(X21) => (predp(X21) & predn(X21))))) & (~? [X22] : (room(X22) => (~predl(X22) | prede(X22))) => ! [X23] : (room(X23) => (~predn(X23) | ~predr(X23)))) & (~! [X24] : (room(X24) => (~preda(X24) | prede(X24))) => ! [X25] : (room(X25) => (predk(X25) => predc(X25)))) & (! [X26] : (room(X26) => (~predf(X26) | ~predh(X26))) => ! [X27] : (room(X27) => (~predf(X27) => ~predn(X27)))) & (! [X28] : (room(X28) => (~preda(X28) | ~predc(X28))) => ! [X29] : (~room(X29) => (~preda(X29) => (predm(X29) <~> predb(X29))))) & (! [X30] : (room(X30) => (predm(X30) | ~predd(X30))) => ! [X31] : (~predt(X31) <=> predb(X31))) & (! [X32] : (room(X32) => predd(X32)) => ! [X33] : (room(X33) => ((~predc(X33) | preda(X33) | ~predf(X33)) => (predr(X33) & ~predq(X33))))) & there_is_a_room [pure predicate removal 47] 49. ! [X0] : (room(X0) => (~predj(X0) => (~predj(X0) & predn(X0) & predt(X0)))) & ! [X1] : (room(X1) => (predt(X1) & predm(X1))) & ! [X2] : (room(X2) => ((~predt(X2) & predj(X2)) => predd(X2))) & ~? [X3] : (room(X3) => ~predj(X3)) & ! [X4] : (anywhere(X4) => predh(X4)) & ! [X6] : (room(X6) => ~predc(X6)) & (mary_dream => ! [X8] : (room(X8) => ((~predk(X8) & predn(X8)) => (~predp(X8) & predq(X8))))) & ! [X9] : (room(X9) => (~preds(X9) <~> predf(X9))) & ! [X10] : (room(X10) => predd(X10)) & ! [X11] : (room(X11) => (predl(X11) => (predp(X11) & predn(X11)))) & ~! [X12] : (anywhere(X12) => ((predj(X12) & ~preda(X12)) => (predc(X12) <~> ~predn(X12)))) & ! [X13] : (prede(X13) <=> predc(X13)) & ! [X14] : (anywhere(X14) => (~predd(X14) => predc(X14))) & ! [X15] : (~room(X15) => (predj(X15) => ~predd(X15))) & ! [X17] : (room(X17) => (predt(X17) <=> (predn(X17) | ~predt(X17) | predr(X17)))) & ~? [X18] : (room(X18) => (predt(X18) & ~predt(X18))) & ! [X19] : (room(X19) => (prede(X19) <=> (predu(X19) & preds(X19) & ~predr(X19)))) & (! [X20] : (room(X20) => (~predn(X20) | ~predr(X20))) => ! [X21] : (room(X21) => (predl(X21) => (predp(X21) & predn(X21))))) & (~? [X22] : (room(X22) => (~predl(X22) | prede(X22))) => ! [X23] : (room(X23) => (~predn(X23) | ~predr(X23)))) & (~! [X24] : (room(X24) => (~preda(X24) | prede(X24))) => ! [X25] : (room(X25) => (predk(X25) => predc(X25)))) & (! [X26] : (room(X26) => (~predf(X26) | ~predh(X26))) => ! [X27] : (room(X27) => (~predf(X27) => ~predn(X27)))) & (! [X28] : (room(X28) => (~preda(X28) | ~predc(X28))) => ! [X29] : (~room(X29) => (~preda(X29) => (predm(X29) <~> predb(X29))))) & (! [X30] : (room(X30) => (predm(X30) | ~predd(X30))) => ! [X31] : (~predt(X31) <=> predb(X31))) & (! [X32] : (room(X32) => predd(X32)) => ! [X33] : (room(X33) => ((~predc(X33) | preda(X33) | ~predf(X33)) => (predr(X33) & ~predq(X33))))) & there_is_a_room [pure predicate removal 48] 50. ! [X0] : (room(X0) => (~predj(X0) => (~predj(X0) & predn(X0) & predt(X0)))) & ! [X1] : (room(X1) => (predt(X1) & predm(X1))) & ! [X2] : (room(X2) => ((~predt(X2) & predj(X2)) => predd(X2))) & ~? [X3] : (room(X3) => ~predj(X3)) & ! [X4] : (anywhere(X4) => predh(X4)) & ! [X6] : (room(X6) => ~predc(X6)) & ! [X9] : (room(X9) => (~preds(X9) <~> predf(X9))) & ! [X10] : (room(X10) => predd(X10)) & ! [X11] : (room(X11) => (predl(X11) => (predp(X11) & predn(X11)))) & ~! [X12] : (anywhere(X12) => ((predj(X12) & ~preda(X12)) => (predc(X12) <~> ~predn(X12)))) & ! [X13] : (prede(X13) <=> predc(X13)) & ! [X14] : (anywhere(X14) => (~predd(X14) => predc(X14))) & ! [X15] : (~room(X15) => (predj(X15) => ~predd(X15))) & ! [X17] : (room(X17) => (predt(X17) <=> (predn(X17) | ~predt(X17) | predr(X17)))) & ~? [X18] : (room(X18) => (predt(X18) & ~predt(X18))) & ! [X19] : (room(X19) => (prede(X19) <=> (predu(X19) & preds(X19) & ~predr(X19)))) & (! [X20] : (room(X20) => (~predn(X20) | ~predr(X20))) => ! [X21] : (room(X21) => (predl(X21) => (predp(X21) & predn(X21))))) & (~? [X22] : (room(X22) => (~predl(X22) | prede(X22))) => ! [X23] : (room(X23) => (~predn(X23) | ~predr(X23)))) & (~! [X24] : (room(X24) => (~preda(X24) | prede(X24))) => ! [X25] : (room(X25) => (predk(X25) => predc(X25)))) & (! [X26] : (room(X26) => (~predf(X26) | ~predh(X26))) => ! [X27] : (room(X27) => (~predf(X27) => ~predn(X27)))) & (! [X28] : (room(X28) => (~preda(X28) | ~predc(X28))) => ! [X29] : (~room(X29) => (~preda(X29) => (predm(X29) <~> predb(X29))))) & (! [X30] : (room(X30) => (predm(X30) | ~predd(X30))) => ! [X31] : (~predt(X31) <=> predb(X31))) & (! [X32] : (room(X32) => predd(X32)) => ! [X33] : (room(X33) => ((~predc(X33) | preda(X33) | ~predf(X33)) => (predr(X33) & ~predq(X33))))) & there_is_a_room [pure predicate removal 49] 51. ! [X0] : (room(X0) => (~predj(X0) => (~predj(X0) & predn(X0) & predt(X0)))) & ! [X1] : (room(X1) => (predt(X1) & predm(X1))) & ! [X2] : (room(X2) => ((~predt(X2) & predj(X2)) => predd(X2))) & ~? [X3] : (room(X3) => ~predj(X3)) & ! [X4] : (anywhere(X4) => predh(X4)) & ! [X6] : (room(X6) => ~predc(X6)) & ! [X9] : (room(X9) => (~preds(X9) <~> predf(X9))) & ! [X10] : (room(X10) => predd(X10)) & ! [X11] : (room(X11) => (predl(X11) => predn(X11))) & ~! [X12] : (anywhere(X12) => ((predj(X12) & ~preda(X12)) => (predc(X12) <~> ~predn(X12)))) & ! [X13] : (prede(X13) <=> predc(X13)) & ! [X14] : (anywhere(X14) => (~predd(X14) => predc(X14))) & ! [X15] : (~room(X15) => (predj(X15) => ~predd(X15))) & ! [X17] : (room(X17) => (predt(X17) <=> (predn(X17) | ~predt(X17) | predr(X17)))) & ~? [X18] : (room(X18) => (predt(X18) & ~predt(X18))) & ! [X19] : (room(X19) => (prede(X19) <=> (predu(X19) & preds(X19) & ~predr(X19)))) & (! [X20] : (room(X20) => (~predn(X20) | ~predr(X20))) => ! [X21] : (room(X21) => (predl(X21) => predn(X21)))) & (~? [X22] : (room(X22) => (~predl(X22) | prede(X22))) => ! [X23] : (room(X23) => (~predn(X23) | ~predr(X23)))) & (~! [X24] : (room(X24) => (~preda(X24) | prede(X24))) => ! [X25] : (room(X25) => (predk(X25) => predc(X25)))) & (! [X26] : (room(X26) => (~predf(X26) | ~predh(X26))) => ! [X27] : (room(X27) => (~predf(X27) => ~predn(X27)))) & (! [X28] : (room(X28) => (~preda(X28) | ~predc(X28))) => ! [X29] : (~room(X29) => (~preda(X29) => (predm(X29) <~> predb(X29))))) & (! [X30] : (room(X30) => (predm(X30) | ~predd(X30))) => ! [X31] : (~predt(X31) <=> predb(X31))) & (! [X32] : (room(X32) => predd(X32)) => ! [X33] : (room(X33) => ((~predc(X33) | preda(X33) | ~predf(X33)) => (predr(X33) & ~predq(X33))))) & there_is_a_room [pure predicate removal 50] 52. ! [X0] : (room(X0) => (~predj(X0) => (~predj(X0) & predn(X0) & predt(X0)))) & ! [X1] : (room(X1) => (predt(X1) & predm(X1))) & ! [X2] : (room(X2) => ((~predt(X2) & predj(X2)) => predd(X2))) & ~? [X3] : (room(X3) => ~predj(X3)) & ! [X4] : (anywhere(X4) => predh(X4)) & ! [X6] : (room(X6) => ~predc(X6)) & ! [X9] : (room(X9) => (~preds(X9) <~> predf(X9))) & ! [X10] : (room(X10) => predd(X10)) & ! [X11] : (room(X11) => (predl(X11) => predn(X11))) & ~! [X12] : (anywhere(X12) => ((predj(X12) & ~preda(X12)) => (predc(X12) <~> ~predn(X12)))) & ! [X13] : (prede(X13) <=> predc(X13)) & ! [X14] : (anywhere(X14) => (~predd(X14) => predc(X14))) & ! [X15] : (~room(X15) => (predj(X15) => ~predd(X15))) & ! [X17] : (room(X17) => (predt(X17) <=> (predn(X17) | ~predt(X17) | predr(X17)))) & ~? [X18] : (room(X18) => (predt(X18) & ~predt(X18))) & ! [X19] : (room(X19) => (prede(X19) <=> (predu(X19) & preds(X19) & ~predr(X19)))) & (! [X20] : (room(X20) => (~predn(X20) | ~predr(X20))) => ! [X21] : (room(X21) => (predl(X21) => predn(X21)))) & (~? [X22] : (room(X22) => (~predl(X22) | prede(X22))) => ! [X23] : (room(X23) => (~predn(X23) | ~predr(X23)))) & (~! [X24] : (room(X24) => (~preda(X24) | prede(X24))) => ! [X25] : (room(X25) => (predk(X25) => predc(X25)))) & (! [X26] : (room(X26) => (~predf(X26) | ~predh(X26))) => ! [X27] : (room(X27) => (~predf(X27) => ~predn(X27)))) & (! [X28] : (room(X28) => (~preda(X28) | ~predc(X28))) => ! [X29] : (~room(X29) => (~preda(X29) => (predm(X29) <~> predb(X29))))) & (! [X30] : (room(X30) => (predm(X30) | ~predd(X30))) => ! [X31] : (~predt(X31) <=> predb(X31))) & (! [X32] : (room(X32) => predd(X32)) => ! [X33] : (room(X33) => ((~predc(X33) | preda(X33) | ~predf(X33)) => predr(X33)))) & there_is_a_room [pure predicate removal 51] 53. ! [X0] : (room(X0) => (~predj(X0) => (~predj(X0) & predn(X0) & predt(X0)))) & ! [X1] : (room(X1) => (predt(X1) & predm(X1))) & ! [X2] : (room(X2) => ((~predt(X2) & predj(X2)) => predd(X2))) & ~? [X3] : (room(X3) => ~predj(X3)) & ! [X4] : (anywhere(X4) => predh(X4)) & ! [X6] : (room(X6) => ~predc(X6)) & ! [X9] : (room(X9) => (~preds(X9) <~> predf(X9))) & ! [X10] : (room(X10) => predd(X10)) & ! [X11] : (room(X11) => (predl(X11) => predn(X11))) & ~! [X12] : (anywhere(X12) => ((predj(X12) & ~preda(X12)) => (predc(X12) <~> ~predn(X12)))) & ! [X13] : (prede(X13) <=> predc(X13)) & ! [X14] : (anywhere(X14) => (~predd(X14) => predc(X14))) & ! [X15] : (~room(X15) => (predj(X15) => ~predd(X15))) & ! [X17] : (room(X17) => (predt(X17) <=> (predn(X17) | ~predt(X17) | predr(X17)))) & ~? [X18] : (room(X18) => (predt(X18) & ~predt(X18))) & ! [X19] : (room(X19) => (prede(X19) <=> (predu(X19) & preds(X19) & ~predr(X19)))) & (! [X20] : (room(X20) => (~predn(X20) | ~predr(X20))) => ! [X21] : (room(X21) => (predl(X21) => predn(X21)))) & (~? [X22] : (room(X22) => (~predl(X22) | prede(X22))) => ! [X23] : (room(X23) => (~predn(X23) | ~predr(X23)))) & (! [X26] : (room(X26) => (~predf(X26) | ~predh(X26))) => ! [X27] : (room(X27) => (~predf(X27) => ~predn(X27)))) & (! [X28] : (room(X28) => (~preda(X28) | ~predc(X28))) => ! [X29] : (~room(X29) => (~preda(X29) => (predm(X29) <~> predb(X29))))) & (! [X30] : (room(X30) => (predm(X30) | ~predd(X30))) => ! [X31] : (~predt(X31) <=> predb(X31))) & (! [X32] : (room(X32) => predd(X32)) => ! [X33] : (room(X33) => ((~predc(X33) | preda(X33) | ~predf(X33)) => predr(X33)))) & there_is_a_room [pure predicate removal 52] 54. ! [X0] : (room(X0) => (~predj(X0) => (~predj(X0) & predn(X0) & predt(X0)))) & ! [X1] : (room(X1) => (predt(X1) & predm(X1))) & ! [X2] : (room(X2) => ((~predt(X2) & predj(X2)) => predd(X2))) & ~? [X3] : (room(X3) => ~predj(X3)) & ! [X4] : (anywhere(X4) => predh(X4)) & ! [X6] : (room(X6) => ~predc(X6)) & ! [X9] : (room(X9) => (~preds(X9) <~> predf(X9))) & ! [X10] : (room(X10) => predd(X10)) & ~! [X12] : (anywhere(X12) => ((predj(X12) & ~preda(X12)) => (predc(X12) <~> ~predn(X12)))) & ! [X13] : (prede(X13) <=> predc(X13)) & ! [X14] : (anywhere(X14) => (~predd(X14) => predc(X14))) & ! [X15] : (~room(X15) => (predj(X15) => ~predd(X15))) & ! [X17] : (room(X17) => (predt(X17) <=> (predn(X17) | ~predt(X17) | predr(X17)))) & ~? [X18] : (room(X18) => (predt(X18) & ~predt(X18))) & ! [X19] : (room(X19) => (prede(X19) <=> (predu(X19) & preds(X19) & ~predr(X19)))) & (! [X26] : (room(X26) => (~predf(X26) | ~predh(X26))) => ! [X27] : (room(X27) => (~predf(X27) => ~predn(X27)))) & (! [X28] : (room(X28) => (~preda(X28) | ~predc(X28))) => ! [X29] : (~room(X29) => (~preda(X29) => (predm(X29) <~> predb(X29))))) & (! [X30] : (room(X30) => (predm(X30) | ~predd(X30))) => ! [X31] : (~predt(X31) <=> predb(X31))) & (! [X32] : (room(X32) => predd(X32)) => ! [X33] : (room(X33) => ((~predc(X33) | preda(X33) | ~predf(X33)) => predr(X33)))) & there_is_a_room [pure predicate removal 53] 55. ! [X0] : (room(X0) => (~predj(X0) => (~predj(X0) & predn(X0) & predt(X0)))) & ! [X1] : (room(X1) => (predt(X1) & predm(X1))) & ! [X2] : (room(X2) => ((~predt(X2) & predj(X2)) => predd(X2))) & ~? [X3] : (room(X3) => ~predj(X3)) & ! [X6] : (room(X6) => ~predc(X6)) & ! [X9] : (room(X9) => (~preds(X9) <~> predf(X9))) & ! [X10] : (room(X10) => predd(X10)) & ~! [X12] : (anywhere(X12) => ((predj(X12) & ~preda(X12)) => (predc(X12) <~> ~predn(X12)))) & ! [X13] : (prede(X13) <=> predc(X13)) & ! [X14] : (anywhere(X14) => (~predd(X14) => predc(X14))) & ! [X15] : (~room(X15) => (predj(X15) => ~predd(X15))) & ! [X17] : (room(X17) => (predt(X17) <=> (predn(X17) | ~predt(X17) | predr(X17)))) & ~? [X18] : (room(X18) => (predt(X18) & ~predt(X18))) & ! [X19] : (room(X19) => (prede(X19) <=> (predu(X19) & preds(X19) & ~predr(X19)))) & (! [X26] : (room(X26) => ~predf(X26)) => ! [X27] : (room(X27) => (~predf(X27) => ~predn(X27)))) & (! [X28] : (room(X28) => (~preda(X28) | ~predc(X28))) => ! [X29] : (~room(X29) => (~preda(X29) => (predm(X29) <~> predb(X29))))) & (! [X30] : (room(X30) => (predm(X30) | ~predd(X30))) => ! [X31] : (~predt(X31) <=> predb(X31))) & (! [X32] : (room(X32) => predd(X32)) => ! [X33] : (room(X33) => ((~predc(X33) | preda(X33) | ~predf(X33)) => predr(X33)))) & there_is_a_room [pure predicate removal 54] 56. ! [X0] : (room(X0) => (~predj(X0) => (~predj(X0) & predn(X0) & predt(X0)))) & ! [X1] : (room(X1) => (predt(X1) & predm(X1))) & ! [X2] : (room(X2) => ((~predt(X2) & predj(X2)) => predd(X2))) & ~? [X3] : (room(X3) => ~predj(X3)) & ! [X6] : (room(X6) => ~predc(X6)) & ! [X9] : (room(X9) => (~preds(X9) <~> predf(X9))) & ! [X10] : (room(X10) => predd(X10)) & ~! [X12] : (anywhere(X12) => ((predj(X12) & ~preda(X12)) => (predc(X12) <~> ~predn(X12)))) & ! [X13] : (prede(X13) <=> predc(X13)) & ! [X14] : (anywhere(X14) => (~predd(X14) => predc(X14))) & ! [X15] : (~room(X15) => (predj(X15) => ~predd(X15))) & ! [X17] : (room(X17) => (predt(X17) <=> (predn(X17) | ~predt(X17) | predr(X17)))) & ~? [X18] : (room(X18) => (predt(X18) & ~predt(X18))) & ! [X19] : (room(X19) => (prede(X19) <=> (predu(X19) & preds(X19) & ~predr(X19)))) & (! [X26] : (room(X26) => ~predf(X26)) => ! [X27] : (room(X27) => (~predf(X27) => ~predn(X27)))) & (! [X28] : (room(X28) => (~preda(X28) | ~predc(X28))) => ! [X29] : (~room(X29) => (~preda(X29) => (predm(X29) <~> predb(X29))))) & (! [X30] : (room(X30) => (predm(X30) | ~predd(X30))) => ! [X31] : (~predt(X31) <=> predb(X31))) & (! [X32] : (room(X32) => predd(X32)) => ! [X33] : (room(X33) => ((~predc(X33) | preda(X33) | ~predf(X33)) => predr(X33)))) [pure predicate removal 55] 57. ! [X0] : (room(X0) => ~predm(X0)) [pure predicate removal 45] 129. ! [X0] : (((~predj(X0) & predn(X0) & predt(X0)) | predj(X0)) | ~room(X0)) & ! [X1] : ((predt(X1) & predm(X1)) | ~room(X1)) & ! [X2] : ((predd(X2) | (predt(X2) | ~predj(X2))) | ~room(X2)) & ! [X3] : (predj(X3) & room(X3)) & ! [X6] : (~predc(X6) | ~room(X6)) & ! [X9] : ((~preds(X9) <~> predf(X9)) | ~room(X9)) & ! [X10] : (predd(X10) | ~room(X10)) & ? [X12] : (((predc(X12) <=> ~predn(X12)) & (predj(X12) & ~preda(X12))) & anywhere(X12)) & ! [X13] : (prede(X13) <=> predc(X13)) & ! [X14] : ((predc(X14) | predd(X14)) | ~anywhere(X14)) & ! [X15] : ((~predd(X15) | ~predj(X15)) | room(X15)) & ! [X17] : ((predt(X17) <=> (predn(X17) | ~predt(X17) | predr(X17))) | ~room(X17)) & ! [X18] : ((~predt(X18) | predt(X18)) & room(X18)) & ! [X19] : ((prede(X19) <=> (predu(X19) & preds(X19) & ~predr(X19))) | ~room(X19)) & (! [X27] : ((~predn(X27) | predf(X27)) | ~room(X27)) | ? [X26] : (predf(X26) & room(X26))) & (! [X29] : (((predm(X29) <~> predb(X29)) | preda(X29)) | room(X29)) | ? [X28] : ((preda(X28) & predc(X28)) & room(X28))) & (! [X31] : (~predt(X31) <=> predb(X31)) | ? [X30] : ((~predm(X30) & predd(X30)) & room(X30))) & (! [X33] : ((predr(X33) | (predc(X33) & ~preda(X33) & predf(X33))) | ~room(X33)) | ? [X32] : (~predd(X32) & room(X32))) [ennf transformation 56] 130. ! [X0] : ((~predj(X0) & predn(X0) & predt(X0)) | predj(X0) | ~room(X0)) & ! [X1] : ((predt(X1) & predm(X1)) | ~room(X1)) & ! [X2] : (predd(X2) | predt(X2) | ~predj(X2) | ~room(X2)) & ! [X3] : (predj(X3) & room(X3)) & ! [X6] : (~predc(X6) | ~room(X6)) & ! [X9] : ((~preds(X9) <~> predf(X9)) | ~room(X9)) & ! [X10] : (predd(X10) | ~room(X10)) & ? [X12] : ((predc(X12) <=> ~predn(X12)) & predj(X12) & ~preda(X12) & anywhere(X12)) & ! [X13] : (prede(X13) <=> predc(X13)) & ! [X14] : (predc(X14) | predd(X14) | ~anywhere(X14)) & ! [X15] : (~predd(X15) | ~predj(X15) | room(X15)) & ! [X17] : ((predt(X17) <=> (predn(X17) | ~predt(X17) | predr(X17))) | ~room(X17)) & ! [X18] : ((~predt(X18) | predt(X18)) & room(X18)) & ! [X19] : ((prede(X19) <=> (predu(X19) & preds(X19) & ~predr(X19))) | ~room(X19)) & (! [X27] : (~predn(X27) | predf(X27) | ~room(X27)) | ? [X26] : (predf(X26) & room(X26))) & (! [X29] : ((predm(X29) <~> predb(X29)) | preda(X29) | room(X29)) | ? [X28] : (preda(X28) & predc(X28) & room(X28))) & (! [X31] : (~predt(X31) <=> predb(X31)) | ? [X30] : (~predm(X30) & predd(X30) & room(X30))) & (! [X33] : (predr(X33) | (predc(X33) & ~preda(X33) & predf(X33)) | ~room(X33)) | ? [X32] : (~predd(X32) & room(X32))) [flattening 129] 131. ! [X0] : (~predm(X0) | ~room(X0)) [ennf transformation 57] 133. ! [X0] : ((~predj(X0) & predn(X0) & predt(X0)) | predj(X0) | ~room(X0)) & ! [X1] : ((predt(X1) & predm(X1)) | ~room(X1)) & ! [X2] : (predd(X2) | predt(X2) | ~predj(X2) | ~room(X2)) & ! [X3] : (predj(X3) & room(X3)) & ! [X6] : (~predc(X6) | ~room(X6)) & ! [X9] : (((~predf(X9) | preds(X9)) & (predf(X9) | ~preds(X9))) | ~room(X9)) & ! [X10] : (predd(X10) | ~room(X10)) & ? [X12] : (((predc(X12) | predn(X12)) & (~predn(X12) | ~predc(X12))) & predj(X12) & ~preda(X12) & anywhere(X12)) & ! [X13] : ((prede(X13) | ~predc(X13)) & (predc(X13) | ~prede(X13))) & ! [X14] : (predc(X14) | predd(X14) | ~anywhere(X14)) & ! [X15] : (~predd(X15) | ~predj(X15) | room(X15)) & ! [X17] : (((predt(X17) | (~predn(X17) & predt(X17) & ~predr(X17))) & ((predn(X17) | ~predt(X17) | predr(X17)) | ~predt(X17))) | ~room(X17)) & ! [X18] : ((~predt(X18) | predt(X18)) & room(X18)) & ! [X19] : (((prede(X19) | (~predu(X19) | ~preds(X19) | predr(X19))) & ((predu(X19) & preds(X19) & ~predr(X19)) | ~prede(X19))) | ~room(X19)) & (! [X27] : (~predn(X27) | predf(X27) | ~room(X27)) | ? [X26] : (predf(X26) & room(X26))) & (! [X29] : (((~predb(X29) | ~predm(X29)) & (predb(X29) | predm(X29))) | preda(X29) | room(X29)) | ? [X28] : (preda(X28) & predc(X28) & room(X28))) & (! [X31] : ((~predt(X31) | ~predb(X31)) & (predb(X31) | predt(X31))) | ? [X30] : (~predm(X30) & predd(X30) & room(X30))) & (! [X33] : (predr(X33) | (predc(X33) & ~preda(X33) & predf(X33)) | ~room(X33)) | ? [X32] : (~predd(X32) & room(X32))) [nnf transformation 130] 134. ! [X0] : ((~predj(X0) & predn(X0) & predt(X0)) | predj(X0) | ~room(X0)) & ! [X1] : ((predt(X1) & predm(X1)) | ~room(X1)) & ! [X2] : (predd(X2) | predt(X2) | ~predj(X2) | ~room(X2)) & ! [X3] : (predj(X3) & room(X3)) & ! [X6] : (~predc(X6) | ~room(X6)) & ! [X9] : (((~predf(X9) | preds(X9)) & (predf(X9) | ~preds(X9))) | ~room(X9)) & ! [X10] : (predd(X10) | ~room(X10)) & ? [X12] : ((predc(X12) | predn(X12)) & (~predn(X12) | ~predc(X12)) & predj(X12) & ~preda(X12) & anywhere(X12)) & ! [X13] : ((prede(X13) | ~predc(X13)) & (predc(X13) | ~prede(X13))) & ! [X14] : (predc(X14) | predd(X14) | ~anywhere(X14)) & ! [X15] : (~predd(X15) | ~predj(X15) | room(X15)) & ! [X17] : (((predt(X17) | (~predn(X17) & predt(X17) & ~predr(X17))) & (predn(X17) | ~predt(X17) | predr(X17) | ~predt(X17))) | ~room(X17)) & ! [X18] : ((~predt(X18) | predt(X18)) & room(X18)) & ! [X19] : (((prede(X19) | ~predu(X19) | ~preds(X19) | predr(X19)) & ((predu(X19) & preds(X19) & ~predr(X19)) | ~prede(X19))) | ~room(X19)) & (! [X27] : (~predn(X27) | predf(X27) | ~room(X27)) | ? [X26] : (predf(X26) & room(X26))) & (! [X29] : (((~predb(X29) | ~predm(X29)) & (predb(X29) | predm(X29))) | preda(X29) | room(X29)) | ? [X28] : (preda(X28) & predc(X28) & room(X28))) & (! [X31] : ((~predt(X31) | ~predb(X31)) & (predb(X31) | predt(X31))) | ? [X30] : (~predm(X30) & predd(X30) & room(X30))) & (! [X33] : (predr(X33) | (predc(X33) & ~preda(X33) & predf(X33)) | ~room(X33)) | ? [X32] : (~predd(X32) & room(X32))) [flattening 133] 135. ! [X0] : ((~predj(X0) & predn(X0) & predt(X0)) | predj(X0) | ~room(X0)) & ! [X1] : ((predt(X1) & predm(X1)) | ~room(X1)) & ! [X2] : (predd(X2) | predt(X2) | ~predj(X2) | ~room(X2)) & ! [X3] : (predj(X3) & room(X3)) & ! [X4] : (~predc(X4) | ~room(X4)) & ! [X5] : (((~predf(X5) | preds(X5)) & (predf(X5) | ~preds(X5))) | ~room(X5)) & ! [X6] : (predd(X6) | ~room(X6)) & ? [X7] : ((predc(X7) | predn(X7)) & (~predn(X7) | ~predc(X7)) & predj(X7) & ~preda(X7) & anywhere(X7)) & ! [X8] : ((prede(X8) | ~predc(X8)) & (predc(X8) | ~prede(X8))) & ! [X9] : (predc(X9) | predd(X9) | ~anywhere(X9)) & ! [X10] : (~predd(X10) | ~predj(X10) | room(X10)) & ! [X11] : (((predt(X11) | (~predn(X11) & predt(X11) & ~predr(X11))) & (predn(X11) | ~predt(X11) | predr(X11) | ~predt(X11))) | ~room(X11)) & ! [X12] : ((~predt(X12) | predt(X12)) & room(X12)) & ! [X13] : (((prede(X13) | ~predu(X13) | ~preds(X13) | predr(X13)) & ((predu(X13) & preds(X13) & ~predr(X13)) | ~prede(X13))) | ~room(X13)) & (! [X14] : (~predn(X14) | predf(X14) | ~room(X14)) | ? [X15] : (predf(X15) & room(X15))) & (! [X16] : (((~predb(X16) | ~predm(X16)) & (predb(X16) | predm(X16))) | preda(X16) | room(X16)) | ? [X17] : (preda(X17) & predc(X17) & room(X17))) & (! [X18] : ((~predt(X18) | ~predb(X18)) & (predb(X18) | predt(X18))) | ? [X19] : (~predm(X19) & predd(X19) & room(X19))) & (! [X20] : (predr(X20) | (predc(X20) & ~preda(X20) & predf(X20)) | ~room(X20)) | ? [X21] : (~predd(X21) & room(X21))) [rectify 134] 136. ? [X7] : ((predc(X7) | predn(X7)) & (~predn(X7) | ~predc(X7)) & predj(X7) & ~preda(X7) & anywhere(X7)) => ((predc(sK0) | predn(sK0)) & (~predn(sK0) | ~predc(sK0)) & predj(sK0) & ~preda(sK0) & anywhere(sK0)) [choice axiom] 137. ? [X15] : (predf(X15) & room(X15)) => (predf(sK1) & room(sK1)) [choice axiom] 138. ? [X17] : (preda(X17) & predc(X17) & room(X17)) => (preda(sK2) & predc(sK2) & room(sK2)) [choice axiom] 139. ? [X19] : (~predm(X19) & predd(X19) & room(X19)) => (~predm(sK3) & predd(sK3) & room(sK3)) [choice axiom] 140. ? [X21] : (~predd(X21) & room(X21)) => (~predd(sK4) & room(sK4)) [choice axiom] 141. ! [X0] : ((~predj(X0) & predn(X0) & predt(X0)) | predj(X0) | ~room(X0)) & ! [X1] : ((predt(X1) & predm(X1)) | ~room(X1)) & ! [X2] : (predd(X2) | predt(X2) | ~predj(X2) | ~room(X2)) & ! [X3] : (predj(X3) & room(X3)) & ! [X4] : (~predc(X4) | ~room(X4)) & ! [X5] : (((~predf(X5) | preds(X5)) & (predf(X5) | ~preds(X5))) | ~room(X5)) & ! [X6] : (predd(X6) | ~room(X6)) & ((predc(sK0) | predn(sK0)) & (~predn(sK0) | ~predc(sK0)) & predj(sK0) & ~preda(sK0) & anywhere(sK0)) & ! [X8] : ((prede(X8) | ~predc(X8)) & (predc(X8) | ~prede(X8))) & ! [X9] : (predc(X9) | predd(X9) | ~anywhere(X9)) & ! [X10] : (~predd(X10) | ~predj(X10) | room(X10)) & ! [X11] : (((predt(X11) | (~predn(X11) & predt(X11) & ~predr(X11))) & (predn(X11) | ~predt(X11) | predr(X11) | ~predt(X11))) | ~room(X11)) & ! [X12] : ((~predt(X12) | predt(X12)) & room(X12)) & ! [X13] : (((prede(X13) | ~predu(X13) | ~preds(X13) | predr(X13)) & ((predu(X13) & preds(X13) & ~predr(X13)) | ~prede(X13))) | ~room(X13)) & (! [X14] : (~predn(X14) | predf(X14) | ~room(X14)) | (predf(sK1) & room(sK1))) & (! [X16] : (((~predb(X16) | ~predm(X16)) & (predb(X16) | predm(X16))) | preda(X16) | room(X16)) | (preda(sK2) & predc(sK2) & room(sK2))) & (! [X18] : ((~predt(X18) | ~predb(X18)) & (predb(X18) | predt(X18))) | (~predm(sK3) & predd(sK3) & room(sK3))) & (! [X20] : (predr(X20) | (predc(X20) & ~preda(X20) & predf(X20)) | ~room(X20)) | (~predd(sK4) & room(sK4))) [skolemisation 135,140,139,138,137,136] 266. room(X3) [cnf transformation 141] 269. ~room(X1) | predm(X1) [cnf transformation 141] 274. ~predm(X0) | ~room(X0) [cnf transformation 131] 310. ~predm(X0) [subsumption resolution 274,266] 311. predm(X0) [resolution 269,266] 312. $false [subsumption resolution 311,310] % SZS output end Proof for 2088794862768579566674504 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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, Ida, Brian are the only persons in the room. If Brian and Ida are not humble then everyone outside the room either is a kind person or is happy but not both if and only if they is not a happy quiet person. Larry is not a kind person. Larry is a wise person. Everyone in the room is a wise person only if they neither is not not old nor is a kind person. Everyone in the room is not a old person, is not brave and is a strong person if they neither is not not old nor is a kind person.

Larry is brave.

contradiction

room(larry)&room(ida)&room(brian)&(![X]:(room(X)=>(X='larry'|X='ida'|X='brian')))& ((~humble(brian)&~humble(ida))=>(![X]:(~room(X)=>(((((kind(X)&person(X))<~>(happy(X))))<=>(~(happy(X)&quiet(X)&person(X))))))))& (((![X]:(room(X)=>(((~kind(X))<~>(~(happy(X)&person(X)))))))=>(creative(larry)))&((~(![X]:(room(X)=>(((~kind(X))<~>(~(happy(X)&person(X))))))))=>(![X]:(room(X)=>(((wise(X)&person(X))=>(richer(matthew,X))))))))& (~(kind(larry)&person(larry)))& (wise(larry)&person(larry))& (brave(ida))& (![X]:(room(X)=>(((((quiet(X)&person(X))&(patient(X))&(wise(X)&person(X))))<=>(wise(X)&person(X))))))& (![X]:(room(X)=>(((~((~~old(X))|(kind(X)&person(X))))<=(wise(X)&person(X))))))& (![X]:(room(X)=>(((~((~~old(X))|(kind(X)&person(X))))=>(((~(old(X)&person(X)))&(~brave(X))&(strong(X)&person(X))))))))& (patient(ida))& (![X]:(~room(X)=>(patient(X))))& (generous(larry))& ((~(funny(larry)&person(larry)))&(((kind(larry)&person(larry))<~>(happy(larry)))))& (![X]:(~room(X)=>(((((kind(X)&person(X))<~>(happy(X))))<=>(~(happy(X)&quiet(X)&person(X)))))))& (((funny(ida))&(older(matthew,ida))&(~(tall(ida)&humble(ida)&person(ida)))))

room(larry)&room(ida)&room(brian)&(![X]:(room(X)=>(X='larry'|X='ida'|X='brian')))& brave(larry)

% SZS status Unsatisfiable for 7777150191328931829189188 % SZS output start Proof for 7777150191328931829189188 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 47. ~(person(mary) & kind(mary)) [input p3] 48. person(mary) & wise(mary) [input p4] 51. ! [X0] : (room(X0) => ((person(X0) & wise(X0)) => ~((person(X0) & kind(X0)) | old(X0)))) [input p7] 52. ! [X0] : (room(X0) => (~((person(X0) & kind(X0)) | old(X0)) => (person(X0) & strong(X0) & ~brave(X0) & ~(person(X0) & old(X0))))) [input p8] 59. brave(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 64. ! [X0] : (room(X0) => (~((person(X0) & kind(X0)) | old(X0)) => (person(X0) & ~brave(X0) & ~(person(X0) & old(X0))))) [pure predicate removal 52] 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] 142. ~person(mary) | ~kind(mary) [ennf transformation 47] 144. ! [X0] : ((((~person(X0) | ~kind(X0)) & ~old(X0)) | (~person(X0) | ~wise(X0))) | ~room(X0)) [ennf transformation 51] 145. ! [X0] : (((~person(X0) | ~kind(X0)) & ~old(X0)) | ~person(X0) | ~wise(X0) | ~room(X0)) [flattening 144] 146. ! [X0] : (((person(X0) & ~brave(X0) & (~person(X0) | ~old(X0))) | ((person(X0) & kind(X0)) | old(X0))) | ~room(X0)) [ennf transformation 64] 147. ! [X0] : ((person(X0) & ~brave(X0) & (~person(X0) | ~old(X0))) | (person(X0) & kind(X0)) | old(X0) | ~room(X0)) [flattening 146] 151. brave(mary) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 59] 152. brave(mary) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 151] 248. room(mary) [cnf transformation 139] 255. ~person(mary) | ~kind(mary) [cnf transformation 142] 256. wise(mary) [cnf transformation 48] 257. person(mary) [cnf transformation 48] 266. ~wise(X0) | ~person(X0) | ~old(X0) | ~room(X0) [cnf transformation 145] 270. ~brave(X0) | kind(X0) | old(X0) | ~room(X0) [cnf transformation 147] 297. brave(mary) [cnf transformation 152] 318. 5 <=> kind(mary) [avatar definition] 320. ~kind(mary) <- (~5) [avatar component clause 318] 322. 6 <=> person(mary) [avatar definition] 323. person(mary) <- (6) [avatar component clause 322] 325. ~5 | ~6 [avatar split clause 255,322,318] 326. 6 [avatar split clause 257,322] 374. ~person(mary) | ~old(mary) | ~room(mary) [resolution 266,256] 375. ~old(mary) | ~room(mary) <- (6) [subsumption resolution 374,323] 376. ~old(mary) <- (6) [subsumption resolution 375,248] 378. kind(mary) | old(mary) | ~room(mary) [resolution 270,297] 385. old(mary) | ~room(mary) <- (~5) [subsumption resolution 378,320] 386. ~room(mary) <- (~5, 6) [subsumption resolution 385,376] 387. $false <- (~5, 6) [subsumption resolution 386,248] 388. 5 | ~6 [avatar contradiction clause 387] 389. $false [avatar sat refutation 325,326,388] % SZS output end Proof for 7777150191328931829189188 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Magan, Julie are the only persons in the room. Either "Magan is right-handed" or "Magan owns a 3D printer" but not both. Magan is right-handed. Someone outside the room does not enjoy coding in Python and does not enjoy spelunking. Julie regularly contributes to tech forums and online communities. Magan has a curated collection of mid-century modern furniture or has lived in exactly three countries or both. Julie is not a Linux enthusiast. If someone is a cybersecurity expert or does not work on fridays or both then he/she is right-handed and vice versa. Magan is a cybersecurity expert. It is not the case that "Magan enjoys spelunking". Magan practices kickboxing. Julie is an enthusiastic bird watcher who travels for rare sightings. Magan owns a high-end gaming PC with custom-built components. Magan works on fridays. If someone enjoys kayaking and exploring remote waterways then he/she reads mystery novels and vice versa.

Magan has a curated collection of mid-century modern furniture.

neutral

room(magan)&room(julie)&(![X]:(room(X)=>(X='magan'|X='julie')))& ((is_right-handed(magan))<~>(owns_a_3D_printer(magan)))& (is_right-handed(magan))& (?[X]:(~room(X)&(((does_not_enjoy_coding_in_Python(X))&(does_not_enjoy_spelunking(X))))))& (regularly_contributes_to_tech_forums_and_online_communities(julie))& (((has_a_curated_collection_of_mid-century_modern_furniture(magan))|(has_lived_in_exactly_three_countries(magan))))& (is_not_a_Linux_enthusiast(julie))& ((![X]:((((is_a_cybersecurity_expert(X))|(does_not_work_on_fridays(X))))<=>(is_right-handed(X)))))& (is_a_cybersecurity_expert(magan))& (~(enjoys_spelunking(magan)))& (practices_kickboxing(magan))& (is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(julie))& (owns_a_high-end_gaming_PC_with_custom-built_components(magan))& (works_on_fridays(magan))& ((![X]:((enjoys_kayaking_and_exploring_remote_waterways(X))<=>(reads_mystery_novels(X)))))

room(magan)&room(julie)&(![X]:(room(X)=>(X='magan'|X='julie')))& has_a_curated_collection_of_mid-century_modern_furniture(magan)

Nakia, Adrian, Nancy, Janel, Neil are the only persons in the room. “It is not the case that “Wanda and Neil like each other”” if “everyone in the room collects rare and antique scientific instruments or does not own a significant collection of rare gemstones and minerals” and vice versa. “Everyone in the room who collects antique jewelry can play the piano” if “Adrian collects antique jewelry”. “Janel is a brave person” if “everyone anywhere is a brave person or does not collect antique jewelry” and vice versa. If “Nakia does not collect rare and antique scientific instruments” then “everyone in the room is not a brave person if they owns a significant collection of rare gemstones and minerals and vice versa”. “Nakia owns a significant collection of rare gemstones and minerals” if “Janel does not collect antique jewelry” and vice versa. If “everyone in the room collects rare and antique scientific instruments or cannot play the piano” then “someone who owns a significant collection of rare gemstones and minerals like someone who does not own a significant collection of rare gemstones and minerals”. “Nancy and Wanda like each other” if “everyone in the room collects rare and antique scientific instruments or does not collect antique jewelry”. Someone who cannot play the piano like someone who does not own a significant collection of rare gemstones and minerals. Everyone outside the room can play the piano if they either can play the piano or collects rare and antique scientific instruments but not both and vice versa. Nakia is not brave. Neil is brave. Everyone in the room is a brave person or cannot play the piano. Nancy and Wanda like each other. Everyone in the room collects antique jewelry if they collects rare and antique scientific instruments. Everyone in the room is a brave person or does not collect antique jewelry.

Janel collects rare and antique scientific instruments.

contradiction

room(nakia)&room(adrian)&room(nancy)&room(janel)&room(neil)&(![X]:(room(X)=>(X='nakia'|X='adrian'|X='nancy'|X='janel'|X='neil')))& ((![X]:(room(X)=>(((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))|(collects_rare_and_antique_scientific_instruments(X))))))<=>(~((like(wanda,neil) & like(neil,wanda)))))& ((collects_antique_jewelry(adrian))=>(![X]:(room(X)=>(((collects_antique_jewelry(X))=>(can_play_the_piano(X)))))))& ((![X]:(anywhere(X)=>(((does_not_collect_antique_jewelry(X))|(brave(X)&person(X))))))<=>(brave(janel)&person(janel)))& ((does_not_collect_rare_and_antique_scientific_instruments(nakia))=>(![X]:(room(X)=>(((~(brave(X)&person(X)))<=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X)))))))& ((does_not_collect_antique_jewelry(janel))<=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(nakia)))& ((![X]:(room(X)=>(((cannot_play_the_piano(X))|(collects_rare_and_antique_scientific_instruments(X))))))=>(?[X,Y]:((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))&(does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(Y))&(like(X,Y)))))& ((![X]:(room(X)=>(((does_not_collect_antique_jewelry(X))|(collects_rare_and_antique_scientific_instruments(X))))))=>((like(nancy,wanda) & like(wanda,nancy))))& (?[X,Y]:((cannot_play_the_piano(X))&(does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(Y))&(like(X,Y))))& (![X]:(~room(X)=>(((can_play_the_piano(X))<=>(((can_play_the_piano(X))<~>(collects_rare_and_antique_scientific_instruments(X))))))))& (~brave(nakia))& (brave(neil))& (![X]:(room(X)=>(((cannot_play_the_piano(X))|(brave(X)&person(X))))))& ((like(nancy,wanda) & like(wanda,nancy)))& (![X]:(room(X)=>(((collects_rare_and_antique_scientific_instruments(X))=>(collects_antique_jewelry(X))))))& (![X]:(room(X)=>(((does_not_collect_antique_jewelry(X))|(brave(X)&person(X))))))

room(nakia)&room(adrian)&room(nancy)&room(janel)&room(neil)&(![X]:(room(X)=>(X='nakia'|X='adrian'|X='nancy'|X='janel'|X='neil')))& collects_rare_and_antique_scientific_instruments(janel)

% SZS status Unsatisfiable for 4136871375583597421470483 % SZS output start Proof for 4136871375583597421470483 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. ~predd(mary) => ! [X0] : (room(X0) => (~(person(X0) & brave(X0)) <=> preds(X0))) [input p4] 49. ~predv(alice) <=> preds(mary) [input p5] 53. ! [X0] : (~room(X0) => (predu(X0) <=> (predu(X0) <~> predd(X0)))) [input p9] 54. ~brave(mary) [input p10] 58. ! [X0] : (room(X0) => (predd(X0) => predv(X0))) [input p14] 59. ! [X0] : (room(X0) => ((person(X0) & brave(X0)) | ~predv(X0))) [input p15] 60. predd(alice) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 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] 141. ! [X0] : (((~person(X0) | ~brave(X0)) <=> preds(X0)) | ~room(X0)) | predd(mary) [ennf transformation 48] 146. ! [X0] : ((predu(X0) <=> (predu(X0) <~> predd(X0))) | room(X0)) [ennf transformation 53] 149. ! [X0] : ((predv(X0) | ~predd(X0)) | ~room(X0)) [ennf transformation 58] 150. ! [X0] : (predv(X0) | ~predd(X0) | ~room(X0)) [flattening 149] 151. ! [X0] : (((person(X0) & brave(X0)) | ~predv(X0)) | ~room(X0)) [ennf transformation 59] 152. ! [X0] : ((person(X0) & brave(X0)) | ~predv(X0) | ~room(X0)) [flattening 151] 153. predd(alice) & ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 60] 154. predd(alice) & ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 153] 168. ! [X0] : ((((~person(X0) | ~brave(X0)) | ~preds(X0)) & (preds(X0) | (person(X0) & brave(X0)))) | ~room(X0)) | predd(mary) [nnf transformation 141] 169. ! [X0] : (((~person(X0) | ~brave(X0) | ~preds(X0)) & (preds(X0) | (person(X0) & brave(X0)))) | ~room(X0)) | predd(mary) [flattening 168] 170. (~predv(alice) | ~preds(mary)) & (preds(mary) | predv(alice)) [nnf transformation 49] 181. ! [X0] : (((predu(X0) | ((predu(X0) | ~predd(X0)) & (predd(X0) | ~predu(X0)))) & (((~predd(X0) | ~predu(X0)) & (predd(X0) | predu(X0))) | ~predu(X0))) | room(X0)) [nnf transformation 146] 263. room(mary) [cnf transformation 134] 283. preds(X0) | brave(X0) | ~room(X0) | predd(mary) [cnf transformation 169] 287. ~predv(alice) | ~preds(mary) [cnf transformation 170] 304. ~predd(X0) | ~predu(X0) | ~predu(X0) | room(X0) [cnf transformation 181] 306. predu(X0) | predu(X0) | ~predd(X0) | room(X0) [cnf transformation 181] 307. ~brave(mary) [cnf transformation 54] 313. predv(X0) | ~predd(X0) | ~room(X0) [cnf transformation 150] 314. ~predv(X0) | brave(X0) | ~room(X0) [cnf transformation 152] 322. predd(alice) [cnf transformation 154] 323. ~predd(X0) | ~predu(X0) | room(X0) [duplicate literal removal 304] 324. ~predd(X0) | predu(X0) | room(X0) [duplicate literal removal 306] 396. 16 <=> predd(mary) [avatar definition] 398. predd(mary) <- (16) [avatar component clause 396] 408. 19 <=> ! [X0] : (preds(X0) | ~room(X0) | brave(X0)) [avatar definition] 409. ~room(X0) | preds(X0) | brave(X0) <- (19) [avatar component clause 408] 410. 16 | 19 [avatar split clause 283,408,396] 412. 20 <=> preds(mary) [avatar definition] 414. ~preds(mary) <- (~20) [avatar component clause 412] 416. 21 <=> predv(alice) [avatar definition] 419. ~20 | ~21 [avatar split clause 287,416,412] 481. ~predd(X0) | room(X0) [subsumption resolution 323,324] 484. ~predd(X0) | predv(X0) [subsumption resolution 313,481] 487. predv(alice) [resolution 484,322] 488. predv(mary) <- (16) [resolution 484,398] 491. 21 [avatar split clause 487,416] 504. brave(mary) | ~room(mary) <- (16) [resolution 314,488] 506. ~room(mary) <- (16) [subsumption resolution 504,307] 507. $false <- (16) [subsumption resolution 506,263] 508. ~16 [avatar contradiction clause 507] 567. preds(mary) | brave(mary) <- (19) [resolution 409,263] 573. brave(mary) <- (19, ~20) [subsumption resolution 567,414] 574. $false <- (19, ~20) [subsumption resolution 573,307] 575. ~19 | 20 [avatar contradiction clause 574] 586. $false [avatar sat refutation 410,419,491,508,575] % SZS output end Proof for 4136871375583597421470483 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.038 s % ------------------------------ % ------------------------------

Sylvia is the only person in the room. Everyone in the room owns a telescope if they enjoys windsurfing. Sylvia plays the violin. Sylvia dreamt that "everyone in the room either does not create YouTube content or is a drone photographer but not both". If someone does not bake bread at home then he/she is passionate about collecting and restoring classic cars. Everyone in the room who bakes bread at home is passionate about collecting and restoring classic cars. Everyone in the room who collect rare sneakers makes homemade pastries. Everyone in the room neither is a drone photographer nor plays eSports competitively if they makes homemade pastries. Sylvia is passionate about collecting and restoring classic cars. Sylvia who builds model airplanes is a cybersecurity expert. Sylvia participates in long-distance cycling events across the country. Someone in the room owns a telescope. Everyone in the room is a drone photographer or does not build model airplanes. Everyone in the room owns a telescope.

Sylvia collect rare sneakers.

contradiction

room(sylvia)&(![X]:(room(X)=>(X='sylvia')))& (![X]:(room(X)=>(((enjoys_windsurfing(X))=>(owns_a_telescope(X))))))& (plays_the_violin(sylvia))& ((sylvia_dream=>(![X]:(room(X)=>(((does_not_create_YouTube_content(X))<~>(is_a_drone_photographer(X))))))))& ((![X]:((does_not_bake_bread_at_home(X))=>(is_passionate_about_collecting_and_restoring_classic_cars(X)))))& (![X]:(room(X)=>(((bakes_bread_at_home(X))=>(is_passionate_about_collecting_and_restoring_classic_cars(X))))))& (![X]:(room(X)=>(((collect_rare_sneakers(X))=>(makes_homemade_pastries(X))))))& (![X]:(room(X)=>(((makes_homemade_pastries(X))=>(~((is_a_drone_photographer(X))|(plays_eSports_competitively(X))))))))& (is_passionate_about_collecting_and_restoring_classic_cars(sylvia))& ((builds_model_airplanes(sylvia))&(is_a_cybersecurity_expert(sylvia)))& (participates_in_long-distance_cycling_events_across_the_country(sylvia))& (?[X]:(room(X)&(owns_a_telescope(X))))& (![X]:(room(X)=>(((does_not_build_model_airplanes(X))|(is_a_drone_photographer(X))))))& (![X]:(room(X)=>(owns_a_telescope(X))))& ((![X]:((regularly_contributes_to_tech_forums_and_online_communities(X))<=>(~((is_a_cybersecurity_expert(X))|(is_a_Linux_enthusiast(X)))))))& (((?[X]:(room(X)&bakes_bread_at_home(X)))&(![X,Y]:((room(X)&room(Y)&(bakes_bread_at_home(X))&(bakes_bread_at_home(Y)))=>(X=Y)))))& (collects_comic_books(sylvia))& (?[X]:(room(X)&(plays_the_violin(X))))& (builds_model_airplanes(sylvia))& (![X]:(room(X)=>(((is_a_drone_photographer(X))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))& (creates_YouTube_content(sylvia))

room(sylvia)&(![X]:(room(X)=>(X='sylvia')))& collect_rare_sneakers(sylvia)

% SZS status Unsatisfiable for 6231915404741590327742989 % SZS output start Proof for 6231915404741590327742989 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 50. ! [X0] : (room(X0) => (predk(X0) => predq(X0))) [input p6] 51. ! [X0] : (room(X0) => (predq(X0) => ~(predp(X0) | predj(X0)))) [input p7] 53. predb(mary) & predn(mary) [input p9] 56. ! [X0] : (room(X0) => (predj(X0) | ~predn(X0))) [input p12] 65. predk(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 67. predn(mary) [pure predicate removal 53] 71. ! [X0] : (room(X0) => (predq(X0) => ~predj(X0))) [pure predicate removal 51] 154. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 155. ! [X0] : ((predq(X0) | ~predk(X0)) | ~room(X0)) [ennf transformation 50] 156. ! [X0] : (predq(X0) | ~predk(X0) | ~room(X0)) [flattening 155] 157. ! [X0] : ((~predj(X0) | ~predq(X0)) | ~room(X0)) [ennf transformation 71] 158. ! [X0] : (~predj(X0) | ~predq(X0) | ~room(X0)) [flattening 157] 159. ! [X0] : ((predj(X0) | ~predn(X0)) | ~room(X0)) [ennf transformation 56] 160. ! [X0] : (predj(X0) | ~predn(X0) | ~room(X0)) [flattening 159] 163. predk(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 65] 251. room(mary) [cnf transformation 154] 253. ~predk(X0) | predq(X0) | ~room(X0) [cnf transformation 156] 254. ~predq(X0) | ~predj(X0) | ~room(X0) [cnf transformation 158] 255. predn(mary) [cnf transformation 67] 257. ~predn(X0) | predj(X0) | ~room(X0) [cnf transformation 160] 265. predk(mary) [cnf transformation 163] 274. predq(mary) | ~room(mary) [resolution 253,265] 275. predq(mary) [subsumption resolution 274,251] 276. ~predj(mary) | ~room(mary) [resolution 254,275] 277. ~predj(mary) [subsumption resolution 276,251] 278. predj(mary) | ~room(mary) [resolution 257,255] 279. ~room(mary) [subsumption resolution 278,277] 280. $false [subsumption resolution 279,251] % SZS output end Proof for 6231915404741590327742989 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.021 s % ------------------------------ % ------------------------------

Carol, Donna are the only persons in the room. Everyone in the room practices and performs acrobatic dance routines.

Carol practices and performs acrobatic dance routines.

entailment

room(carol)&room(donna)&(![X]:(room(X)=>(X='carol'|X='donna')))& ((~(collects_classic_novels(donna)))=>(![X]:(~room(X)=>(((~((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))|(enjoys_bird_watching(X))))=>(enjoys_logic_puzzles(X)))))))& ((![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))|(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))))))=>(creates_large-scale_murals_for_public_art_installations(carol)))& (![X]:(room(X)=>(((drives_a_hybrid_car(X))<=(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& (![X]:(room(X)=>(practices_and_performs_acrobatic_dance_routines(X))))& (![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))=>(enjoys_logic_puzzles(X))))))& (~![X]:(room(X)=>(((enjoys_logic_puzzles(X))=>(has_a_tattoo(X))))))& (((?[X]:(room(X)&has_a_tattoo(X)))&(![X,Y]:((room(X)&room(Y)&(has_a_tattoo(X))&(has_a_tattoo(Y)))=>(X=Y)))))& ((~((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(donna))|(enjoys_bird_watching(donna))))&(is_a_certified_yoga_instructor_teaching_classes_weekly(donna)))

room(carol)&room(donna)&(![X]:(room(X)=>(X='carol'|X='donna')))& practices_and_performs_acrobatic_dance_routines(carol)

% SZS status Unsatisfiable for 5935820456415908114140806 % SZS output start Proof for 5935820456415908114140806 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 48. ! [X0] : (room(X0) => predu(X0)) [input p4] 53. ~(predu(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 135. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 136. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 135] 137. ! [X0] : (predu(X0) | ~room(X0)) [ennf transformation 48] 141. ~predu(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 53] 142. ~predu(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 141] 148. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 149. ~predu(mary) | (paul != sK2 & mary != sK2 & room(sK2)) | ~room(paul) | ~room(mary) [skolemisation 142,148] 230. room(mary) [cnf transformation 136] 231. room(paul) [cnf transformation 136] 232. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 136] 233. ~room(X0) | predu(X0) [cnf transformation 137] 239. ~predu(mary) | room(sK2) | ~room(paul) | ~room(mary) [cnf transformation 149] 240. ~predu(mary) | mary != sK2 | ~room(paul) | ~room(mary) [cnf transformation 149] 241. ~predu(mary) | paul != sK2 | ~room(paul) | ~room(mary) [cnf transformation 149] 242. ~predu(mary) | paul != sK2 | ~room(mary) [subsumption resolution 241,231] 243. ~predu(mary) | paul != sK2 [subsumption resolution 242,230] 245. 1 <=> paul = sK2 [avatar definition] 247. paul != sK2 <- (~1) [avatar component clause 245] 249. 2 <=> predu(mary) [avatar definition] 252. ~1 | ~2 [avatar split clause 243,249,245] 253. ~predu(mary) | mary != sK2 | ~room(mary) [subsumption resolution 240,231] 254. ~predu(mary) | mary != sK2 [subsumption resolution 253,230] 256. 3 <=> mary = sK2 [avatar definition] 258. mary != sK2 <- (~3) [avatar component clause 256] 259. ~3 | ~2 [avatar split clause 254,249,256] 260. ~predu(mary) | room(sK2) | ~room(mary) [subsumption resolution 239,231] 261. ~predu(mary) | room(sK2) [subsumption resolution 260,230] 263. 4 <=> room(sK2) [avatar definition] 265. room(sK2) <- (4) [avatar component clause 263] 266. 4 | ~2 [avatar split clause 261,249,263] 267. predu(mary) [resolution 233,230] 273. 2 [avatar split clause 267,249] 279. mary = sK2 | paul = sK2 <- (4) [resolution 232,265] 298. paul = sK2 <- (~3, 4) [subsumption resolution 279,258] 299. $false <- (~1, ~3, 4) [subsumption resolution 298,247] 300. 1 | 3 | ~4 [avatar contradiction clause 299] 301. $false [avatar sat refutation 252,259,266,273,300] % SZS output end Proof for 5935820456415908114140806 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Kenneth, Janice, Byron, Richard are the only persons in the room. All brave persons are kind if Janice and Byron are not curious, not quiet, not calm, not generous, not kind or are curious generous quiet funny europeans or both. Either Wanda is a client of Janice or everyone in the room is a client of Mary or is not a member of a local theater group specializing in improv but not both.

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

neutral

room(kenneth)&room(janice)&room(byron)&room(richard)&(![X]:(room(X)=>(X='kenneth'|X='janice'|X='byron'|X='richard')))& ((((~curious(janice)&~quiet(janice)&~calm(janice)&~generous(janice)&~kind(janice))|(curious(janice)&generous(janice)&quiet(janice)&funny(janice)&european(janice)))&((~curious(byron)&~quiet(byron)&~calm(byron)&~generous(byron)&~kind(byron))|(curious(byron)&generous(byron)&quiet(byron)&funny(byron)&european(byron))))=>(![X]:(brave(X)=>kind(X))))& ((client(janice,wanda))<~>(![X]:(room(X)=>(((is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))|(client(mary,X)))))))& ((![X]:(room(X)=>(((does_not_work_on_fridays(X))|(client(wanda,X))))))<=>(![X]:(room(X)=>(((does_not_work_on_fridays(X))|(~(funny(X)&tall(X)&tourist(X))))))))& ((creative(janice)&creative(richard))=>(((?[X]:(room(X)&sibling(alan,X))))))& ((![X]:(room(X)=>(((does_not_work_on_fridays(X))|(client(alan,X))))))<~>(~(funny(byron)&happy(byron)&european(byron))&~(funny(richard)&happy(richard)&european(richard))))& (((like(richard,mary) & like(mary,richard)))<=>(![X]:(room(X)=>(((does_not_use_contact_lenses(X))|(client(mary,X)))))))& (((![X]:(room(X)=>(((does_not_play_video_games(X))|(sibling(alan,X))))))=>(![X]:(room(X)=>(((sibling(alan,X))=>(collects_vintage_stamps(X)))))))&((~(![X]:(room(X)=>(((does_not_play_video_games(X))|(sibling(alan,X)))))))=>(![X]:(anywhere(X)=>(((collects_vintage_stamps(X))=>(watches_fantasy_movies(X))))))))& ((like(wanda,kenneth))=>(![X]:(room(X)=>(((~(kind(X)&tourist(X)))=>(~hate(X,mary)))))))& ((sibling(wanda,richard)&sibling(wanda,janice))=>(![X]:(creative(X)=>happy(X))))& ((![X]:(room(X)=>(((is_not_a_chess_master_who_participates_in_national_tournaments(X))|(can_play_the_piano(X))))))=>(![X]:((~room(X)&(X!=kenneth))=>younger(kenneth,X))))& (![X]:(room(X)=>(((uses_a_Windows_laptop(X))=>(watches_fantasy_movies(X))))))& (~![X]:(room(X)=>(((works_on_fridays(X))<=(does_practice_yoga(X))))))& (wise(janice)&calm(janice)&strong(janice)&person(janice)&wise(richard)&calm(richard)&strong(richard)&person(richard))& (![X]:(room(X)=>(((~(brave(X)&european(X)))=>(wise(X)&humble(X)&kind(X)&funny(X)&tourist(X))))))& (![X]:(creative(X)=>curious(X)))& (~![X]:(room(X)=>(((louder(mary,X))<=(~(humble(X)&quiet(X)&strong(X)&tourist(X)))))))& (![X]:(room(X)=>(((louder(mary,X))=>(~((participates_in_long-distance_cycling_events_across_the_country(X))|(drives_a_hybrid_car(X))))))))& (client(richard,wanda))& (![X]:(room(X)=>(((client(wanda,X))=>(client(alan,X))))))& ((![X]:((creative(X)&person(X))=>(develops_open-source_software_projects_in_their_free_time(X)))))& (![X]:(room(X)=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))=>(sibling(mary,X))))))& ((hate(alan,kenneth) & hate(kenneth,alan)))& ((funny(byron))&(quiet(richard)))& ((?[X,Y]:(room(X)&room(Y)&(client(wanda,X)&client(wanda,Y))&(X!=Y))))& (![X]:(generous(X)=>brave(X)))& (~((sibling(wanda,byron))|(~(funny(byron)&tourist(byron))))&~((sibling(wanda,kenneth))|(~(funny(kenneth)&tourist(kenneth)))))

room(kenneth)&room(janice)&room(byron)&room(richard)&(![X]:(room(X)=>(X='kenneth'|X='janice'|X='byron'|X='richard')))& ![X]:(anywhere(X)=>(~((happy(X)&person(X))|(kind(X)&happy(X)&person(X)))))

There is a room. If everyone in the room enjoys stargazing or cannot play the piano then no one in the room who enjoys stargazing can play the piano otherwise everyone outside the room who can play the guitar practices tai chi. If no one in the room has a piercing or does not volunteer for local environmental conservation projects then everyone in the room who makes intricate hand-cut paper art for exhibitions enjoys cross-country skiing. If everyone in the room does not design and sews custom cosplay costumes for conventions or volunteers for local environmental conservation projects then everyone in the room who can play the piano collect rare sneakers. Everyone in the room who collect rare sneakers is a craft beer aficionado. Everyone outside the room is a craft beer aficionado only if they can play the piano. Not everyone anywhere who can play the piano makes intricate hand-cut paper art for exhibitions. Everyone in the room does not mentor a youth basketball team on weekends or enjoys snowboarding. Everyone in the room enjoys stargazing or is not a craft beer aficionado. If someone enjoys deep-sea diving and exploring underwater caves then he/she has a piercing and vice versa. Everyone outside the room who volunteers for local environmental conservation projects enjoys stargazing. Everyone in the room who enjoys stargazing enjoys cross-country skiing. If someone is a craft beer aficionado then he/she has a piercing. Everyone in the room who practices tai chi collects classic novels.

Everyone in the room is a craft beer aficionado.

contradiction

(there_is_a_room)& (((![X]:(room(X)=>(((cannot_play_the_piano(X))|(enjoys_stargazing(X))))))=>(~?[X]:(room(X)=>(((enjoys_stargazing(X))=>(can_play_the_piano(X)))))))&((~(![X]:(room(X)=>(((cannot_play_the_piano(X))|(enjoys_stargazing(X)))))))=>(![X]:(~room(X)=>(((can_play_the_guitar(X))=>(practices_tai_chi(X))))))))& ((~?[X]:(room(X)=>(((does_not_volunteer_for_local_environmental_conservation_projects(X))|(has_a_piercing(X))))))=>(![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))=>(enjoys_cross-country_skiing(X)))))))& ((![X]:(room(X)=>(((volunteers_for_local_environmental_conservation_projects(X))|(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))))))=>(![X]:(room(X)=>(((can_play_the_piano(X))=>(collect_rare_sneakers(X)))))))& (![X]:(room(X)=>(((collect_rare_sneakers(X))=>(is_a_craft_beer_aficionado(X))))))& (![X]:(~room(X)=>(((can_play_the_piano(X))<=(is_a_craft_beer_aficionado(X))))))& (~![X]:(anywhere(X)=>(((can_play_the_piano(X))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))& (![X]:(room(X)=>(((enjoys_snowboarding(X))|(does_not_mentor_a_youth_basketball_team_on_weekends(X))))))& (![X]:(room(X)=>(((is_not_a_craft_beer_aficionado(X))|(enjoys_stargazing(X))))))& ((![X]:((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))<=>(has_a_piercing(X)))))& (![X]:(~room(X)=>(((volunteers_for_local_environmental_conservation_projects(X))=>(enjoys_stargazing(X))))))& (![X]:(room(X)=>(((enjoys_stargazing(X))=>(enjoys_cross-country_skiing(X))))))& ((![X]:((is_a_craft_beer_aficionado(X))=>(has_a_piercing(X)))))& (![X]:(room(X)=>(((practices_tai_chi(X))=>(collects_classic_novels(X))))))& (![X]:(room(X)=>(((((enjoys_stargazing(X))&(mentors_a_youth_basketball_team_on_weekends(X))&(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))=>(enjoys_cross-country_skiing(X))))))& (![X]:(room(X)=>(((enjoys_snowboarding(X))=>(is_a_craft_beer_aficionado(X))))))& (![X]:(anywhere(X)=>(((is_a_craft_beer_aficionado(X))=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))

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

% SZS status Unsatisfiable for 7127831533339212652536286 % SZS output start Proof for 7127831533339212652536286 45. (~! [X0] : (room(X0) => (predo(X0) | ~predb(X0))) => ! [X0] : (~room(X0) => (predi(X0) => preda(X0)))) & (! [X0] : (room(X0) => (predo(X0) | ~predb(X0))) => ~? [X0] : (room(X0) => (predo(X0) => predb(X0)))) [input p1] 50. ~! [X0] : (anywhere(X0) => (predb(X0) => predm(X0))) [input p6] 52. ! [X0] : (room(X0) => (predo(X0) | ~predc(X0))) [input p8] 61. ! [X0] : (room(X0) => predc(X0)) & there_is_a_room [input hypothesis] 62. (~! [X0] : (room(X0) => (predo(X0) | ~predb(X0))) => ! [X1] : (~room(X1) => (predi(X1) => preda(X1)))) & (! [X2] : (room(X2) => (predo(X2) | ~predb(X2))) => ~? [X3] : (room(X3) => (predo(X3) => predb(X3)))) [rectify 45] 68. ! [X2] : (room(X2) => (predo(X2) | ~predb(X2))) => ~? [X3] : (room(X3) => (predo(X3) => predb(X3))) [pure predicate removal 62] 74. ~! [X0] : (predb(X0) => predm(X0)) [pure predicate removal 50] 77. ~! [X0] : ~predb(X0) [pure predicate removal 74] 81. ! [X0] : (room(X0) => predc(X0)) [pure predicate removal 61] 153. ! [X3] : ((~predb(X3) & predo(X3)) & room(X3)) | ? [X2] : ((~predo(X2) & predb(X2)) & room(X2)) [ennf transformation 68] 154. ! [X3] : (~predb(X3) & predo(X3) & room(X3)) | ? [X2] : (~predo(X2) & predb(X2) & room(X2)) [flattening 153] 161. ? [X0] : predb(X0) [ennf transformation 77] 162. ! [X0] : ((predo(X0) | ~predc(X0)) | ~room(X0)) [ennf transformation 52] 163. ! [X0] : (predo(X0) | ~predc(X0) | ~room(X0)) [flattening 162] 164. ! [X0] : (predc(X0) | ~room(X0)) [ennf transformation 81] 165. ? [X2] : (~predo(X2) & predb(X2) & room(X2)) | ~sP0 [predicate definition introduction] 166. ! [X3] : (~predb(X3) & predo(X3) & room(X3)) | sP0 [definition folding 154,165] 168. ? [X2] : (~predo(X2) & predb(X2) & room(X2)) | ~sP0 [nnf transformation 165] 169. ? [X0] : (~predo(X0) & predb(X0) & room(X0)) | ~sP0 [rectify 168] 170. ? [X0] : (~predo(X0) & predb(X0) & room(X0)) => (~predo(sK1) & predb(sK1) & room(sK1)) [choice axiom] 171. (~predo(sK1) & predb(sK1) & room(sK1)) | ~sP0 [skolemisation 169,170] 172. ! [X0] : (~predb(X0) & predo(X0) & room(X0)) | sP0 [rectify 166] 176. ? [X0] : predb(X0) => predb(sK3) [choice axiom] 177. predb(sK3) [skolemisation 161,176] 258. room(sK1) | ~sP0 [cnf transformation 171] 260. ~predo(sK1) | ~sP0 [cnf transformation 171] 263. ~predb(X0) | sP0 [cnf transformation 172] 267. predb(sK3) [cnf transformation 177] 268. ~predc(X0) | predo(X0) | ~room(X0) [cnf transformation 163] 269. ~room(X0) | predc(X0) [cnf transformation 164] 271. 1 <=> sP0 [avatar definition] 275. 2 <=> predo(sK1) [avatar definition] 277. ~predo(sK1) <- (~2) [avatar component clause 275] 278. ~1 | ~2 [avatar split clause 260,275,271] 285. 4 <=> room(sK1) [avatar definition] 287. room(sK1) <- (4) [avatar component clause 285] 288. ~1 | 4 [avatar split clause 258,285,271] 290. 5 <=> ! [X0] : ~predb(X0) [avatar definition] 291. ~predb(X0) <- (5) [avatar component clause 290] 292. 1 | 5 [avatar split clause 263,290,271] 309. $false <- (5) [resolution 291,267] 310. ~5 [avatar contradiction clause 309] 319. predc(sK1) <- (4) [resolution 287,269] 323. predo(sK1) | ~room(sK1) <- (4) [resolution 319,268] 325. ~room(sK1) <- (~2, 4) [subsumption resolution 323,277] 326. $false <- (~2, 4) [subsumption resolution 325,287] 327. 2 | ~4 [avatar contradiction clause 326] 328. $false [avatar sat refutation 278,288,292,310,327] % SZS output end Proof for 7127831533339212652536286 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Virgina is the only person in the room. If 'it is true that 'everyone in the room watches fantasy movies or does not watche fantasy movies'' then 'Virgina does not write a travel blog'. If 'Virgina can play the guitar' then 'Virgina does not watche fantasy movies'. 'Everyone in the room is not a cybersecurity expert or plays eSports competitively' if 'Virgina neither does not enjoy windsurfing nor enjoys cross-country skiing' and vice versa. 'Everyone in the room who enjoys stargazing enjoys wildlife photography' unless 'everyone in the room does not own a microscope or plays eSports competitively'. If 'no one in the room does not enjoy cross-country skiing or participates in long-distance cycling events across the country' then 'Virgina drives a hybrid car'. 'Everyone in the room uses a Windows laptop or does not enjoy cross-country skiing' if 'everyone in the room enjoys salsa dancing' and vice versa. If 'Virgina practices and performs acrobatic dance routines' then 'everyone outside the room drives a hybrid car and can play the guitar if they cannot play the guitar and practices and performs acrobatic dance routines' otherwise 'everyone in the room enjoys stargazing if they drives a hybrid car and can play the guitar'. If 'Virgina enjoys stargazing' then 'if someone drives a hybrid car then he/she does not practice and performs acrobatic dance routines'. If 'everyone in the room enjoys wildlife photography or does not enjoy stargazing' then 'Virgina does not own a microscope'. Everyone in the room who is a cybersecurity expert enjoys wildlife photography. Virgina can play the guitar. Everyone in the room enjoys salsa dancing if they plays eSports competitively. Virgina does not watche fantasy movies. Everyone in the room enjoys wildlife photography or does not enjoy stargazing.

Virgina drives a hybrid car.

neutral

room(virgina)&(![X]:(room(X)=>(X='virgina')))& ((![X]:(room(X)=>(((does_not_watche_fantasy_movies(X))|(watches_fantasy_movies(X))))))=>(does_not_write_a_travel_blog(virgina)))& ((can_play_the_guitar(virgina))=>(does_not_watche_fantasy_movies(virgina)))& ((~((does_not_enjoy_windsurfing(virgina))|(enjoys_cross-country_skiing(virgina))))<=>(![X]:(room(X)=>(((plays_eSports_competitively(X))|(is_not_a_cybersecurity_expert(X)))))))& (~(![X]:(room(X)=>(((plays_eSports_competitively(X))|(does_not_own_a_microscope(X))))))=>(![X]:(room(X)=>(((enjoys_stargazing(X))=>(enjoys_wildlife_photography(X)))))))& ((~?[X]:(room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))|(does_not_enjoy_cross-country_skiing(X))))))=>(drives_a_hybrid_car(virgina)))& ((![X]:(room(X)=>(enjoys_salsa_dancing(X))))<=>(![X]:(room(X)=>(((does_not_enjoy_cross-country_skiing(X))|(uses_a_Windows_laptop(X)))))))& (((practices_and_performs_acrobatic_dance_routines(virgina))=>(![X]:(~room(X)=>(((((cannot_play_the_guitar(X))&(practices_and_performs_acrobatic_dance_routines(X))))=>(((drives_a_hybrid_car(X))&(can_play_the_guitar(X)))))))))&((~(practices_and_performs_acrobatic_dance_routines(virgina)))=>(![X]:(room(X)=>(((((drives_a_hybrid_car(X))&(can_play_the_guitar(X))))=>(enjoys_stargazing(X))))))))& ((enjoys_stargazing(virgina))=>((![X]:((drives_a_hybrid_car(X))=>(does_not_practice_and_performs_acrobatic_dance_routines(X))))))& ((![X]:(room(X)=>(((does_not_enjoy_stargazing(X))|(enjoys_wildlife_photography(X))))))=>(does_not_own_a_microscope(virgina)))& (![X]:(room(X)=>(((is_a_cybersecurity_expert(X))=>(enjoys_wildlife_photography(X))))))& (can_play_the_guitar(virgina))& (![X]:(room(X)=>(((plays_eSports_competitively(X))=>(enjoys_salsa_dancing(X))))))& (does_not_watche_fantasy_movies(virgina))& (![X]:(room(X)=>(((does_not_enjoy_stargazing(X))|(enjoys_wildlife_photography(X))))))& (![X]:(~room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))=>(does_not_participate_in_long-distance_cycling_events_across_the_country(X))))))& (((?[X]:(room(X)&enjoys_stargazing(X)))))& ((can_play_the_guitar(virgina))&(does_not_participate_in_long-distance_cycling_events_across_the_country(virgina)))& (uses_a_Windows_laptop(virgina))& (plays_eSports_competitively(virgina))

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

Mark is the only person in the room. If “everyone in the room does not train for and competes in international triathlons or creates bespoke furniture pieces from reclaimed wood” then “someone in the room creates bespoke furniture pieces from reclaimed wood”.

It is not the case that “Mark collects vintage vinyl records”.

neutral

room(mark)&(![X]:(room(X)=>(X='mark')))& ((![X]:(room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))|(does_not_train_for_and_competes_in_international_triathlons(X))))))=>(?[X]:(room(X)&(creates_bespoke_furniture_pieces_from_reclaimed_wood(X)))))& (?[X]:(room(X)&(does_not_practice_kickboxing(X))))& ((![X]:((drives_a_hybrid_car(X))<=>(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X)))))& ((![X]:((streams_on_Twitch(X))=>(practices_kickboxing(X)))))& ((mark_dream=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(mark))))& (![X]:(anywhere(X)=>(((cannot_play_the_flute(X))=>(((does_not_collect_vintage_vinyl_records(X))&(makes_homemade_pastries(X))))))))& (?[X]:(room(X)&(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))& (![X]:(room(X)=>(((((can_play_the_flute(X))&(is_a_professional_photographer_specializing_in_portrait_photography(X))))<=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))& (?[X]:(room(X)&(~((does_not_make_homemade_pastries(X))|(reads_mystery_novels(X))))))& (![X]:(room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))=>(streams_on_Twitch(X))))))& (((?[X]:(~room(X)&creates_bespoke_furniture_pieces_from_reclaimed_wood(X)))&(![X,Y]:((~room(X)&~room(Y)&(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))&(creates_bespoke_furniture_pieces_from_reclaimed_wood(Y)))=>(X=Y)))))& (enjoys_stand-up_paddleboarding(mark))& (practices_tai_chi(mark))& (![X]:(room(X)=>(((trains_for_and_competes_in_international_triathlons(X))=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))&(reads_mystery_novels(X))))))))& (collect_rare_sneakers(mark))& (?[X]:(room(X)&(collect_rare_sneakers(X))))& (![X]:(room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))|(does_not_train_for_and_competes_in_international_triathlons(X))))))& (![X]:(room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))<=(practices_kickboxing(X))))))& (~((?[X,Y]:(room(X)&room(Y)&(is_a_member_of_a_local_theater_group_specializing_in_improv(X)&is_a_member_of_a_local_theater_group_specializing_in_improv(Y))&(X!=Y)))))& (~![X]:(room(X)=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))<=>(practices_tai_chi(X))))))& (![X]:(room(X)=>(((practices_tai_chi(X))<=>(collects_historical_artifacts_related_to_ancient_civilizations(X))))))& (![X]:(room(X)=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))=>(is_a_Linux_enthusiast(X))))))& (![X]:(~room(X)=>(((is_a_Linux_enthusiast(X))=>(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))))

room(mark)&(![X]:(room(X)=>(X='mark')))& ~(collects_vintage_vinyl_records(mark))

Charlotte, Donna, Veronica, Jason, Kevin are the only persons in the room. “Everyone in the room is a creative person if they is not a patient person” if “Charlotte is not a humble person”. Charlotte is tall. No curious person is old. Donna is a kind humble tall person. Veronica is a generous person. Jason is not a happy person. Charlotte is not a humble person. It is not the case that “it is not the case that “Jason is not patient””. Everyone in the room is not a kind person only if they is a old person. Donna is a kind person. Donna is a brave person. Jason is curious. Charlotte is not a strong person. Everyone outside the room is not a patient person if they is a patient person. Donna is not a patient person. Everyone in the room is not a strong person only if they is not a curious humble person. Jason is not a patient person. No brave person is patient. Everyone in the room is a tall person.

Kevin is a creative person.

entailment

room(charlotte)&room(donna)&room(veronica)&room(jason)&room(kevin)&(![X]:(room(X)=>(X='charlotte'|X='donna'|X='veronica'|X='jason'|X='kevin')))& ((~(humble(charlotte)&person(charlotte)))=>(![X]:(room(X)=>(((~(patient(X)&person(X)))=>(creative(X)&person(X)))))))& (tall(charlotte))& (~?[X]:(curious(X)=>old(X)))& (kind(donna)&humble(donna)&tall(donna)&person(donna))& (generous(veronica)&person(veronica))& (~(happy(jason)&person(jason)))& (~(humble(charlotte)&person(charlotte)))& (~(~(~patient(jason))))& (![X]:(room(X)=>(((old(X)&person(X))<=(~(kind(X)&person(X)))))))& (kind(donna)&person(donna))& (brave(donna)&person(donna))& (curious(jason))& (~(strong(charlotte)&person(charlotte)))& (![X]:(~room(X)=>(((patient(X)&person(X))=>(~(patient(X)&person(X)))))))& (~(patient(donna)&person(donna)))& (![X]:(room(X)=>(((~(curious(X)&humble(X)&person(X)))<=(~(strong(X)&person(X)))))))& (~(patient(jason)&person(jason)))& (~?[X]:(brave(X)=>patient(X)))& (![X]:(room(X)=>(tall(X)&person(X))))

room(charlotte)&room(donna)&room(veronica)&room(jason)&room(kevin)&(![X]:(room(X)=>(X='charlotte'|X='donna'|X='veronica'|X='jason'|X='kevin')))& creative(kevin)&person(kevin)

% SZS status Unsatisfiable for 616559467541400800641804 % SZS output start Proof for 616559467541400800641804 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 45. ~(person(mary) & humble(mary)) => ! [X0] : (room(X0) => (~(person(X0) & patient(X0)) => (person(X0) & creative(X0)))) [input p1] 51. ~(person(mary) & humble(mary)) [input p7] 62. ~? [X0] : (brave(X0) => patient(X0)) [input p18] 63. ! [X0] : (room(X0) => (person(X0) & tall(X0))) [input p19] 64. ~(person(john) & creative(john) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 66. ~? [X0] : patient(X0) [pure predicate removal 62] 74. ! [X0] : (room(X0) => person(X0)) [pure predicate removal 63] 147. ! [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] 148. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 147] 149. ! [X0] : (((person(X0) & creative(X0)) | (person(X0) & patient(X0))) | ~room(X0)) | (person(mary) & humble(mary)) [ennf transformation 45] 150. ! [X0] : ((person(X0) & creative(X0)) | (person(X0) & patient(X0)) | ~room(X0)) | (person(mary) & humble(mary)) [flattening 149] 152. ~person(mary) | ~humble(mary) [ennf transformation 51] 162. ! [X0] : ~patient(X0) [ennf transformation 66] 163. ! [X0] : (person(X0) | ~room(X0)) [ennf transformation 74] 164. ~person(john) | ~creative(john) | ? [X0] : ((john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 64] 165. ~person(john) | ~creative(john) | ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 164] 167. ? [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] 168. ~person(john) | ~creative(john) | (john != sK0 & alice != sK0 & fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 165,167] 249. room(mary) [cnf transformation 148] 250. room(paul) [cnf transformation 148] 251. room(fred) [cnf transformation 148] 252. room(alice) [cnf transformation 148] 253. room(john) [cnf transformation 148] 254. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 148] 255. creative(X0) | patient(X0) | ~room(X0) | humble(mary) [cnf transformation 150] 268. ~person(mary) | ~humble(mary) [cnf transformation 152] 281. ~patient(X0) [cnf transformation 162] 282. person(X0) | ~room(X0) [cnf transformation 163] 283. ~person(john) | ~creative(john) | room(sK0) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 168] 284. ~person(john) | ~creative(john) | mary != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 168] 285. ~person(john) | ~creative(john) | paul != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 168] 286. ~person(john) | ~creative(john) | fred != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 168] 287. ~person(john) | ~creative(john) | alice != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 168] 288. ~person(john) | ~creative(john) | john != sK0 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 168] 294. 1 <=> person(mary) [avatar definition] 298. 2 <=> ! [X0] : (person(X0) | ~room(X0)) [avatar definition] 299. ~room(X0) | person(X0) <- (2) [avatar component clause 298] 302. 3 <=> humble(mary) [avatar definition] 317. 6 <=> ! [X0] : (creative(X0) | ~room(X0) | patient(X0)) [avatar definition] 318. creative(X0) | ~room(X0) | patient(X0) <- (6) [avatar component clause 317] 320. 3 | 6 [avatar split clause 255,317,302] 321. ~3 | ~1 [avatar split clause 268,294,302] 332. 2 [avatar split clause 282,298] 333. ~person(john) | ~creative(john) | john != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 288,253] 334. ~person(john) | ~creative(john) | john != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 333,252] 335. ~person(john) | ~creative(john) | john != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 334,251] 336. ~person(john) | ~creative(john) | john != sK0 | ~room(mary) [subsumption resolution 335,250] 337. ~person(john) | ~creative(john) | john != sK0 [subsumption resolution 336,249] 339. 8 <=> john = sK0 [avatar definition] 341. john != sK0 <- (~8) [avatar component clause 339] 343. 9 <=> creative(john) [avatar definition] 347. 10 <=> person(john) [avatar definition] 350. ~8 | ~9 | ~10 [avatar split clause 337,347,343,339] 351. ~person(john) | ~creative(john) | alice != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 287,253] 352. ~person(john) | ~creative(john) | alice != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 351,252] 353. ~person(john) | ~creative(john) | alice != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 352,251] 354. ~person(john) | ~creative(john) | alice != sK0 | ~room(mary) [subsumption resolution 353,250] 355. ~person(john) | ~creative(john) | alice != sK0 [subsumption resolution 354,249] 357. 11 <=> alice = sK0 [avatar definition] 359. alice != sK0 <- (~11) [avatar component clause 357] 360. ~11 | ~9 | ~10 [avatar split clause 355,347,343,357] 361. ~person(john) | ~creative(john) | fred != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 286,253] 362. ~person(john) | ~creative(john) | fred != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 361,252] 363. ~person(john) | ~creative(john) | fred != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 362,251] 364. ~person(john) | ~creative(john) | fred != sK0 | ~room(mary) [subsumption resolution 363,250] 365. ~person(john) | ~creative(john) | fred != sK0 [subsumption resolution 364,249] 367. 12 <=> fred = sK0 [avatar definition] 369. fred != sK0 <- (~12) [avatar component clause 367] 370. ~12 | ~9 | ~10 [avatar split clause 365,347,343,367] 371. ~person(john) | ~creative(john) | paul != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 285,253] 372. ~person(john) | ~creative(john) | paul != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 371,252] 373. ~person(john) | ~creative(john) | paul != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 372,251] 374. ~person(john) | ~creative(john) | paul != sK0 | ~room(mary) [subsumption resolution 373,250] 375. ~person(john) | ~creative(john) | paul != sK0 [subsumption resolution 374,249] 377. 13 <=> paul = sK0 [avatar definition] 379. paul != sK0 <- (~13) [avatar component clause 377] 380. ~13 | ~9 | ~10 [avatar split clause 375,347,343,377] 381. ~person(john) | ~creative(john) | mary != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 284,253] 382. ~person(john) | ~creative(john) | mary != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 381,252] 383. ~person(john) | ~creative(john) | mary != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 382,251] 384. ~person(john) | ~creative(john) | mary != sK0 | ~room(mary) [subsumption resolution 383,250] 385. ~person(john) | ~creative(john) | mary != sK0 [subsumption resolution 384,249] 387. 14 <=> mary = sK0 [avatar definition] 389. mary != sK0 <- (~14) [avatar component clause 387] 390. ~14 | ~9 | ~10 [avatar split clause 385,347,343,387] 391. ~person(john) | ~creative(john) | room(sK0) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 283,253] 392. ~person(john) | ~creative(john) | room(sK0) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 391,252] 393. ~person(john) | ~creative(john) | room(sK0) | ~room(paul) | ~room(mary) [subsumption resolution 392,251] 394. ~person(john) | ~creative(john) | room(sK0) | ~room(mary) [subsumption resolution 393,250] 395. ~person(john) | ~creative(john) | room(sK0) [subsumption resolution 394,249] 397. 15 <=> room(sK0) [avatar definition] 399. room(sK0) <- (15) [avatar component clause 397] 400. 15 | ~9 | ~10 [avatar split clause 395,347,343,397] 401. ~room(X0) | creative(X0) <- (6) [subsumption resolution 318,281] 404. person(mary) <- (2) [resolution 299,249] 408. person(john) <- (2) [resolution 299,253] 411. 10 | ~2 [avatar split clause 408,298,347] 412. 1 | ~2 [avatar split clause 404,298,294] 417. creative(john) <- (6) [resolution 401,253] 420. 9 | ~6 [avatar split clause 417,317,343] 467. alice = sK0 | fred = sK0 | paul = sK0 | mary = sK0 | john = sK0 <- (15) [resolution 254,399] 468. fred = sK0 | paul = sK0 | mary = sK0 | john = sK0 <- (~11, 15) [subsumption resolution 467,359] 469. paul = sK0 | mary = sK0 | john = sK0 <- (~11, ~12, 15) [subsumption resolution 468,369] 470. mary = sK0 | john = sK0 <- (~11, ~12, ~13, 15) [subsumption resolution 469,379] 471. john = sK0 <- (~11, ~12, ~13, ~14, 15) [subsumption resolution 470,389] 472. $false <- (~8, ~11, ~12, ~13, ~14, 15) [subsumption resolution 471,341] 473. 8 | 11 | 12 | 13 | 14 | ~15 [avatar contradiction clause 472] 474. $false [avatar sat refutation 320,321,332,350,360,370,380,390,400,411,412,420,473] % SZS output end Proof for 616559467541400800641804 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.023 s % ------------------------------ % ------------------------------

Alberto, Jesse are the only persons in the room. Everyone in the room is a chess master who participates in national tournaments if they uses a Windows laptop. Alberto enjoys origami. Alberto does not use a Windows laptop. Everyone in the room does not enjoy origami if they collects rare minerals. Jesse enjoys origami. Everyone in the room collects classic novels if they is a chess master who participates in national tournaments. Everyone in the room who collects classic novels uses a Windows laptop.

Jesse either does not enjoy origami or does not collect rare minerals but not both.

entailment

room(alberto)&room(jesse)&(![X]:(room(X)=>(X='alberto'|X='jesse')))& (![X]:(room(X)=>(((uses_a_Windows_laptop(X))=>(is_a_chess_master_who_participates_in_national_tournaments(X))))))& (enjoys_origami(alberto))& (does_not_use_a_Windows_laptop(alberto))& (![X]:(room(X)=>(((collects_rare_minerals(X))=>(does_not_enjoy_origami(X))))))& (enjoys_origami(jesse))& (![X]:(room(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))=>(collects_classic_novels(X))))))& (![X]:(room(X)=>(((collects_classic_novels(X))=>(uses_a_Windows_laptop(X))))))

room(alberto)&room(jesse)&(![X]:(room(X)=>(X='alberto'|X='jesse')))& ((does_not_enjoy_origami(jesse))<~>(does_not_collect_rare_minerals(jesse)))

% SZS status Unsatisfiable for 6551194378824769881675293 % SZS output start Proof for 6551194378824769881675293 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 48. ! [X0] : (room(X0) => (predd(X0) => ~predb(X0))) [input p4] 49. predb(paul) [input p5] 52. ~((~predb(paul) <~> ~predd(paul)) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 125. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 126. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 125] 129. ! [X0] : ((~predb(X0) | ~predd(X0)) | ~room(X0)) [ennf transformation 48] 130. ! [X0] : (~predb(X0) | ~predd(X0) | ~room(X0)) [flattening 129] 135. (~predb(paul) <=> ~predd(paul)) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 52] 136. (~predb(paul) <=> ~predd(paul)) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 135] 138. ((~predb(paul) | predd(paul)) & (~predd(paul) | predb(paul))) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [nnf transformation 136] 139. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK0 & mary != sK0 & room(sK0)) [choice axiom] 140. ((~predb(paul) | predd(paul)) & (~predd(paul) | predb(paul))) | (paul != sK0 & mary != sK0 & room(sK0)) | ~room(paul) | ~room(mary) [skolemisation 138,139] 221. room(mary) [cnf transformation 126] 222. room(paul) [cnf transformation 126] 223. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 126] 227. ~predd(X0) | ~predb(X0) | ~room(X0) [cnf transformation 130] 228. predb(paul) [cnf transformation 49] 234. ~predb(paul) | predd(paul) | room(sK0) | ~room(paul) | ~room(mary) [cnf transformation 140] 235. ~predb(paul) | predd(paul) | mary != sK0 | ~room(paul) | ~room(mary) [cnf transformation 140] 236. ~predb(paul) | predd(paul) | paul != sK0 | ~room(paul) | ~room(mary) [cnf transformation 140] 237. predd(paul) | paul != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 236,228] 238. predd(paul) | paul != sK0 | ~room(mary) [subsumption resolution 237,222] 239. predd(paul) | paul != sK0 [subsumption resolution 238,221] 241. 1 <=> paul = sK0 [avatar definition] 243. paul != sK0 <- (~1) [avatar component clause 241] 245. 2 <=> predd(paul) [avatar definition] 247. predd(paul) <- (2) [avatar component clause 245] 248. ~1 | 2 [avatar split clause 239,245,241] 249. predd(paul) | mary != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 235,228] 250. predd(paul) | mary != sK0 | ~room(mary) [subsumption resolution 249,222] 251. predd(paul) | mary != sK0 [subsumption resolution 250,221] 253. 3 <=> mary = sK0 [avatar definition] 255. mary != sK0 <- (~3) [avatar component clause 253] 256. ~3 | 2 [avatar split clause 251,245,253] 257. predd(paul) | room(sK0) | ~room(paul) | ~room(mary) [subsumption resolution 234,228] 258. predd(paul) | room(sK0) | ~room(mary) [subsumption resolution 257,222] 259. predd(paul) | room(sK0) [subsumption resolution 258,221] 261. 4 <=> room(sK0) [avatar definition] 263. room(sK0) <- (4) [avatar component clause 261] 264. 4 | 2 [avatar split clause 259,245,261] 265. ~predb(paul) | ~room(paul) <- (2) [resolution 227,247] 266. ~room(paul) <- (2) [subsumption resolution 265,228] 267. $false <- (2) [subsumption resolution 266,222] 268. ~2 [avatar contradiction clause 267] 271. mary = sK0 | paul = sK0 <- (4) [resolution 223,263] 272. paul = sK0 <- (~3, 4) [subsumption resolution 271,255] 273. $false <- (~1, ~3, 4) [subsumption resolution 272,243] 274. 1 | 3 | ~4 [avatar contradiction clause 273] 275. $false [avatar sat refutation 248,256,264,268,274] % SZS output end Proof for 6551194378824769881675293 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

David is the only person in the room. If "David is a tall quiet person" then "everyone anywhere is tall if they is a tall person, is old or is richer than Marian". If "David is a old person" then "everyone in the room who is not a old quiet person neither is not a tall person nor is a quiet person". If "Maria is quieter than David" then "David is not a old quiet person". David is not a quiet old person. David is not a tall person. David is the least rich in the room. David is older than Karen. David is older than Marian. All tall person is old.

Maria is quieter than David.

neutral

room(david)&(![X]:(room(X)=>(X='david')))& ((tall(david)&quiet(david)&person(david))=>(![X]:(anywhere(X)=>(((((tall(X)&person(X))|(old(X))|(richer(marian,X))))=>(tall(X)))))))& ((old(david)&person(david))=>(![X]:(room(X)=>(((~(old(X)&quiet(X)&person(X)))=>(~((~(tall(X)&person(X)))|(quiet(X)&person(X)))))))))& ((quieter(david,maria))=>(~(old(david)&quiet(david)&person(david))))& (~(quiet(david)&old(david)&person(david)))& (~(tall(david)&person(david)))& (![X]:((room(X)&(X!=david))=>richer(david,X)))& (older(karen,david))& (older(marian,david))& (![X]:(tall(X)=>old(X)))

room(david)&(![X]:(room(X)=>(X='david')))& quieter(david,maria)

Ronnie is the only person in the room. Either "Ronnie does not collect antique jewelry" or "everyone in the room does not practice yoga or is not a culinary enthusiast who experiments with international cuisines" but not both. Everyone outside the room is not an active member of a local robotics club. Everyone in the room does not have a vast collection of first-edition science fiction novels if they enjoys spelunking. Everyone in the room is a dedicated advocate for digital privacy and encryption if they collects antique clocks. Everyone in the room who is a dedicated advocate for digital privacy and encryption enjoys deep-sea diving and exploring underwater caves. Everyone in the room who is not a dedicated volunteer for local community service projects is a culinary enthusiast who experiments with international cuisines. Everyone in the room neither is a dedicated advocate for digital privacy and encryption nor does not enjoy wildlife photography. Everyone in the room does not bake bread at home, owns an extensive assortment of vintage comic book memorabilia or collects first edition books only if they enjoys macrame. Everyone in the room collects first edition books. Everyone in the room enjoys macrame if they is a culinary enthusiast who experiments with international cuisines. If someone does not read mystery novels then he/she collects antique jewelry. Everyone in the room does not enjoy deep-sea diving and exploring underwater caves, has completed a triathlon or collects antique clocks. At least one person anywhere cannot play the piano. Ronnie collects rare minerals, is a dedicated volunteer for local community service projects or does not practice pilates. Everyone anywhere who reads mystery novels bakes bread at home, enjoys macrame or is a certified scuba diver with advanced underwater photography skills. Everyone anywhere is not an active member of a local robotics club if they enjoys spelunking. Ronnie is a culinary enthusiast who experiments with international cuisines. Everyone in the room has completed a triathlon. Everyone in the room does not bake bread at home if they is a dedicated volunteer for local community service projects. Everyone in the room collects rare minerals if they participates in long-distance cycling events across the country.

It is not the case that "it is not the case that "Ronnie collects rare minerals"".

neutral

room(ronnie)&(![X]:(room(X)=>(X='ronnie')))& ((does_not_collect_antique_jewelry(ronnie))<~>(![X]:(room(X)=>(((is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(does_not_practice_yoga(X)))))))& (![X]:(~room(X)=>(is_not_an_active_member_of_a_local_robotics_club(X))))& (![X]:(room(X)=>(((enjoys_spelunking(X))=>(does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))))))& (![X]:(room(X)=>(((collects_antique_clocks(X))=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))& (![X]:(room(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))& (![X]:(room(X)=>(((is_not_a_dedicated_volunteer_for_local_community_service_projects(X))=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))& (![X]:(room(X)=>(~((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(does_not_enjoy_wildlife_photography(X))))))& (![X]:(room(X)=>(((enjoys_macrame(X))<=(((does_not_bake_bread_at_home(X))|(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))|(collects_first_edition_books(X))))))))& (![X]:(room(X)=>(collects_first_edition_books(X))))& (![X]:(room(X)=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))=>(enjoys_macrame(X))))))& ((![X]:((does_not_read_mystery_novels(X))=>(collects_antique_jewelry(X)))))& (![X]:(room(X)=>(((does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))|(has_completed_a_triathlon(X))|(collects_antique_clocks(X))))))& (((?[X]:(anywhere(X)&cannot_play_the_piano(X)))))& (((collects_rare_minerals(ronnie))|(is_a_dedicated_volunteer_for_local_community_service_projects(ronnie))|(does_not_practice_pilates(ronnie))))& (![X]:(anywhere(X)=>(((reads_mystery_novels(X))=>(((bakes_bread_at_home(X))|(enjoys_macrame(X))|(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))))& (![X]:(anywhere(X)=>(((enjoys_spelunking(X))=>(is_not_an_active_member_of_a_local_robotics_club(X))))))& (is_a_culinary_enthusiast_who_experiments_with_international_cuisines(ronnie))& (![X]:(room(X)=>(has_completed_a_triathlon(X))))& (![X]:(room(X)=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))=>(does_not_bake_bread_at_home(X))))))& (![X]:(room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))=>(collects_rare_minerals(X))))))& (![X]:(room(X)=>(plays_video_games(X))))& (![X]:(room(X)=>(((is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))=>(~((is_not_a_coffee_connoisseur(X))|(does_not_have_completed_a_triathlon(X))))))))& (![X]:(room(X)=>(((has_completed_a_triathlon(X))=>(does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))))))& (![X]:(room(X)=>(((does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))

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

Juan, Carlton, Millard, Sara, Mitzi are the only persons in the room. Millard does not enjoy coding in Python. Everyone in the room is an active member of a local robotics club or is not right-handed or both. No one anywhere uses a Windows laptop. Only one person in the room does not collect antique clocks, owns a smart tv and is not a coffee connoisseur. Everyone anywhere does not volunteer for local environmental conservation projects. Everyone in the room does not practice urban gardening or is not a certified yoga instructor teaching classes weekly or both. Sara is not a certified yoga instructor teaching classes weekly and does not enjoy coding in Python. Everyone in the room does not own a smartwatch, does not collect antique clocks and does not collect foreign coins if they does not stream on Twitch. Millard does not stream on Twitch, is not a coffee connoisseur and does not collect antique clocks. Everyone in the room cannot play the flute. Carlton cannot play the flute or does not watche fantasy movies or both. Everyone in the room is not a member of a local theater group specializing in improv or is not a culinary enthusiast who experiments with international cuisines or both if they does not have a pet dog and vice versa. Millard does not stream on Twitch. Everyone in the room neither does not practice urban gardening nor is a certified yoga instructor teaching classes weekly. It is true that “everyone in the room does not volunteer for local environmental conservation projects if they does not practice urban gardening”. Everyone in the room does not enjoy coding in Python. Juan does not stream on Twitch. Millard is not right-handed. Juan is not a certified yoga instructor teaching classes weekly. Everyone in the room does not own a smartwatch. Carlton is a skilled home brewer experimenting with craft beer recipes or volunteers for local environmental conservation projects or both.

Juan collects antique clocks.

contradiction

room(juan)&room(carlton)&room(millard)&room(sara)&room(mitzi)&(![X]:(room(X)=>(X='juan'|X='carlton'|X='millard'|X='sara'|X='mitzi')))& (does_not_enjoy_coding_in_Python(millard))& (![X]:(room(X)=>(((is_an_active_member_of_a_local_robotics_club(X))|(is_not_right-handed(X))))))& (~?[X]:(anywhere(X)=>(uses_a_Windows_laptop(X))))& (((?[X]:(room(X)&((does_not_collect_antique_clocks(X))&(owns_a_smart_tv(X))&(is_not_a_coffee_connoisseur(X)))))&(![X,Y]:((room(X)&room(Y)&(((does_not_collect_antique_clocks(X))&(owns_a_smart_tv(X))&(is_not_a_coffee_connoisseur(X))))&(((does_not_collect_antique_clocks(Y))&(owns_a_smart_tv(Y))&(is_not_a_coffee_connoisseur(Y)))))=>(X=Y)))))& (![X]:(anywhere(X)=>(does_not_volunteer_for_local_environmental_conservation_projects(X))))& (![X]:(room(X)=>(((does_not_practice_urban_gardening(X))|(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& (((is_not_a_certified_yoga_instructor_teaching_classes_weekly(sara))&(does_not_enjoy_coding_in_Python(sara))))& (![X]:(room(X)=>(((does_not_stream_on_Twitch(X))=>(((does_not_own_a_smartwatch(X))&(does_not_collect_antique_clocks(X))&(does_not_collect_foreign_coins(X))))))))& (((does_not_stream_on_Twitch(millard))&(is_not_a_coffee_connoisseur(millard))&(does_not_collect_antique_clocks(millard))))& (![X]:(room(X)=>(cannot_play_the_flute(X))))& (((cannot_play_the_flute(carlton))|(does_not_watche_fantasy_movies(carlton))))& (![X]:(room(X)=>(((((is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))|(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))<=>(does_not_have_a_pet_dog(X))))))& (does_not_stream_on_Twitch(millard))& (![X]:(room(X)=>(~((does_not_practice_urban_gardening(X))|(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& (![X]:(room(X)=>(((does_not_practice_urban_gardening(X))=>(does_not_volunteer_for_local_environmental_conservation_projects(X))))))& (![X]:(room(X)=>(does_not_enjoy_coding_in_Python(X))))& (does_not_stream_on_Twitch(juan))& (is_not_right-handed(millard))& (is_not_a_certified_yoga_instructor_teaching_classes_weekly(juan))& (![X]:(room(X)=>(does_not_own_a_smartwatch(X))))& (((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(carlton))|(volunteers_for_local_environmental_conservation_projects(carlton))))

room(juan)&room(carlton)&room(millard)&room(sara)&room(mitzi)&(![X]:(room(X)=>(X='juan'|X='carlton'|X='millard'|X='sara'|X='mitzi')))& collects_antique_clocks(juan)

% SZS status Unsatisfiable for 40386800679985908401468 % SZS output start Proof for 40386800679985908401468 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 52. ! [X0] : (room(X0) => (~predv(X0) => (~preda(X0) & ~predm(X0) & ~predo(X0)))) [input p8] 61. ~predv(mary) [input p17] 66. predm(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] 75. ! [X0] : (room(X0) => (~predv(X0) => (~predm(X0) & ~predo(X0)))) [pure predicate removal 52] 77. ! [X0] : (room(X0) => (~predv(X0) => ~predm(X0))) [pure predicate removal 75] 160. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 161. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 160] 164. ! [X0] : ((~predm(X0) | predv(X0)) | ~room(X0)) [ennf transformation 77] 165. ! [X0] : (~predm(X0) | predv(X0) | ~room(X0)) [flattening 164] 167. predm(mary) & ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 66] 168. predm(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 167] 254. room(mary) [cnf transformation 161] 265. ~predm(X0) | predv(X0) | ~room(X0) [cnf transformation 165] 273. ~predv(mary) [cnf transformation 61] 280. predm(mary) [cnf transformation 168] 281. predv(mary) | ~room(mary) [resolution 265,280] 282. ~room(mary) [subsumption resolution 281,273] 283. $false [subsumption resolution 282,254] % SZS output end Proof for 40386800679985908401468 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Bernie, Carol, Diana, Harry, Jennifer are the only persons in the room. “No one outside the room does not practice pilates or has a tattoo” only if “Ralph is a sibling of Bernie”. If “someone outside the room is not a craft beer aficionado” then “Ann is older than Bernie” otherwise “everyone in the room is not liked by Ann if they streams on Twitch”. “Bernie is a creative curious old quiet calm person” if “Ann is a client of Diana” and vice versa. “Neither “A car runs solely on saltwater.” nor “Socks do not disappear worldwide every full moon.”” unless ““A bridge does not sing when it is crossed.” and “Socks do not disappear worldwide every full moon.””. If “everyone in the room is not an active member of a local robotics club or does not play the drums” then “everyone in the room who is not an active member of a local robotics club is a creative european”. If “Diana has a piercing” then “neither “Socks do not disappear worldwide every full moon.” nor “Glass rain does not fall on a distant planet.””. “Ann is richer than Bernie” only if “no strong person is tall”. Either “everyone in the room is a wise european” or “Harry and Carol are not a patient europeans” but not both. If “someone in the room is not happy, not kind, not calm” then “Harry is a client of Ralph”. If ““A car runs solely on saltwater.” or “A car does not run solely on saltwater.” or both” then “Bernie is a dedicated volunteer for local community service projects”. Bernie is a dedicated volunteer for local community service projects. Jennifer has a piercing. Someone in the room is a sibling of Ralph. Harry practices pilates. Harry and Ralph like each other. Glass rain falls on a distant planet. All kind persons are old. Someone in the room is an avid collector of autographed memorabilia from famous musicians, is curious or is a client of Ralph. More than one person in the room is not brave, not old, not happy. Someone who is a client of Ann hate someone who is a tall wise european. All creative persons are calm.

Harry practices pilates.

entailment

room(bernie)&room(carol)&room(diana)&room(harry)&room(jennifer)&(![X]:(room(X)=>(X='bernie'|X='carol'|X='diana'|X='harry'|X='jennifer')))& ((~?[X]:(~room(X)=>(((has_a_tattoo(X))|(does_not_practice_pilates(X))))))=>(sibling(bernie,ralph)))& (((?[X]:(~room(X)&(is_not_a_craft_beer_aficionado(X))))=>(older(bernie,ann)))&((~(?[X]:(~room(X)&(is_not_a_craft_beer_aficionado(X)))))=>(![X]:(room(X)=>(((streams_on_Twitch(X))=>(~like(X,ann))))))))& ((client(diana,ann))<=>(creative(bernie)&curious(bernie)&old(bernie)&quiet(bernie)&calm(bernie)&person(bernie)))& (~(((A_bridge_does_not_sing_when_it_is_crossed.)&(Socks_do_not_disappear_worldwide_every_full_moon.)))=>(~((A_car_runs_solely_on_saltwater.)|(Socks_do_not_disappear_worldwide_every_full_moon.))))& ((![X]:(room(X)=>(((does_not_play_the_drums(X))|(is_not_an_active_member_of_a_local_robotics_club(X))))))=>(![X]:(room(X)=>(((is_not_an_active_member_of_a_local_robotics_club(X))=>(creative(X)&european(X)))))))& ((has_a_piercing(diana))=>(~((Socks_do_not_disappear_worldwide_every_full_moon.)|(Glass_rain_does_not_fall_on_a_distant_planet.))))& ((richer(bernie,ann))=>(~?[X]:(strong(X)=>tall(X))))& ((![X]:(room(X)=>(wise(X)&european(X))))<~>(~(patient(harry)&european(harry))&~(patient(carol)&european(carol))))& ((?[X]:(room(X)&(~happy(X)&~kind(X)&~calm(X))))=>(client(ralph,harry)))& ((((A_car_runs_solely_on_saltwater.)|(A_car_does_not_run_solely_on_saltwater.)))=>(is_a_dedicated_volunteer_for_local_community_service_projects(bernie)))& (is_a_dedicated_volunteer_for_local_community_service_projects(bernie))& (has_a_piercing(jennifer))& (?[X]:(room(X)&(sibling(ralph,X))))& (practices_pilates(harry))& ((like(harry,ralph) & like(ralph,harry)))& (Glass_rain_falls_on_a_distant_planet.)& (![X]:(kind(X)=>old(X)))& (?[X]:(room(X)&(((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))|(curious(X))|(client(ralph,X))))))& ((?[X,Y]:(room(X)&room(Y)&(~brave(X)&~old(X)&~happy(X)&~brave(Y)&~old(Y)&~happy(Y))&(X!=Y))))& (?[X,Y]:((client(ann,X))&(tall(Y)&wise(Y)&european(Y))&(hate(X,Y))))& (![X]:(creative(X)=>calm(X)))

room(bernie)&room(carol)&room(diana)&room(harry)&room(jennifer)&(![X]:(room(X)=>(X='bernie'|X='carol'|X='diana'|X='harry'|X='jennifer')))& practices_pilates(harry)

% SZS status Unsatisfiable for 773615718966505433590682 % SZS output start Proof for 773615718966505433590682 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 58. predg(alice) [input p14] 66. ~(predg(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] 156. ! [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] 157. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 156] 165. ~predg(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 66] 166. ~predg(alice) | ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 165] 186. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK8 & alice != sK8 & fred != sK8 & paul != sK8 & mary != sK8 & room(sK8)) [choice axiom] 187. ~predg(alice) | (john != sK8 & alice != sK8 & fred != sK8 & paul != sK8 & mary != sK8 & room(sK8)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 166,186] 271. room(mary) [cnf transformation 157] 272. room(paul) [cnf transformation 157] 273. room(fred) [cnf transformation 157] 274. room(alice) [cnf transformation 157] 275. room(john) [cnf transformation 157] 276. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 157] 301. predg(alice) [cnf transformation 58] 319. ~predg(alice) | room(sK8) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 187] 320. ~predg(alice) | mary != sK8 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 187] 321. ~predg(alice) | paul != sK8 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 187] 322. ~predg(alice) | fred != sK8 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 187] 323. ~predg(alice) | alice != sK8 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 187] 324. ~predg(alice) | john != sK8 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 187] 433. john != sK8 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 324,301] 434. john != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 433,275] 435. john != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 434,274] 436. john != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 435,273] 437. john != sK8 | ~room(mary) [subsumption resolution 436,272] 438. john != sK8 [subsumption resolution 437,271] 439. alice != sK8 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 323,301] 440. alice != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 439,275] 441. alice != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 440,274] 442. alice != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 441,273] 443. alice != sK8 | ~room(mary) [subsumption resolution 442,272] 444. alice != sK8 [subsumption resolution 443,271] 445. fred != sK8 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 322,301] 446. fred != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 445,275] 447. fred != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 446,274] 448. fred != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 447,273] 449. fred != sK8 | ~room(mary) [subsumption resolution 448,272] 450. fred != sK8 [subsumption resolution 449,271] 451. paul != sK8 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 321,301] 452. paul != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 451,275] 453. paul != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 452,274] 454. paul != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 453,273] 455. paul != sK8 | ~room(mary) [subsumption resolution 454,272] 456. paul != sK8 [subsumption resolution 455,271] 457. mary != sK8 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 320,301] 458. mary != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 457,275] 459. mary != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 458,274] 460. mary != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 459,273] 461. mary != sK8 | ~room(mary) [subsumption resolution 460,272] 462. mary != sK8 [subsumption resolution 461,271] 463. room(sK8) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 319,301] 464. room(sK8) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 463,275] 465. room(sK8) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 464,274] 466. room(sK8) | ~room(paul) | ~room(mary) [subsumption resolution 465,273] 467. room(sK8) | ~room(mary) [subsumption resolution 466,272] 468. room(sK8) [subsumption resolution 467,271] 700. alice = sK8 | fred = sK8 | paul = sK8 | mary = sK8 | john = sK8 [resolution 276,468] 791. fred = sK8 | paul = sK8 | mary = sK8 | john = sK8 [subsumption resolution 700,444] 792. paul = sK8 | mary = sK8 | john = sK8 [subsumption resolution 791,450] 793. mary = sK8 | john = sK8 [subsumption resolution 792,456] 794. john = sK8 [subsumption resolution 793,462] 795. $false [subsumption resolution 794,438] % SZS output end Proof for 773615718966505433590682 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5500 % Time elapsed: 0.038 s % ------------------------------ % ------------------------------

Ronnie, Micheal, Luis, Patricia are the only persons in the room. "Ronnie enjoys origami, does not practice archery or hosts regular workshops on creative writing" only if "it is not the case that "Patricia enjoys origami"". If "at least one person in the room enjoys origami" then "everyone in the room is a drone photographer if they does not practice tai chi" otherwise "Patricia does not practice tai chi". If "someone in the room practices archery" then "everyone in the room practices tai chi if they creates augmented reality experiences for mobile applications". "Ronnie has lived in exactly three countries" only if "everyone in the room who does not compete in national level swimming championships is not a drone photographer". "Ronnie collects rare minerals" if "Patricia is an avid mountain climber who has scaled several peaks" and vice versa. "Everyone in the room collects classic novels if they competes in national level swimming championships" unless "everyone in the room creates augmented reality experiences for mobile applications or does not compete in national level swimming championships". Everyone anywhere who creates augmented reality experiences for mobile applications practices archery. Patricia does not practice tai chi. Everyone in the room owns an extensive assortment of vintage comic book memorabilia if and only if they collects classic novels. Ronnie hosts regular workshops on creative writing. Someone in the room practices archery.

Patricia creates augmented reality experiences for mobile applications.

contradiction

room(ronnie)&room(micheal)&room(luis)&room(patricia)&(![X]:(room(X)=>(X='ronnie'|X='micheal'|X='luis'|X='patricia')))& ((((enjoys_origami(ronnie))|(does_not_practice_archery(ronnie))|(hosts_regular_workshops_on_creative_writing(ronnie))))=>(~(enjoys_origami(patricia))))& (((((?[X]:(room(X)&enjoys_origami(X)))))=>(![X]:(room(X)=>(((does_not_practice_tai_chi(X))=>(is_a_drone_photographer(X)))))))&((~(((?[X]:(room(X)&enjoys_origami(X))))))=>(does_not_practice_tai_chi(patricia))))& ((?[X]:(room(X)&(practices_archery(X))))=>(![X]:(room(X)=>(((creates_augmented_reality_experiences_for_mobile_applications(X))=>(practices_tai_chi(X)))))))& ((has_lived_in_exactly_three_countries(ronnie))=>(![X]:(room(X)=>(((does_not_compete_in_national_level_swimming_championships(X))=>(is_not_a_drone_photographer(X)))))))& ((is_an_avid_mountain_climber_who_has_scaled_several_peaks(patricia))<=>(collects_rare_minerals(ronnie)))& (~(![X]:(room(X)=>(((does_not_compete_in_national_level_swimming_championships(X))|(creates_augmented_reality_experiences_for_mobile_applications(X))))))=>(![X]:(room(X)=>(((competes_in_national_level_swimming_championships(X))=>(collects_classic_novels(X)))))))& (![X]:(anywhere(X)=>(((creates_augmented_reality_experiences_for_mobile_applications(X))=>(practices_archery(X))))))& (does_not_practice_tai_chi(patricia))& (![X]:(room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))<=>(collects_classic_novels(X))))))& (hosts_regular_workshops_on_creative_writing(ronnie))& (creates_augmented_reality_experiences_for_mobile_applications(ronnie))& (works_on_fridays(micheal))& ((![X]:((does_not_host_regular_workshops_on_creative_writing(X))=>(does_not_collect_rare_minerals(X)))))& (?[X]:(room(X)&(practices_archery(X))))& (((?[X]:(~room(X)&does_not_host_regular_workshops_on_creative_writing(X)))))& (![X]:(room(X)=>(((is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))|(reads_mystery_novels(X))))))& (does_not_have_completed_a_triathlon(luis))& (![X]:(room(X)=>(((is_not_a_drone_photographer(X))=>(((creates_augmented_reality_experiences_for_mobile_applications(X))&(drives_a_hybrid_car(X))&(does_enjoy_trail_running(X))))))))& (![X]:(room(X)=>(((((creates_augmented_reality_experiences_for_mobile_applications(X))&(drives_a_hybrid_car(X))&(does_enjoy_trail_running(X))))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))& (![X]:(room(X)=>(((practices_archery(X))<=>(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))& (![X]:(~room(X)=>(((creates_augmented_reality_experiences_for_mobile_applications(X))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))& (reads_mystery_novels(patricia))& (![X]:(room(X)=>(((does_not_compete_in_national_level_swimming_championships(X))=>(drives_a_hybrid_car(X))))))

room(ronnie)&room(micheal)&room(luis)&room(patricia)&(![X]:(room(X)=>(X='ronnie'|X='micheal'|X='luis'|X='patricia')))& creates_augmented_reality_experiences_for_mobile_applications(patricia)

% SZS status Unsatisfiable for 572194347874064095343229 % SZS output start Proof for 572194347874064095343229 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 47. ? [X0] : (preds(X0) & room(X0)) => ! [X0] : (room(X0) => (predb(X0) => predj(X0))) [input p3] 52. ~predj(alice) [input p8] 58. ? [X0] : (preds(X0) & room(X0)) [input p14] 68. predb(alice) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 70. ? [X0] : (preds(X0) & room(X0)) => ! [X1] : (room(X1) => (predb(X1) => predj(X1))) [rectify 47] 156. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 157. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 156] 160. ! [X1] : ((predj(X1) | ~predb(X1)) | ~room(X1)) | ! [X0] : (~preds(X0) | ~room(X0)) [ennf transformation 70] 161. ! [X1] : (predj(X1) | ~predb(X1) | ~room(X1)) | ! [X0] : (~preds(X0) | ~room(X0)) [flattening 160] 167. predb(alice) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 68] 168. predb(alice) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 167] 172. ! [X0] : (predj(X0) | ~predb(X0) | ~room(X0)) | ! [X1] : (~preds(X1) | ~room(X1)) [rectify 161] 175. ? [X0] : (preds(X0) & room(X0)) => (preds(sK1) & room(sK1)) [choice axiom] 176. preds(sK1) & room(sK1) [skolemisation 58,175] 264. room(alice) [cnf transformation 157] 271. predj(X0) | ~predb(X0) | ~room(X0) | ~preds(X1) | ~room(X1) [cnf transformation 172] 275. ~predj(alice) [cnf transformation 52] 281. room(sK1) [cnf transformation 176] 282. preds(sK1) [cnf transformation 176] 292. predb(alice) [cnf transformation 168] 317. 6 <=> predj(alice) [avatar definition] 319. ~predj(alice) <- (~6) [avatar component clause 317] 327. 8 <=> ! [X1] : (~preds(X1) | ~room(X1)) [avatar definition] 328. ~preds(X1) | ~room(X1) <- (8) [avatar component clause 327] 330. 9 <=> ! [X0] : (predj(X0) | ~room(X0) | ~predb(X0)) [avatar definition] 331. ~predb(X0) | ~room(X0) | predj(X0) <- (9) [avatar component clause 330] 332. 8 | 9 [avatar split clause 271,330,327] 344. ~6 [avatar split clause 275,317] 346. ~room(sK1) <- (8) [resolution 328,282] 347. $false <- (8) [subsumption resolution 346,281] 348. ~8 [avatar contradiction clause 347] 361. ~room(alice) | predj(alice) <- (9) [resolution 331,292] 363. predj(alice) <- (9) [subsumption resolution 361,264] 364. $false <- (~6, 9) [subsumption resolution 363,319] 365. 6 | ~9 [avatar contradiction clause 364] 366. $false [avatar sat refutation 332,344,348,365] % SZS output end Proof for 572194347874064095343229 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Jane, Jean are the only persons in the room. If someone is a quiet person then he/she is quieter than Gwendolyn. Renae is older than Jane. Everyone in the room who either is a curious funny happy person or is a curious quiet person but not both is not wise. If someone is quieter than Renae then he/she is not a strong person and vice versa. Everyone in the room either is not quiet or is quieter than Renae but not both if they is a brave person. Everyone in the room is richer than Gwendolyn if they is a calm person. Jane is quieter than Renae. Someone in the room is a old generous creative person. Someone in the room is older than Renae.

Jean is old.

entailment

room(jane)&room(jean)&(![X]:(room(X)=>(X='jane'|X='jean')))& ((![X]:((quiet(X)&person(X))=>(quieter(gwendolyn,X)))))& (older(jane,renae))& (![X]:(room(X)=>(((((curious(X)&funny(X)&happy(X)&person(X))<~>(curious(X)&quiet(X)&person(X))))=>(~wise(X))))))& ((![X]:((quieter(renae,X))<=>(~(strong(X)&person(X))))))& (![X]:(room(X)=>(((brave(X)&person(X))=>(((~quiet(X))<~>(quieter(renae,X))))))))& (![X]:(room(X)=>(((calm(X)&person(X))=>(richer(gwendolyn,X))))))& (quieter(renae,jane))& (?[X]:(room(X)&(old(X)&generous(X)&creative(X)&person(X))))& (tall(jean)&person(jean))& (![X]:(~room(X)=>(((((~kind(X))<~>(quieter(gwendolyn,X))))=>(quieter(renae,X))))))& (![X]:((room(X)&(X!=jean))=>richer(X,jean)))& (![X]:(room(X)=>(older(gwendolyn,X))))& (((~quiet(jean))<~>(quieter(renae,jean))))& (~?[X]:(patient(X)=>funny(X)))& (?[X]:(room(X)&(older(renae,X))))& (older(gwendolyn,jane))& ((![X]:((~brave(X))<=>(quieter(renae,X)))))& (quieter(gwendolyn,jane))& (![X]:(room(X)=>(~(quiet(X)&happy(X)&brave(X)&calm(X)&curious(X)&person(X)))))& (~(brave(jane)&person(jane)))

room(jane)&room(jean)&(![X]:(room(X)=>(X='jane'|X='jean')))& old(jean)

% SZS status Unsatisfiable for 826715889410041577471603 % SZS output start Proof for 826715889410041577471603 20. ! [X0,X1] : (X0 != X1 => (older(X0,X1) => ~older(X1,X0))) [input b19] 21. ! [X0,X1] : (X0 != X1 => ((old(X0) & older(X0,X1)) => old(X1))) [input b20] 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 46. older(mary,alice) [input p2] 52. ? [X0] : (person(X0) & creative(X0) & generous(X0) & old(X0) & room(X0)) [input p8] 59. ? [X0] : (older(alice,X0) & room(X0)) [input p15] 65. ~(old(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 69. ? [X0] : (person(X0) & generous(X0) & old(X0) & room(X0)) [pure predicate removal 52] 70. ? [X0] : (person(X0) & old(X0) & room(X0)) [pure predicate removal 69] 105. ! [X0,X1] : ((~older(X1,X0) | ~older(X0,X1)) | X0 = X1) [ennf transformation 20] 106. ! [X0,X1] : (~older(X1,X0) | ~older(X0,X1) | X0 = X1) [flattening 105] 107. ! [X0,X1] : ((old(X1) | (~old(X0) | ~older(X0,X1))) | X0 = X1) [ennf transformation 21] 108. ! [X0,X1] : (old(X1) | ~old(X0) | ~older(X0,X1) | X0 = X1) [flattening 107] 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] 161. ~old(paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 65] 162. ~old(paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 161] 167. ? [X0] : (person(X0) & old(X0) & room(X0)) => (person(sK0) & old(sK0) & room(sK0)) [choice axiom] 168. person(sK0) & old(sK0) & room(sK0) [skolemisation 70,167] 171. ? [X0] : (older(alice,X0) & room(X0)) => (older(alice,sK1) & room(sK1)) [choice axiom] 172. older(alice,sK1) & room(sK1) [skolemisation 59,171] 173. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 174. ~old(paul) | (paul != sK2 & mary != sK2 & room(sK2)) | ~room(paul) | ~room(mary) [skolemisation 162,173] 190. ~older(X1,X0) | ~older(X0,X1) | X0 = X1 [cnf transformation 106] 191. ~older(X0,X1) | ~old(X0) | old(X1) | X0 = X1 [cnf transformation 108] 231. mary != alice [cnf transformation 43] 232. paul != alice [cnf transformation 43] 255. room(mary) [cnf transformation 148] 256. room(paul) [cnf transformation 148] 257. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 148] 259. older(mary,alice) [cnf transformation 46] 266. room(sK0) [cnf transformation 168] 267. old(sK0) [cnf transformation 168] 276. room(sK1) [cnf transformation 172] 277. older(alice,sK1) [cnf transformation 172] 282. ~old(paul) | room(sK2) | ~room(paul) | ~room(mary) [cnf transformation 174] 283. ~old(paul) | mary != sK2 | ~room(paul) | ~room(mary) [cnf transformation 174] 284. ~old(paul) | paul != sK2 | ~room(paul) | ~room(mary) [cnf transformation 174] 305. ~old(paul) | paul != sK2 | ~room(mary) [subsumption resolution 284,256] 306. ~old(paul) | paul != sK2 [subsumption resolution 305,255] 308. 5 <=> paul = sK2 [avatar definition] 310. paul != sK2 <- (~5) [avatar component clause 308] 312. 6 <=> old(paul) [avatar definition] 314. ~old(paul) <- (~6) [avatar component clause 312] 315. ~5 | ~6 [avatar split clause 306,312,308] 316. ~old(paul) | mary != sK2 | ~room(mary) [subsumption resolution 283,256] 317. ~old(paul) | mary != sK2 [subsumption resolution 316,255] 319. 7 <=> mary = sK2 [avatar definition] 322. ~7 | ~6 [avatar split clause 317,312,319] 323. ~old(paul) | room(sK2) | ~room(mary) [subsumption resolution 282,256] 324. ~old(paul) | room(sK2) [subsumption resolution 323,255] 326. 8 <=> room(sK2) [avatar definition] 328. room(sK2) <- (8) [avatar component clause 326] 329. 8 | ~6 [avatar split clause 324,312,326] 344. mary = sK0 | paul = sK0 [resolution 257,266] 345. mary = sK1 | paul = sK1 [resolution 257,276] 347. 10 <=> paul = sK0 [avatar definition] 349. paul = sK0 <- (10) [avatar component clause 347] 351. 11 <=> mary = sK0 [avatar definition] 353. mary = sK0 <- (11) [avatar component clause 351] 354. 10 | 11 [avatar split clause 344,351,347] 356. 12 <=> paul = sK1 [avatar definition] 358. paul = sK1 <- (12) [avatar component clause 356] 360. 13 <=> mary = sK1 [avatar definition] 362. mary = sK1 <- (13) [avatar component clause 360] 363. 12 | 13 [avatar split clause 345,360,356] 365. older(alice,paul) <- (12) [backward demodulation 277,358] 367. old(paul) <- (10) [backward demodulation 267,349] 371. 6 | ~10 [avatar split clause 367,347,312] 372. mary = sK2 | paul = sK2 <- (8) [resolution 328,257] 376. mary = sK2 <- (~5, 8) [subsumption resolution 372,310] 377. 7 | 5 | ~8 [avatar split clause 376,326,308,319] 379. old(mary) <- (11) [backward demodulation 267,353] 410. ~older(alice,mary) | mary = alice [resolution 190,259] 414. ~older(alice,mary) [subsumption resolution 410,231] 514. ~old(mary) | old(alice) | mary = alice [resolution 191,259] 517. ~old(alice) | old(paul) | paul = alice <- (12) [resolution 191,365] 518. old(alice) | mary = alice <- (11) [subsumption resolution 514,379] 519. old(alice) <- (11) [subsumption resolution 518,231] 528. old(paul) | paul = alice <- (11, 12) [subsumption resolution 517,519] 529. paul = alice <- (~6, 11, 12) [subsumption resolution 528,314] 530. $false <- (~6, 11, 12) [subsumption resolution 529,232] 531. 6 | ~11 | ~12 [avatar contradiction clause 530] 533. older(alice,mary) <- (13) [backward demodulation 277,362] 534. $false <- (13) [subsumption resolution 533,414] 535. ~13 [avatar contradiction clause 534] 537. $false [avatar sat refutation 315,322,329,354,363,371,377,531,535] % SZS output end Proof for 826715889410041577471603 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Latasha is the only person in the room. Everyone in the room who volunteers for local environmental conservation projects enjoys deep-sea diving and exploring underwater caves. Someone in the room is not strong. Everyone anywhere who is a strong person volunteers for local environmental conservation projects. Everyone in the room does not read mystery novels or does not enjoy deep-sea diving and exploring underwater caves. Everyone outside the room does not read mystery novels if they does not volunteer for local environmental conservation projects. It is true that 'if someone does not enjoy deep-sea diving and exploring underwater caves then he/she volunteers for local environmental conservation projects'. Everyone in the room who enjoys deep-sea diving and exploring underwater caves either reads mystery novels or is not strong but not both. Everyone in the room who enjoys deep-sea diving and exploring underwater caves either is strong or does not read mystery novels but not both. If someone enjoys deep-sea diving and exploring underwater caves then he/she does not volunteer for local environmental conservation projects. Everyone in the room who is strong enjoys deep-sea diving and exploring underwater caves or volunteers for local environmental conservation projects or both.

Latasha reads mystery novels.

contradiction

room(latasha)&(![X]:(room(X)=>(X='latasha')))& (![X]:(room(X)=>(((volunteers_for_local_environmental_conservation_projects(X))=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))& (?[X]:(room(X)&(~strong(X))))& (![X]:(anywhere(X)=>(((strong(X)&person(X))=>(volunteers_for_local_environmental_conservation_projects(X))))))& (![X]:(room(X)=>(((does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))|(does_not_read_mystery_novels(X))))))& (![X]:(~room(X)=>(((does_not_volunteer_for_local_environmental_conservation_projects(X))=>(does_not_read_mystery_novels(X))))))& ((![X]:((does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))=>(volunteers_for_local_environmental_conservation_projects(X)))))& (![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))=>(((reads_mystery_novels(X))<~>(~strong(X))))))))& (![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))=>(((strong(X))<~>(does_not_read_mystery_novels(X))))))))& ((![X]:((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))=>(does_not_volunteer_for_local_environmental_conservation_projects(X)))))& (![X]:(room(X)=>(((strong(X))=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))|(volunteers_for_local_environmental_conservation_projects(X))))))))

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

% SZS status Unsatisfiable for 627337369445922968752180 % SZS output start Proof for 627337369445922968752180 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 45. ! [X0] : (room(X0) => (predo(X0) => predn(X0))) [input p1] 48. ! [X0] : (room(X0) => (~predp(X0) | ~predn(X0))) [input p4] 50. ! [X0] : (~predn(X0) => predo(X0)) [input p6] 55. predp(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 129. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 130. ! [X0] : ((predn(X0) | ~predo(X0)) | ~room(X0)) [ennf transformation 45] 131. ! [X0] : (predn(X0) | ~predo(X0) | ~room(X0)) [flattening 130] 132. ! [X0] : ((~predp(X0) | ~predn(X0)) | ~room(X0)) [ennf transformation 48] 133. ! [X0] : (~predp(X0) | ~predn(X0) | ~room(X0)) [flattening 132] 136. ! [X0] : (predo(X0) | predn(X0)) [ennf transformation 50] 144. predp(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 55] 230. room(mary) [cnf transformation 129] 232. ~predo(X0) | predn(X0) | ~room(X0) [cnf transformation 131] 235. ~predp(X0) | ~predn(X0) | ~room(X0) [cnf transformation 133] 237. predn(X0) | predo(X0) [cnf transformation 136] 246. predp(mary) [cnf transformation 144] 253. ~predn(mary) | ~room(mary) [resolution 235,246] 254. ~predn(mary) [subsumption resolution 253,230] 256. predo(mary) [resolution 254,237] 257. predn(mary) | ~room(mary) [resolution 256,232] 258. ~room(mary) [subsumption resolution 257,254] 259. $false [subsumption resolution 258,230] % SZS output end Proof for 627337369445922968752180 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Maria, Ivory, Kathryn, Charles are the only persons in the room. 'Everyone in the room practices archery or does not write and illustrates their own graphic novels' only if 'everyone in the room neither practices archery nor is a sibling of Lenore if they writes and illustrates their own graphic novels'. 'Only one person in the room writes and illustrates their own graphic novels' unless 'everyone in the room is not a certified yoga instructor teaching classes weekly or is quieter than Lenore'. If 'everyone in the room is a quiet calm person or does not write and illustrates their own graphic novels' then 'all quiet persons are calm'. If 'everyone in the room neither is calm nor is quieter than Lenore' then 'Maria practices archery'. 'Everyone in the room practices archery if they writes and illustrates their own graphic novels' unless 'Lenore is a sibling of Maria'. Maria is quieter than Lenore. If someone practices archery then he/she is quiet. Everyone in the room is a certified yoga instructor teaching classes weekly if they either writes and illustrates their own graphic novels or is quieter than Lenore but not both. Everyone in the room who is a certified yoga instructor teaching classes weekly does not practice archery. Everyone outside the room is quiet or does not write and illustrates their own graphic novels. Maria is a sibling of Richard. Maria is a certified yoga instructor teaching classes weekly. Not everyone in the room is a certified yoga instructor teaching classes weekly if and only if they is a sibling of Lenore. Maria is quieter than Richard. Maria who makes intricate hand-cut paper art for exhibitions writes and illustrates their own graphic novels. All quiet persons are calm. Maria makes intricate hand-cut paper art for exhibitions.

Everyone in the room is not quiet.

neutral

room(maria)&room(ivory)&room(kathryn)&room(charles)&(![X]:(room(X)=>(X='maria'|X='ivory'|X='kathryn'|X='charles')))& ((![X]:(room(X)=>(((does_not_write_and_illustrates_their_own_graphic_novels(X))|(practices_archery(X))))))=>(![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))=>(~((practices_archery(X))|(sibling(lenore,X)))))))))& (~(![X]:(room(X)=>(((quieter(lenore,X))|(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))))))=>(((?[X]:(room(X)&writes_and_illustrates_their_own_graphic_novels(X)))&(![X,Y]:((room(X)&room(Y)&(writes_and_illustrates_their_own_graphic_novels(X))&(writes_and_illustrates_their_own_graphic_novels(Y)))=>(X=Y))))))& ((![X]:(room(X)=>(((does_not_write_and_illustrates_their_own_graphic_novels(X))|(quiet(X)&calm(X)&person(X))))))=>(![X]:(quiet(X)=>calm(X))))& ((![X]:(room(X)=>(~((calm(X))|(quieter(lenore,X))))))=>(practices_archery(maria)))& (~(sibling(maria,lenore))=>(![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))=>(practices_archery(X)))))))& (quieter(lenore,maria))& ((![X]:((practices_archery(X))=>(quiet(X)))))& (![X]:(room(X)=>(((((writes_and_illustrates_their_own_graphic_novels(X))<~>(quieter(lenore,X))))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& (![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(does_not_practice_archery(X))))))& (![X]:(~room(X)=>(((does_not_write_and_illustrates_their_own_graphic_novels(X))|(quiet(X))))))& (sibling(richard,maria))& (is_a_certified_yoga_instructor_teaching_classes_weekly(maria))& (~![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))<=>(sibling(lenore,X))))))& (quieter(richard,maria))& ((makes_intricate_hand-cut_paper_art_for_exhibitions(maria))&(writes_and_illustrates_their_own_graphic_novels(maria)))& (![X]:(quiet(X)=>calm(X)))& (makes_intricate_hand-cut_paper_art_for_exhibitions(maria))

room(maria)&room(ivory)&room(kathryn)&room(charles)&(![X]:(room(X)=>(X='maria'|X='ivory'|X='kathryn'|X='charles')))& ![X]:(room(X)=>(~quiet(X)))

Bonnie, Lisa are the only persons in the room. If “at least one person outside the room does not host regular workshops on creative writing and does not enjoy bird watching” then “everyone in the room does not enjoy fishing, does not play the drums or is not allergic to anything”. If “everyone in the room does not enjoy fishing, does not play the drums or is not allergic to anything” then “everyone in the room does not enjoy fishing”. Everyone in the room does not own a microscope. Everyone outside the room does not enjoy snowboarding, is not a professional photographer specializing in portrait photography or does not enjoy bird watching. Everyone in the room does not collect modern art. More than one person in the room does not enjoy stargazing. Everyone in the room does not enjoy snowboarding, does not collect modern art or does not host a YouTube channel dedicated to art tutorials.

Bonnie collects modern art and enjoys kayaking.

contradiction

room(bonnie)&room(lisa)&(![X]:(room(X)=>(X='bonnie'|X='lisa')))& (((((?[X]:(~room(X)&((does_not_host_regular_workshops_on_creative_writing(X))&(does_not_enjoy_bird_watching(X)))))))=>(![X]:(room(X)=>(((does_not_enjoy_fishing(X))|(does_not_play_the_drums(X))|(is_not_allergic_to_anything(X)))))))& ((![X]:(room(X)=>(((does_not_enjoy_fishing(X))|(does_not_play_the_drums(X))|(is_not_allergic_to_anything(X))))))=>(![X]:(room(X)=>(does_not_enjoy_fishing(X))))))& (![X]:(room(X)=>(does_not_own_a_microscope(X))))& (![X]:(~room(X)=>(((does_not_enjoy_snowboarding(X))|(is_not_a_professional_photographer_specializing_in_portrait_photography(X))|(does_not_enjoy_bird_watching(X))))))& (![X]:(room(X)=>(does_not_collect_modern_art(X))))& ((?[X,Y]:(room(X)&room(Y)&(does_not_enjoy_stargazing(X)&does_not_enjoy_stargazing(Y))&(X!=Y))))& (![X]:(room(X)=>(((does_not_enjoy_snowboarding(X))|(does_not_collect_modern_art(X))|(does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))))))& (![X]:(room(X)=>(does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))))& (![X]:(room(X)=>(does_not_enjoy_kayaking(X))))

room(bonnie)&room(lisa)&(![X]:(room(X)=>(X='bonnie'|X='lisa')))& ((collects_modern_art(bonnie))&(enjoys_kayaking(bonnie)))

% SZS status Unsatisfiable for 309611701811290452388518 % SZS output start Proof for 309611701811290452388518 44. ! [X0] : (room(X0) => ~predb(X0)) & ! [X0] : (room(X0) => ~prede(X0)) & ! [X0] : (room(X0) => (~prede(X0) | ~predh(X0) | ~predw(X0))) & ? [X0,X1] : (X0 != X1 & ~predz(X1) & ~predz(X0) & room(X1) & room(X0)) & ! [X0] : (room(X0) => ~predh(X0)) & ! [X0] : (~room(X0) => (~predp(X0) | ~predi(X0) | ~predw(X0))) & ! [X0] : (room(X0) => ~predk(X0)) & (! [X0] : (room(X0) => (~predm(X0) | ~predr(X0) | ~predq(X0))) => ! [X0] : (room(X0) => ~predq(X0))) & (? [X0] : (~predp(X0) & ~predo(X0) & ~room(X0)) => ! [X0] : (room(X0) => (~predm(X0) | ~predr(X0) | ~predq(X0)))) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. predb(mary) & predh(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 46. ! [X0] : (room(X0) => ~predb(X0)) & ! [X1] : (room(X1) => ~prede(X1)) & ! [X2] : (room(X2) => (~prede(X2) | ~predh(X2) | ~predw(X2))) & ? [X3,X4] : (X3 != X4 & ~predz(X4) & ~predz(X3) & room(X4) & room(X3)) & ! [X5] : (room(X5) => ~predh(X5)) & ! [X6] : (~room(X6) => (~predp(X6) | ~predi(X6) | ~predw(X6))) & ! [X7] : (room(X7) => ~predk(X7)) & (! [X8] : (room(X8) => (~predm(X8) | ~predr(X8) | ~predq(X8))) => ! [X9] : (room(X9) => ~predq(X9))) & (? [X10] : (~predp(X10) & ~predo(X10) & ~room(X10)) => ! [X11] : (room(X11) => (~predm(X11) | ~predr(X11) | ~predq(X11)))) & ! [X12] : (room(X12) => (paul = X12 | mary = X12)) & room(paul) & room(mary) [rectify 44] 47. ! [X0] : (room(X0) => ~predb(X0)) & ? [X3,X4] : (X3 != X4 & ~predz(X4) & ~predz(X3) & room(X4) & room(X3)) & ! [X5] : (room(X5) => ~predh(X5)) & ! [X6] : (~room(X6) => (~predp(X6) | ~predi(X6) | ~predw(X6))) & ! [X7] : (room(X7) => ~predk(X7)) & (! [X8] : (room(X8) => (~predm(X8) | ~predr(X8) | ~predq(X8))) => ! [X9] : (room(X9) => ~predq(X9))) & (? [X10] : (~predp(X10) & ~predo(X10) & ~room(X10)) => ! [X11] : (room(X11) => (~predm(X11) | ~predr(X11) | ~predq(X11)))) & ! [X12] : (room(X12) => (paul = X12 | mary = X12)) & room(paul) & room(mary) [pure predicate removal 46] 48. ! [X0] : (room(X0) => ~predb(X0)) & ? [X3,X4] : (X3 != X4 & room(X4) & room(X3)) & ! [X5] : (room(X5) => ~predh(X5)) & ! [X6] : (~room(X6) => (~predp(X6) | ~predi(X6) | ~predw(X6))) & ! [X7] : (room(X7) => ~predk(X7)) & (! [X8] : (room(X8) => (~predm(X8) | ~predr(X8) | ~predq(X8))) => ! [X9] : (room(X9) => ~predq(X9))) & (? [X10] : (~predp(X10) & ~predo(X10) & ~room(X10)) => ! [X11] : (room(X11) => (~predm(X11) | ~predr(X11) | ~predq(X11)))) & ! [X12] : (room(X12) => (paul = X12 | mary = X12)) & room(paul) & room(mary) [pure predicate removal 47] 49. ! [X0] : (room(X0) => ~predb(X0)) & ? [X3,X4] : (X3 != X4 & room(X4) & room(X3)) & ! [X5] : (room(X5) => ~predh(X5)) & ! [X7] : (room(X7) => ~predk(X7)) & (! [X8] : (room(X8) => (~predm(X8) | ~predr(X8) | ~predq(X8))) => ! [X9] : (room(X9) => ~predq(X9))) & (? [X10] : (~predp(X10) & ~predo(X10) & ~room(X10)) => ! [X11] : (room(X11) => (~predm(X11) | ~predr(X11) | ~predq(X11)))) & ! [X12] : (room(X12) => (paul = X12 | mary = X12)) & room(paul) & room(mary) [pure predicate removal 48] 50. ! [X0] : (room(X0) => ~predb(X0)) & ? [X3,X4] : (X3 != X4 & room(X4) & room(X3)) & ! [X5] : (room(X5) => ~predh(X5)) & ! [X7] : (room(X7) => ~predk(X7)) & (! [X8] : (room(X8) => (~predm(X8) | ~predr(X8) | ~predq(X8))) => ! [X9] : (room(X9) => ~predq(X9))) & ! [X12] : (room(X12) => (paul = X12 | mary = X12)) & room(paul) & room(mary) [pure predicate removal 49] 51. ! [X0] : (room(X0) => ~predb(X0)) & ? [X3,X4] : (X3 != X4 & room(X4) & room(X3)) & ! [X5] : (room(X5) => ~predh(X5)) & ! [X7] : (room(X7) => ~predk(X7)) & (! [X8] : (room(X8) => (~predr(X8) | ~predq(X8))) => ! [X9] : (room(X9) => ~predq(X9))) & ! [X12] : (room(X12) => (paul = X12 | mary = X12)) & room(paul) & room(mary) [pure predicate removal 50] 52. ! [X0] : (room(X0) => ~predb(X0)) & ? [X3,X4] : (X3 != X4 & room(X4) & room(X3)) & ! [X5] : (room(X5) => ~predh(X5)) & ! [X7] : (room(X7) => ~predk(X7)) & (! [X8] : (room(X8) => ~predq(X8)) => ! [X9] : (room(X9) => ~predq(X9))) & ! [X12] : (room(X12) => (paul = X12 | mary = X12)) & room(paul) & room(mary) [pure predicate removal 51] 53. ! [X0] : (room(X0) => ~predb(X0)) & ? [X3,X4] : (X3 != X4 & room(X4) & room(X3)) & ! [X5] : (room(X5) => ~predh(X5)) & (! [X8] : (room(X8) => ~predq(X8)) => ! [X9] : (room(X9) => ~predq(X9))) & ! [X12] : (room(X12) => (paul = X12 | mary = X12)) & room(paul) & room(mary) [pure predicate removal 52] 126. ! [X0] : (~predb(X0) | ~room(X0)) & ? [X3,X4] : (X3 != X4 & room(X4) & room(X3)) & ! [X5] : (~predh(X5) | ~room(X5)) & (! [X9] : (~predq(X9) | ~room(X9)) | ? [X8] : (predq(X8) & room(X8))) & ! [X12] : ((paul = X12 | mary = X12) | ~room(X12)) & room(paul) & room(mary) [ennf transformation 53] 127. ! [X0] : (~predb(X0) | ~room(X0)) & ? [X3,X4] : (X3 != X4 & room(X4) & room(X3)) & ! [X5] : (~predh(X5) | ~room(X5)) & (! [X9] : (~predq(X9) | ~room(X9)) | ? [X8] : (predq(X8) & room(X8))) & ! [X12] : (paul = X12 | mary = X12 | ~room(X12)) & room(paul) & room(mary) [flattening 126] 128. predb(mary) & predh(mary) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 45] 129. predb(mary) & predh(mary) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 128] 131. ! [X0] : (~predb(X0) | ~room(X0)) & ? [X1,X2] : (X1 != X2 & room(X2) & room(X1)) & ! [X3] : (~predh(X3) | ~room(X3)) & (! [X4] : (~predq(X4) | ~room(X4)) | ? [X5] : (predq(X5) & room(X5))) & ! [X6] : (paul = X6 | mary = X6 | ~room(X6)) & room(paul) & room(mary) [rectify 127] 132. ? [X1,X2] : (X1 != X2 & room(X2) & room(X1)) => (sK0 != sK1 & room(sK1) & room(sK0)) [choice axiom] 133. ? [X5] : (predq(X5) & room(X5)) => (predq(sK2) & room(sK2)) [choice axiom] 134. ! [X0] : (~predb(X0) | ~room(X0)) & (sK0 != sK1 & room(sK1) & room(sK0)) & ! [X3] : (~predh(X3) | ~room(X3)) & (! [X4] : (~predq(X4) | ~room(X4)) | (predq(sK2) & room(sK2))) & ! [X6] : (paul = X6 | mary = X6 | ~room(X6)) & room(paul) & room(mary) [skolemisation 131,133,132] 215. room(mary) [cnf transformation 134] 220. ~predh(X3) | ~room(X3) [cnf transformation 134] 228. predh(mary) [cnf transformation 129] 243. ~room(mary) [resolution 220,228] 244. $false [subsumption resolution 243,215] % SZS output end Proof for 309611701811290452388518 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

There is a room. It is true that everyone in the room does not build model airplanes or does not drive a hybrid car or both. Everyone in the room does not enjoy camping and organizing outdoor survival workshops or is not a client of Meta or both. Everyone outside the room neither does not own a high-end gaming PC with custom-built components nor does not have a pet dog. Everyone anywhere neither does not work on fridays nor does not use an ios phone. Someone in the room is not a drone photographer. Everyone in the room does not collect limited-edition art prints from contemporary artists. Everyone anywhere either does not host a popular podcast about emerging technologies or is not a client of Meta but not both. Everyone in the room does not have a pet dog and does not create augmented reality experiences for mobile applications.

Everyone in the room enjoys camping and organizing outdoor survival workshops.

neutral

(there_is_a_room)& (![X]:(room(X)=>(((does_not_build_model_airplanes(X))|(does_not_drive_a_hybrid_car(X))))))& (![X]:(room(X)=>(((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))|(is_not_a_client_of_Meta(X))))))& (![X]:(~room(X)=>(~((does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))|(does_not_have_a_pet_dog(X))))))& (![X]:(anywhere(X)=>(~((does_not_work_on_fridays(X))|(does_not_use_an_ios_phone(X))))))& (?[X]:(room(X)&(is_not_a_drone_photographer(X))))& (![X]:(room(X)=>(does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))))& (![X]:(anywhere(X)=>(((does_not_host_a_popular_podcast_about_emerging_technologies(X))<~>(is_not_a_client_of_Meta(X))))))& (![X]:(room(X)=>(((does_not_have_a_pet_dog(X))&(does_not_create_augmented_reality_experiences_for_mobile_applications(X))))))& (![X]:(anywhere(X)=>(((does_not_drive_a_hybrid_car(X))&(does_not_compose_and_performs_experimental_electronic_music(X))&(does_not_have_a_pet_dog(X))))))& (![X]:(room(X)=>(((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))|(does_not_host_a_popular_podcast_about_emerging_technologies(X))|(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))))))& ((![X]:((does_not_enjoy_virtual_reality_gaming(X))=>(~((does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))|(cannot_play_the_piano(X)))))))& (![X]:(room(X)=>(does_not_own_a_telescope(X))))& (![X]:(room(X)=>(((does_not_have_a_pet_dog(X))|(does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))))))& (![X]:(room(X)=>(~((cannot_play_the_piano(X))|(does_not_host_a_popular_podcast_about_emerging_technologies(X))))))& (![X]:(anywhere(X)=>(((is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))<~>(does_not_own_a_telescope(X))))))& (![X]:(room(X)=>(((is_not_a_drone_photographer(X))|(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))))))& (![X]:(room(X)=>(((does_not_own_a_telescope(X))|(does_not_create_augmented_reality_experiences_for_mobile_applications(X))))))

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

Richard, Nancy, William, Eva, Marilyn are the only persons in the room. If “not everyone in the room is an avid mountain climber who has scaled several peaks or is not an avid mountain climber who has scaled several peaks” then “Richard is not an avid mountain climber who has scaled several peaks”. Either “no one in the room enjoys spelunking or is not an avid mountain climber who has scaled several peaks” or “everyone in the room is not an avid mountain climber who has scaled several peaks or is an avid mountain climber who has scaled several peaks” but not both. If “everyone in the room is not an avid mountain climber who has scaled several peaks or is an avid mountain climber who has scaled several peaks” then “it is not the case that ““A bird does not tweet using morse code.” or “A clock measures time in various colors.” or both””. Not everyone in the room enjoys spelunking. “A frog does not sing opera in the swamp at night.” or “A bird does not tweet using morse code.” or both. Richard is an avid mountain climber who has scaled several peaks. “A clock does not measure time in various colors.” or “A frog does not sing opera in the swamp at night.” or both. William is not an avid mountain climber who has scaled several peaks. Everyone in the room who enjoys spelunking is an avid mountain climber who has scaled several peaks. Eva is an avid mountain climber who has scaled several peaks. If someone is an avid mountain climber who has scaled several peaks then he/she enjoys spelunking.

A bird does not tweet using morse code.

contradiction

room(richard)&room(nancy)&room(william)&room(eva)&room(marilyn)&(![X]:(room(X)=>(X='richard'|X='nancy'|X='william'|X='eva'|X='marilyn')))& ((~![X]:(room(X)=>(((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))=>(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(richard)))& ((~?[X]:(room(X)=>(((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(enjoys_spelunking(X))))))<~>(![X]:(room(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X)))))))& ((![X]:(room(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))|(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))=>(~(((A_bird_does_not_tweet_using_morse_code.)|(A_clock_measures_time_in_various_colors.)))))& (~![X]:(room(X)=>(enjoys_spelunking(X))))& (((A_frog_does_not_sing_opera_in_the_swamp_at_night.)|(A_bird_does_not_tweet_using_morse_code.)))& (is_an_avid_mountain_climber_who_has_scaled_several_peaks(richard))& (((A_clock_does_not_measure_time_in_various_colors.)|(A_frog_does_not_sing_opera_in_the_swamp_at_night.)))& (is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(william))& (![X]:(room(X)=>(((enjoys_spelunking(X))=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))& (is_an_avid_mountain_climber_who_has_scaled_several_peaks(eva))& ((![X]:((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(enjoys_spelunking(X)))))& (((is_an_avid_mountain_climber_who_has_scaled_several_peaks(richard))|(enjoys_spelunking(richard))|(does_not_enjoy_spelunking(richard))))

room(richard)&room(nancy)&room(william)&room(eva)&room(marilyn)&(![X]:(room(X)=>(X='richard'|X='nancy'|X='william'|X='eva'|X='marilyn')))& A_bird_does_not_tweet_using_morse_code.

% SZS status Unsatisfiable for 4043106025443159031745391 % SZS output start Proof for 4043106025443159031745391 47. ! [X0] : (room(X0) => (~predo(X0) | predo(X0))) => ~(propositionc | ~propositionb) [input p3] 57. ~propositionb & ! [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] 61. ! [X0] : (room(X0) => (~predo(X0) | predo(X0))) => ~~propositionb [pure predicate removal 47] 140. propositionb | ? [X0] : ((predo(X0) & ~predo(X0)) & room(X0)) [ennf transformation 61] 141. propositionb | ? [X0] : (predo(X0) & ~predo(X0) & room(X0)) [flattening 140] 146. ~propositionb & ! [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 57] 147. ~propositionb & ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 146] 159. ? [X0] : (predo(X0) & ~predo(X0) & room(X0)) => (predo(sK3) & ~predo(sK3) & room(sK3)) [choice axiom] 160. propositionb | (predo(sK3) & ~predo(sK3) & room(sK3)) [skolemisation 141,159] 259. propositionb | ~predo(sK3) [cnf transformation 160] 260. propositionb | predo(sK3) [cnf transformation 160] 275. ~propositionb [cnf transformation 147] 317. 10 <=> predo(sK3) [avatar definition] 321. 11 <=> propositionb [avatar definition] 324. 10 | 11 [avatar split clause 260,321,317] 325. ~10 | 11 [avatar split clause 259,321,317] 331. ~11 [avatar split clause 275,321] 332. $false [avatar sat refutation 324,325,331] % SZS output end Proof for 4043106025443159031745391 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Cody, Janice, Roger, Donald, Allison are the only persons in the room. “Cody enjoys stargazing” if “everyone in the room knows morse code or does not train for and competes in international triathlons”. “Everyone in the room who does enjoy trail running participates in citizen science projects related to wildlife monitoring” if “Donald neither trains for and competes in international triathlons nor collects comic books”. Cody knows morse code. Everyone in the room knows morse code only if they does enjoy trail running. Everyone in the room does enjoy trail running if and only if they does not enjoy stargazing. Everyone anywhere who does not enjoy trail running participates in citizen science projects related to wildlife monitoring. Everyone in the room does not enjoy trail running if they participates in citizen science projects related to wildlife monitoring.

Roger does not participate in citizen science projects related to wildlife monitoring and enjoys stargazing.

contradiction

room(cody)&room(janice)&room(roger)&room(donald)&room(allison)&(![X]:(room(X)=>(X='cody'|X='janice'|X='roger'|X='donald'|X='allison')))& ((![X]:(room(X)=>(((does_not_train_for_and_competes_in_international_triathlons(X))|(knows_morse_code(X))))))=>(enjoys_stargazing(cody)))& ((~((trains_for_and_competes_in_international_triathlons(donald))|(collects_comic_books(donald))))=>(![X]:(room(X)=>(((does_enjoy_trail_running(X))=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X)))))))& (knows_morse_code(cody))& (![X]:(room(X)=>(((does_enjoy_trail_running(X))<=(knows_morse_code(X))))))& (![X]:(room(X)=>(((does_enjoy_trail_running(X))<=>(does_not_enjoy_stargazing(X))))))& (![X]:(anywhere(X)=>(((does_not_enjoy_trail_running(X))=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))& (![X]:(room(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))=>(does_not_enjoy_trail_running(X))))))

room(cody)&room(janice)&room(roger)&room(donald)&room(allison)&(![X]:(room(X)=>(X='cody'|X='janice'|X='roger'|X='donald'|X='allison')))& ((does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(roger))&(enjoys_stargazing(roger)))

% SZS status Unsatisfiable for 6949295199007932538619304 % SZS output start Proof for 6949295199007932538619304 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 49. ! [X0] : (room(X0) => (predg(X0) <=> ~predf(X0))) [input p5] 50. ! [X0] : (anywhere(X0) => (~predg(X0) => predk(X0))) [input p6] 52. predf(fred) & ~predk(fred) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 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] 131. ! [X0] : ((predg(X0) <=> ~predf(X0)) | ~room(X0)) [ennf transformation 49] 132. ! [X0] : ((predk(X0) | predg(X0)) | ~anywhere(X0)) [ennf transformation 50] 133. ! [X0] : (predk(X0) | predg(X0) | ~anywhere(X0)) [flattening 132] 136. predf(fred) & ~predk(fred) & ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 52] 137. predf(fred) & ~predk(fred) & ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 136] 141. ! [X0] : (((predg(X0) | predf(X0)) & (~predf(X0) | ~predg(X0))) | ~room(X0)) [nnf transformation 131] 142. anywhere(X0) [cnf transformation 5] 225. room(fred) [cnf transformation 127] 233. ~predg(X0) | ~predf(X0) | ~room(X0) [cnf transformation 141] 235. predk(X0) | predg(X0) | ~anywhere(X0) [cnf transformation 133] 243. ~predk(fred) [cnf transformation 137] 244. predf(fred) [cnf transformation 137] 259. predk(X0) | predg(X0) [subsumption resolution 235,142] 260. predg(fred) [resolution 259,243] 263. ~predf(fred) | ~room(fred) [resolution 233,260] 264. ~room(fred) [subsumption resolution 263,244] 265. $false [subsumption resolution 264,225] % SZS output end Proof for 6949295199007932538619304 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.036 s % ------------------------------ % ------------------------------

There is a room. Everyone in the room is not right-handed. Everyone outside the room does not own a telescope. No one in the room does not collect historical artifacts related to ancient civilizations. Everyone in the room does not collect modern art, is not a Linux enthusiast and does not enjoy deep-sea diving and exploring underwater caves.

Everyone outside the room does not enjoy deep-sea diving and exploring underwater caves.

entailment

(there_is_a_room)& (![X]:(room(X)=>(is_not_right-handed(X))))& (![X]:(~room(X)=>(does_not_own_a_telescope(X))))& (![X]:(anywhere(X)=>(does_not_work_on_fridays(X))))& (![X]:(room(X)=>(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))& (~?[X]:(room(X)=>(does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))))& (![X]:(room(X)=>(((does_not_own_a_telescope(X))&(does_not_know_morse_code(X))&(is_not_right-handed(X))))))& (![X]:(room(X)=>(((does_not_collect_modern_art(X))&(is_not_a_Linux_enthusiast(X))&(does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))))))& (![X]:(room(X)=>(does_not_know_morse_code(X))))& (![X]:(~room(X)=>(does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))))& (![X]:(anywhere(X)=>(is_not_a_scotch_connoisseur(X))))& (![X]:(room(X)=>(does_not_collect_modern_art(X))))& (![X]:(room(X)=>(((does_not_own_a_telescope(X))&(does_not_enjoy_trail_running(X))&(does_not_work_on_fridays(X))))))& (![X]:(room(X)=>(((is_not_a_Linux_enthusiast(X))&(does_not_own_a_telescope(X))&(does_not_know_morse_code(X))))))& (![X]:(room(X)=>(((is_not_a_Linux_enthusiast(X))&(does_not_own_a_telescope(X))&(does_not_enjoy_trail_running(X))))))& (![X]:(anywhere(X)=>(is_not_a_Linux_enthusiast(X))))& (![X]:(room(X)=>(does_not_own_a_telescope(X))))& (![X]:(~room(X)=>(does_not_work_on_fridays(X))))& (![X]:(room(X)=>(does_not_enjoy_trail_running(X))))& (![X]:(room(X)=>(does_not_work_on_fridays(X))))

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

% SZS status Unsatisfiable for 5736178829002711814968271 % SZS output start Proof for 5736178829002711814968271 44. there_is_a_room [input p0] 49. ~? [X0] : (room(X0) => ~predd(X0)) [input p5] 51. ! [X0] : (room(X0) => (~preda(X0) & ~prede(X0) & ~predi(X0))) [input p7] 64. ~(! [X0] : (~room(X0) => ~preda(X0)) & there_is_a_room) [input hypothesis] 69. ! [X0] : (room(X0) => (~preda(X0) & ~predi(X0))) [pure predicate removal 51] 74. ! [X0] : (room(X0) => ~preda(X0)) [pure predicate removal 69] 163. ! [X0] : (predd(X0) & room(X0)) [ennf transformation 49] 164. ! [X0] : (~preda(X0) | ~room(X0)) [ennf transformation 74] 166. ? [X0] : (preda(X0) & ~room(X0)) | ~there_is_a_room [ennf transformation 64] 168. ? [X0] : (preda(X0) & ~room(X0)) => (preda(sK0) & ~room(sK0)) [choice axiom] 169. (preda(sK0) & ~room(sK0)) | ~there_is_a_room [skolemisation 166,168] 250. there_is_a_room [cnf transformation 44] 251. room(X0) [cnf transformation 163] 253. ~preda(X0) | ~room(X0) [cnf transformation 164] 256. preda(sK0) | ~there_is_a_room [cnf transformation 169] 257. ~preda(X0) [subsumption resolution 253,251] 258. ~there_is_a_room [subsumption resolution 256,257] 259. $false [subsumption resolution 258,250] % SZS output end Proof for 5736178829002711814968271 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Joseph, Clarence, Nickolas, William, Brian are the only persons in the room. Joseph cannot play the harmonica. Everyone in the room who plays the violin creates large-scale murals for public art installations. Everyone in the room has a piercing if they creates large-scale murals for public art installations and vice versa. Joseph has a piercing. If someone can play the harmonica then he/she plays the violin and vice versa. Everyone in the room does not create large-scale murals for public art installations or can play the guitar or both if they does not play the violin.

Joseph can play the guitar.

entailment

room(joseph)&room(clarence)&room(nickolas)&room(william)&room(brian)&(![X]:(room(X)=>(X='joseph'|X='clarence'|X='nickolas'|X='william'|X='brian')))& (cannot_play_the_harmonica(joseph))& (![X]:(room(X)=>(((plays_the_violin(X))=>(creates_large-scale_murals_for_public_art_installations(X))))))& (can_play_the_harmonica(clarence))& (((?[X]:(room(X)&~((collects_classic_novels(X))|(does_not_play_the_violin(X)))))))& (![X]:(room(X)=>(((has_a_piercing(X))<=>(creates_large-scale_murals_for_public_art_installations(X))))))& (does_enjoy_mountain_biking(nickolas))& (has_a_piercing(joseph))& (uses_an_ios_phone(clarence))& (?[X]:(room(X)&(((plays_the_violin(X))&(uses_an_ios_phone(X))&(does_enjoy_mountain_biking(X))))))& ((![X]:((((does_enjoy_mountain_biking(X))<~>(collects_classic_novels(X))))<=>(~((does_enjoy_mountain_biking(X))|(uses_an_ios_phone(X)))))))& ((![X]:((can_play_the_harmonica(X))<=>(plays_the_violin(X)))))& (![X]:(room(X)=>(((does_not_play_the_violin(X))=>(((does_not_create_large-scale_murals_for_public_art_installations(X))|(can_play_the_guitar(X))))))))& (does_not_collect_classic_novels(joseph))& (plays_the_violin(nickolas))& (does_not_collect_vintage_stamps(joseph))& (![X]:(room(X)=>(((is_an_avid_hiker(X))=>(((does_not_use_an_ios_phone(X))|(uses_an_ios_phone(X))|(can_play_the_harmonica(X))))))))& ((is_an_avid_hiker(clarence))&(collects_vintage_stamps(clarence)))& (can_play_the_guitar(clarence))& (![X]:(room(X)=>(((can_play_the_piano(X))=>(has_a_piercing(X))))))

room(joseph)&room(clarence)&room(nickolas)&room(william)&room(brian)&(![X]:(room(X)=>(X='joseph'|X='clarence'|X='nickolas'|X='william'|X='brian')))& can_play_the_guitar(joseph)

% SZS status Unsatisfiable for 3346895428400817850887998 % SZS output start Proof for 3346895428400817850887998 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 45. ~predb(mary) [input p1] 49. ! [X0] : (room(X0) => (predj(X0) <=> predi(X0))) [input p5] 51. predj(mary) [input p7] 55. ! [X0] : (predb(X0) <=> predk(X0)) [input p11] 56. ! [X0] : (room(X0) => (~predk(X0) => (preda(X0) | ~predi(X0)))) [input p12] 64. ~(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] 138. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 139. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 138] 144. ! [X0] : ((predj(X0) <=> predi(X0)) | ~room(X0)) [ennf transformation 49] 146. ! [X0] : (((preda(X0) | ~predi(X0)) | predk(X0)) | ~room(X0)) [ennf transformation 56] 147. ! [X0] : (preda(X0) | ~predi(X0) | predk(X0) | ~room(X0)) [flattening 146] 150. ~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 64] 151. ~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 150] 155. ! [X0] : (((predj(X0) | ~predi(X0)) & (predi(X0) | ~predj(X0))) | ~room(X0)) [nnf transformation 144] 160. ! [X0] : ((predb(X0) | ~predk(X0)) & (predk(X0) | ~predb(X0))) [nnf transformation 55] 161. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK2 & alice != sK2 & fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 162. ~preda(mary) | (john != sK2 & alice != sK2 & fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 151,161] 243. room(mary) [cnf transformation 139] 244. room(paul) [cnf transformation 139] 245. room(fred) [cnf transformation 139] 246. room(alice) [cnf transformation 139] 247. room(john) [cnf transformation 139] 248. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 139] 249. ~predb(mary) [cnf transformation 45] 255. ~predj(X0) | predi(X0) | ~room(X0) [cnf transformation 155] 258. predj(mary) [cnf transformation 51] 271. ~predk(X0) | predb(X0) [cnf transformation 160] 272. ~predi(X0) | preda(X0) | predk(X0) | ~room(X0) [cnf transformation 147] 280. ~preda(mary) | room(sK2) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162] 281. ~preda(mary) | mary != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162] 282. ~preda(mary) | paul != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162] 283. ~preda(mary) | fred != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162] 284. ~preda(mary) | alice != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162] 285. ~preda(mary) | john != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 162] 288. ~preda(mary) | john != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 285,247] 289. ~preda(mary) | john != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 288,246] 290. ~preda(mary) | john != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 289,245] 291. ~preda(mary) | john != sK2 | ~room(mary) [subsumption resolution 290,244] 292. ~preda(mary) | john != sK2 [subsumption resolution 291,243] 294. 1 <=> john = sK2 [avatar definition] 296. john != sK2 <- (~1) [avatar component clause 294] 298. 2 <=> preda(mary) [avatar definition] 300. ~preda(mary) <- (~2) [avatar component clause 298] 301. ~1 | ~2 [avatar split clause 292,298,294] 302. ~preda(mary) | alice != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 284,247] 303. ~preda(mary) | alice != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 302,246] 304. ~preda(mary) | alice != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 303,245] 305. ~preda(mary) | alice != sK2 | ~room(mary) [subsumption resolution 304,244] 306. ~preda(mary) | alice != sK2 [subsumption resolution 305,243] 308. 3 <=> alice = sK2 [avatar definition] 310. alice != sK2 <- (~3) [avatar component clause 308] 311. ~3 | ~2 [avatar split clause 306,298,308] 312. ~preda(mary) | fred != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 283,247] 313. ~preda(mary) | fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 312,246] 314. ~preda(mary) | fred != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 313,245] 315. ~preda(mary) | fred != sK2 | ~room(mary) [subsumption resolution 314,244] 316. ~preda(mary) | fred != sK2 [subsumption resolution 315,243] 318. 4 <=> fred = sK2 [avatar definition] 320. fred != sK2 <- (~4) [avatar component clause 318] 321. ~4 | ~2 [avatar split clause 316,298,318] 322. ~preda(mary) | paul != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 282,247] 323. ~preda(mary) | paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 322,246] 324. ~preda(mary) | paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 323,245] 325. ~preda(mary) | paul != sK2 | ~room(mary) [subsumption resolution 324,244] 326. ~preda(mary) | paul != sK2 [subsumption resolution 325,243] 328. 5 <=> paul = sK2 [avatar definition] 330. paul != sK2 <- (~5) [avatar component clause 328] 331. ~5 | ~2 [avatar split clause 326,298,328] 332. ~preda(mary) | mary != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 281,247] 333. ~preda(mary) | mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 332,246] 334. ~preda(mary) | mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 333,245] 335. ~preda(mary) | mary != sK2 | ~room(mary) [subsumption resolution 334,244] 336. ~preda(mary) | mary != sK2 [subsumption resolution 335,243] 338. 6 <=> mary = sK2 [avatar definition] 340. mary != sK2 <- (~6) [avatar component clause 338] 341. ~6 | ~2 [avatar split clause 336,298,338] 342. ~preda(mary) | room(sK2) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 280,247] 343. ~preda(mary) | room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 342,246] 344. ~preda(mary) | room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 343,245] 345. ~preda(mary) | room(sK2) | ~room(mary) [subsumption resolution 344,244] 346. ~preda(mary) | room(sK2) [subsumption resolution 345,243] 348. 7 <=> room(sK2) [avatar definition] 350. room(sK2) <- (7) [avatar component clause 348] 351. 7 | ~2 [avatar split clause 346,298,348] 369. predi(mary) | ~room(mary) [resolution 255,258] 370. predi(mary) [subsumption resolution 369,243] 398. preda(mary) | predk(mary) | ~room(mary) [resolution 370,272] 400. predk(mary) | ~room(mary) <- (~2) [subsumption resolution 398,300] 401. predk(mary) <- (~2) [subsumption resolution 400,243] 409. predb(mary) <- (~2) [resolution 401,271] 410. $false <- (~2) [subsumption resolution 409,249] 411. 2 [avatar contradiction clause 410] 462. alice = sK2 | fred = sK2 | paul = sK2 | mary = sK2 | john = sK2 <- (7) [resolution 248,350] 505. fred = sK2 | paul = sK2 | mary = sK2 | john = sK2 <- (~3, 7) [subsumption resolution 462,310] 506. paul = sK2 | mary = sK2 | john = sK2 <- (~3, ~4, 7) [subsumption resolution 505,320] 507. mary = sK2 | john = sK2 <- (~3, ~4, ~5, 7) [subsumption resolution 506,330] 508. john = sK2 <- (~3, ~4, ~5, ~6, 7) [subsumption resolution 507,340] 509. $false <- (~1, ~3, ~4, ~5, ~6, 7) [subsumption resolution 508,296] 510. 1 | 3 | 4 | 5 | 6 | ~7 [avatar contradiction clause 509] 511. $false [avatar sat refutation 301,311,321,331,341,351,411,510] % SZS output end Proof for 3346895428400817850887998 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

Juan, Eric, Dong, Timothy, Leon are the only persons in the room. “Juan is patient” unless “everyone in the room is creative”. “Timothy neither is creative nor is a calm person” if “Juan is humble”.

Juan is humble.

neutral

room(juan)&room(eric)&room(dong)&room(timothy)&room(leon)&(![X]:(room(X)=>(X='juan'|X='eric'|X='dong'|X='timothy'|X='leon')))& (~(![X]:(room(X)=>(creative(X))))=>(patient(juan)))& ((humble(juan))=>(~((creative(timothy))|(calm(timothy)&person(timothy)))))& ((~((~(generous(leon)&person(leon)))|(~(patient(leon)&person(leon)))))=>(tall(juan)))& ((~(strong(leon)&person(leon)))=>(![X]:(room(X)=>(~kind(X)))))& ((![X]:(room(X)=>(~happy(X)&~tall(X))))<~>(((~(creative(leon)&person(leon)))<~>(curious(leon)))))& (![X]:(room(X)=>(strong(X))))& (![X]:(creative(X)=>strong(X)))& (((~(creative(leon)&person(leon)))<~>(curious(leon))))& (![X]:(room(X)=>(brave(X))))& (![X]:(room(X)=>(((~(brave(X)&person(X)))&(wise(X))&(~(quiet(X)&person(X)))))))& ((![X]:((~(kind(X)&person(X)))=>(~(quiet(X)&person(X))))))& (![X]:(room(X)=>(((~((~(generous(X)&person(X)))|(kind(X))))<=>(tall(X))))))& (![X]:((room(X)&(X!=eric))=>richer(X,eric)))& (![X]:(anywhere(X)=>(wise(X))))& (![X]:(anywhere(X)=>(((happy(X))=>(~(humble(X)&person(X)))))))& (wise(dong))& (![X]:(room(X)=>(~curious(X))))& (![X]:(creative(X)=>brave(X)))& (~(tall(eric)&person(eric)))& ((~(generous(juan)&person(juan)))&(~(strong(juan)&person(juan))))

room(juan)&room(eric)&room(dong)&room(timothy)&room(leon)&(![X]:(room(X)=>(X='juan'|X='eric'|X='dong'|X='timothy'|X='leon')))& humble(juan)

Tabatha, Maria, Nancy, Kathy, Tammi are the only persons in the room. Tabatha is not a humble person only if all strong persons are calm. If it is true that Tabatha is not a humble person then only one person in the room is a curious person otherwise if someone is patient then he/she is strong. If it is not the case that it is true that Tabatha is quiet then Kathy is the oldest in the room otherwise Tabatha is the quietest in the room. Kathy is not a strong person if everyone in the room is patient. Either Nancy is humble or Maria is not a creative person but not both. If someone is not a creative person then he/she is not a quiet person if Maria is a humble person. Either Maria and Tabatha are respectively quiet and tall or everyone in the room is not a tall person but not both. Everyone in the room is not a creative person if Tabatha is not a happy person and vice versa. Kathy is funny only if Kathy is not a quiet person. If someone is not a happy person then he/she is funny. If someone is not a strong person then he/she is happy. Everyone in the room is not a creative person. Maria is not a curious person. Nancy is a kind person. Kathy is not a quiet person. It is not the case that Tabatha is not a brave person. No quiet person is wise. All humble persons are strong. If someone is not a patient person then he/she is not a creative person.

Tabatha is funny.

entailment

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

room(tabatha)&room(maria)&room(nancy)&room(kathy)&room(tammi)&(![X]:(room(X)=>(X='tabatha'|X='maria'|X='nancy'|X='kathy'|X='tammi')))& funny(tabatha)

% SZS status Unsatisfiable for 2768561803935441385675786 % SZS output start Proof for 2768561803935441385675786 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. ~(person(mary) & happy(mary)) <=> ! [X0] : (room(X0) => ~(person(X0) & creative(X0))) [input p8] 54. ! [X0] : (~(person(X0) & happy(X0)) => funny(X0)) [input p10] 56. ! [X0] : (room(X0) => ~(person(X0) & creative(X0))) [input p12] 60. ~~(person(mary) & brave(mary)) [input p16] 64. ~(funny(mary) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 68. person(mary) & brave(mary) [flattening 60] 70. person(mary) [pure predicate removal 68] 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] 158. (~person(mary) | ~happy(mary)) <=> ! [X0] : ((~person(X0) | ~creative(X0)) | ~room(X0)) [ennf transformation 52] 159. (~person(mary) | ~happy(mary)) <=> ! [X0] : (~person(X0) | ~creative(X0) | ~room(X0)) [flattening 158] 162. ! [X0] : (funny(X0) | (person(X0) & happy(X0))) [ennf transformation 54] 164. ! [X0] : ((~person(X0) | ~creative(X0)) | ~room(X0)) [ennf transformation 56] 165. ! [X0] : (~person(X0) | ~creative(X0) | ~room(X0)) [flattening 164] 172. ~funny(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 64] 173. ~funny(mary) | ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 172] 186. ((~person(mary) | ~happy(mary)) | ? [X0] : (person(X0) & creative(X0) & room(X0))) & (! [X0] : (~person(X0) | ~creative(X0) | ~room(X0)) | (person(mary) & happy(mary))) [nnf transformation 159] 187. (~person(mary) | ~happy(mary) | ? [X0] : (person(X0) & creative(X0) & room(X0))) & (! [X0] : (~person(X0) | ~creative(X0) | ~room(X0)) | (person(mary) & happy(mary))) [flattening 186] 188. (~person(mary) | ~happy(mary) | ? [X0] : (person(X0) & creative(X0) & room(X0))) & (! [X1] : (~person(X1) | ~creative(X1) | ~room(X1)) | (person(mary) & happy(mary))) [rectify 187] 189. ? [X0] : (person(X0) & creative(X0) & room(X0)) => (person(sK3) & creative(sK3) & room(sK3)) [choice axiom] 190. (~person(mary) | ~happy(mary) | (person(sK3) & creative(sK3) & room(sK3))) & (! [X1] : (~person(X1) | ~creative(X1) | ~room(X1)) | (person(mary) & happy(mary))) [skolemisation 188,189] 191. ? [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] 192. ~funny(mary) | (john != sK4 & alice != sK4 & fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 173,191] 273. room(mary) [cnf transformation 146] 274. room(paul) [cnf transformation 146] 275. room(fred) [cnf transformation 146] 276. room(alice) [cnf transformation 146] 277. room(john) [cnf transformation 146] 278. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 146] 304. ~person(mary) | ~happy(mary) | room(sK3) [cnf transformation 190] 305. ~person(mary) | ~happy(mary) | creative(sK3) [cnf transformation 190] 306. ~person(mary) | ~happy(mary) | person(sK3) [cnf transformation 190] 308. funny(X0) | happy(X0) [cnf transformation 162] 312. ~person(X0) | ~creative(X0) | ~room(X0) [cnf transformation 165] 316. person(mary) [cnf transformation 70] 321. ~funny(mary) | room(sK4) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192] 322. ~funny(mary) | mary != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192] 323. ~funny(mary) | paul != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192] 324. ~funny(mary) | fred != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192] 325. ~funny(mary) | alice != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192] 326. ~funny(mary) | john != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 192] 332. 2 <=> person(mary) [avatar definition] 444. 26 <=> person(sK3) [avatar definition] 446. person(sK3) <- (26) [avatar component clause 444] 448. 27 <=> happy(mary) [avatar definition] 451. 26 | ~27 | ~2 [avatar split clause 306,332,448,444] 453. 28 <=> creative(sK3) [avatar definition] 455. creative(sK3) <- (28) [avatar component clause 453] 456. 28 | ~27 | ~2 [avatar split clause 305,332,448,453] 458. 29 <=> room(sK3) [avatar definition] 461. 29 | ~27 | ~2 [avatar split clause 304,332,448,458] 463. 30 <=> ! [X1] : (~person(X1) | ~room(X1) | ~creative(X1)) [avatar definition] 464. ~creative(X1) | ~room(X1) | ~person(X1) <- (30) [avatar component clause 463] 476. 30 [avatar split clause 312,463] 483. 2 [avatar split clause 316,332] 484. ~funny(mary) | john != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 326,277] 485. ~funny(mary) | john != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 484,276] 486. ~funny(mary) | john != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 485,275] 487. ~funny(mary) | john != sK4 | ~room(mary) [subsumption resolution 486,274] 488. ~funny(mary) | john != sK4 [subsumption resolution 487,273] 490. 34 <=> john = sK4 [avatar definition] 492. john != sK4 <- (~34) [avatar component clause 490] 494. 35 <=> funny(mary) [avatar definition] 496. ~funny(mary) <- (~35) [avatar component clause 494] 497. ~34 | ~35 [avatar split clause 488,494,490] 498. ~funny(mary) | alice != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 325,277] 499. ~funny(mary) | alice != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 498,276] 500. ~funny(mary) | alice != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 499,275] 501. ~funny(mary) | alice != sK4 | ~room(mary) [subsumption resolution 500,274] 502. ~funny(mary) | alice != sK4 [subsumption resolution 501,273] 504. 36 <=> alice = sK4 [avatar definition] 506. alice != sK4 <- (~36) [avatar component clause 504] 507. ~36 | ~35 [avatar split clause 502,494,504] 508. ~funny(mary) | fred != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 324,277] 509. ~funny(mary) | fred != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 508,276] 510. ~funny(mary) | fred != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 509,275] 511. ~funny(mary) | fred != sK4 | ~room(mary) [subsumption resolution 510,274] 512. ~funny(mary) | fred != sK4 [subsumption resolution 511,273] 514. 37 <=> fred = sK4 [avatar definition] 516. fred != sK4 <- (~37) [avatar component clause 514] 517. ~37 | ~35 [avatar split clause 512,494,514] 518. ~funny(mary) | paul != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 323,277] 519. ~funny(mary) | paul != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 518,276] 520. ~funny(mary) | paul != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 519,275] 521. ~funny(mary) | paul != sK4 | ~room(mary) [subsumption resolution 520,274] 522. ~funny(mary) | paul != sK4 [subsumption resolution 521,273] 524. 38 <=> paul = sK4 [avatar definition] 526. paul != sK4 <- (~38) [avatar component clause 524] 527. ~38 | ~35 [avatar split clause 522,494,524] 528. ~funny(mary) | mary != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 322,277] 529. ~funny(mary) | mary != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 528,276] 530. ~funny(mary) | mary != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 529,275] 531. ~funny(mary) | mary != sK4 | ~room(mary) [subsumption resolution 530,274] 532. ~funny(mary) | mary != sK4 [subsumption resolution 531,273] 534. 39 <=> mary = sK4 [avatar definition] 536. mary != sK4 <- (~39) [avatar component clause 534] 537. ~39 | ~35 [avatar split clause 532,494,534] 538. ~funny(mary) | room(sK4) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 321,277] 539. ~funny(mary) | room(sK4) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 538,276] 540. ~funny(mary) | room(sK4) | ~room(paul) | ~room(mary) [subsumption resolution 539,275] 541. ~funny(mary) | room(sK4) | ~room(mary) [subsumption resolution 540,274] 542. ~funny(mary) | room(sK4) [subsumption resolution 541,273] 544. 40 <=> room(sK4) [avatar definition] 546. room(sK4) <- (40) [avatar component clause 544] 547. 40 | ~35 [avatar split clause 542,494,544] 548. happy(mary) <- (~35) [resolution 308,496] 551. 27 | 35 [avatar split clause 548,494,448] 555. ~room(sK3) | ~person(sK3) <- (28, 30) [resolution 464,455] 559. ~room(sK3) <- (26, 28, 30) [subsumption resolution 555,446] 560. ~29 | ~26 | ~28 | ~30 [avatar split clause 559,463,453,444,458] 638. alice = sK4 | fred = sK4 | paul = sK4 | mary = sK4 | john = sK4 <- (40) [resolution 278,546] 681. fred = sK4 | paul = sK4 | mary = sK4 | john = sK4 <- (~36, 40) [subsumption resolution 638,506] 682. paul = sK4 | mary = sK4 | john = sK4 <- (~36, ~37, 40) [subsumption resolution 681,516] 683. mary = sK4 | john = sK4 <- (~36, ~37, ~38, 40) [subsumption resolution 682,526] 684. john = sK4 <- (~36, ~37, ~38, ~39, 40) [subsumption resolution 683,536] 685. $false <- (~34, ~36, ~37, ~38, ~39, 40) [subsumption resolution 684,492] 686. 34 | 36 | 37 | 38 | 39 | ~40 [avatar contradiction clause 685] 687. $false [avatar sat refutation 451,456,461,476,483,497,507,517,527,537,547,551,560,686] % SZS output end Proof for 2768561803935441385675786 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Oscar, Mark are the only persons in the room. If Oscar collects classic novels then Oscar is a client of LVMH. Mark practices graffiti art, enjoys fishing or can play the harmonica. Someone in the room hosts regular workshops on creative writing. Not everyone in the room is allergic to anything if they practices graffiti art. Everyone in the room uses contact lenses or is not allergic to anything or both if they is allergic to anything. Everyone anywhere uses contact lenses or is not allergic to anything or both if and only if they uses contact lenses. Mark is a client of LVMH and cannot play the harmonica. Oscar does enjoy mountain biking. Everyone in the room does not enjoy fishing, is not a cybersecurity expert or collects modern art if they enjoys bird watching, makes homemade pastries and is allergic to anything. Not everyone anywhere hosts regular workshops on creative writing if they does not enjoy fishing, is not a cybersecurity expert or collects modern art. At least one person in the room does not make homemade pastries. Everyone in the room who collects classic novels uses contact lenses. Oscar creates bespoke furniture pieces from reclaimed wood. Not everyone in the room practices graffiti art or does not use contact lenses. Mark creates bespoke furniture pieces from reclaimed wood. Oscar collects classic novels. Everyone outside the room practices graffiti art if they is a cybersecurity expert. Everyone in the room collects modern art if they is a cybersecurity expert. Everyone in the room who hosts regular workshops on creative writing is a client of LVMH. Oscar collects limited-edition art prints from contemporary artists.

Mark uses contact lenses.

entailment

room(oscar)&room(mark)&(![X]:(room(X)=>(X='oscar'|X='mark')))& ((collects_classic_novels(oscar))=>(is_a_client_of_LVMH(oscar)))& (((practices_graffiti_art(mark))|(enjoys_fishing(mark))|(can_play_the_harmonica(mark))))& (?[X]:(room(X)&(hosts_regular_workshops_on_creative_writing(X))))& (~![X]:(room(X)=>(((practices_graffiti_art(X))=>(is_allergic_to_anything(X))))))& (![X]:(room(X)=>(((is_allergic_to_anything(X))=>(((uses_contact_lenses(X))|(is_not_allergic_to_anything(X))))))))& (![X]:(anywhere(X)=>(((((uses_contact_lenses(X))|(is_not_allergic_to_anything(X))))<=>(uses_contact_lenses(X))))))& (((is_a_client_of_LVMH(mark))&(cannot_play_the_harmonica(mark))))& (does_enjoy_mountain_biking(oscar))& (![X]:(room(X)=>(((((enjoys_bird_watching(X))&(makes_homemade_pastries(X))&(is_allergic_to_anything(X))))=>(((does_not_enjoy_fishing(X))|(is_not_a_cybersecurity_expert(X))|(collects_modern_art(X))))))))& (~![X]:(anywhere(X)=>(((((does_not_enjoy_fishing(X))|(is_not_a_cybersecurity_expert(X))|(collects_modern_art(X))))=>(hosts_regular_workshops_on_creative_writing(X))))))& (((?[X]:(room(X)&does_not_make_homemade_pastries(X)))))& (![X]:(room(X)=>(((collects_classic_novels(X))=>(uses_contact_lenses(X))))))& (creates_bespoke_furniture_pieces_from_reclaimed_wood(oscar))& (~![X]:(room(X)=>(((does_not_use_contact_lenses(X))|(practices_graffiti_art(X))))))& (creates_bespoke_furniture_pieces_from_reclaimed_wood(mark))& (collects_classic_novels(oscar))& (![X]:(~room(X)=>(((is_a_cybersecurity_expert(X))=>(practices_graffiti_art(X))))))& (![X]:(room(X)=>(((is_a_cybersecurity_expert(X))=>(collects_modern_art(X))))))& (![X]:(room(X)=>(((hosts_regular_workshops_on_creative_writing(X))=>(is_a_client_of_LVMH(X))))))& (collects_limited-edition_art_prints_from_contemporary_artists(oscar))& (collects_modern_art(mark))& (![X]:(~room(X)=>(((is_a_client_of_LVMH(X))=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))|(is_a_cybersecurity_expert(X))|(collects_limited-edition_art_prints_from_contemporary_artists(X))))))))& (~![X]:(room(X)=>(((((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))|(is_a_cybersecurity_expert(X))|(collects_limited-edition_art_prints_from_contemporary_artists(X))))=>(does_enjoy_mountain_biking(X))))))& (![X]:(room(X)=>(((does_enjoy_mountain_biking(X))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& ((((enjoys_bird_watching(mark))|(cannot_play_the_harmonica(mark))|(does_not_collect_modern_art(mark))))&(makes_homemade_pastries(mark)))& (![X]:(room(X)=>(((is_a_cybersecurity_expert(X))=>(((makes_homemade_pastries(X))&(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))))))))& (?[X]:(room(X)&(cannot_play_the_harmonica(X))))& (is_a_cybersecurity_expert(mark))

room(oscar)&room(mark)&(![X]:(room(X)=>(X='oscar'|X='mark')))& uses_contact_lenses(mark)

% SZS status Unsatisfiable for 1871693078632199000890660 % SZS output start Proof for 1871693078632199000890660 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 49. ! [X0] : (room(X0) => (predh(X0) => (~predh(X0) | predd(X0)))) [input p5] 50. ! [X0] : (anywhere(X0) => ((~predh(X0) | predd(X0)) <=> predd(X0))) [input p6] 73. ~(predd(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 153. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 154. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 153] 157. ! [X0] : (((~predh(X0) | predd(X0)) | ~predh(X0)) | ~room(X0)) [ennf transformation 49] 158. ! [X0] : (~predh(X0) | predd(X0) | ~predh(X0) | ~room(X0)) [flattening 157] 159. ! [X0] : (((~predh(X0) | predd(X0)) <=> predd(X0)) | ~anywhere(X0)) [ennf transformation 50] 177. ~predd(paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 73] 178. ~predd(paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 177] 184. ! [X0] : ((((~predh(X0) | predd(X0)) | ~predd(X0)) & (predd(X0) | (predh(X0) & ~predd(X0)))) | ~anywhere(X0)) [nnf transformation 159] 185. ! [X0] : (((~predh(X0) | predd(X0) | ~predd(X0)) & (predd(X0) | (predh(X0) & ~predd(X0)))) | ~anywhere(X0)) [flattening 184] 196. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK7 & mary != sK7 & room(sK7)) [choice axiom] 197. ~predd(paul) | (paul != sK7 & mary != sK7 & room(sK7)) | ~room(paul) | ~room(mary) [skolemisation 178,196] 198. anywhere(X0) [cnf transformation 5] 279. room(mary) [cnf transformation 154] 280. room(paul) [cnf transformation 154] 281. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 154] 288. ~predh(X0) | predd(X0) | ~predh(X0) | ~room(X0) [cnf transformation 158] 290. predd(X0) | predh(X0) | ~anywhere(X0) [cnf transformation 185] 318. ~predd(paul) | room(sK7) | ~room(paul) | ~room(mary) [cnf transformation 197] 319. ~predd(paul) | mary != sK7 | ~room(paul) | ~room(mary) [cnf transformation 197] 320. ~predd(paul) | paul != sK7 | ~room(paul) | ~room(mary) [cnf transformation 197] 321. ~predh(X0) | predd(X0) | ~room(X0) [duplicate literal removal 288] 335. predd(X0) | predh(X0) [subsumption resolution 290,198] 356. ~predd(paul) | paul != sK7 | ~room(mary) [subsumption resolution 320,280] 357. ~predd(paul) | paul != sK7 [subsumption resolution 356,279] 359. 8 <=> paul = sK7 [avatar definition] 361. paul != sK7 <- (~8) [avatar component clause 359] 363. 9 <=> predd(paul) [avatar definition] 365. ~predd(paul) <- (~9) [avatar component clause 363] 366. ~8 | ~9 [avatar split clause 357,363,359] 367. ~predd(paul) | mary != sK7 | ~room(mary) [subsumption resolution 319,280] 368. ~predd(paul) | mary != sK7 [subsumption resolution 367,279] 370. 10 <=> mary = sK7 [avatar definition] 372. mary != sK7 <- (~10) [avatar component clause 370] 373. ~10 | ~9 [avatar split clause 368,363,370] 374. ~predd(paul) | room(sK7) | ~room(mary) [subsumption resolution 318,280] 375. ~predd(paul) | room(sK7) [subsumption resolution 374,279] 377. 11 <=> room(sK7) [avatar definition] 379. room(sK7) <- (11) [avatar component clause 377] 380. 11 | ~9 [avatar split clause 375,363,377] 381. predh(paul) <- (~9) [resolution 335,365] 391. predd(paul) | ~room(paul) <- (~9) [resolution 321,381] 392. ~room(paul) <- (~9) [subsumption resolution 391,365] 393. $false <- (~9) [subsumption resolution 392,280] 394. 9 [avatar contradiction clause 393] 403. mary = sK7 | paul = sK7 <- (11) [resolution 281,379] 458. paul = sK7 <- (~10, 11) [subsumption resolution 403,372] 459. $false <- (~8, ~10, 11) [subsumption resolution 458,361] 460. 8 | 10 | ~11 [avatar contradiction clause 459] 461. $false [avatar sat refutation 366,373,380,394,460] % SZS output end Proof for 1871693078632199000890660 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Sarah is the only person in the room. If "Sarah is not an enthusiastic bird watcher who travels for rare sightings" then "no one in the room collects limited-edition art prints from contemporary artists if and only if they is an avid mountain climber who has scaled several peaks". "Sarah collects limited-edition art prints from contemporary artists" if "Sarah is an enthusiastic bird watcher who travels for rare sightings". Sarah reads mystery novels. Everyone in the room who enjoys bird watching does not practice yoga. Everyone in the room does not enjoy snowboarding only if they does not practice kickboxing. Sarah collects limited-edition art prints from contemporary artists. Everyone in the room does not own a 3D printer if and only if they enjoys snowboarding. Everyone outside the room reads mystery novels. Everyone in the room who enjoys bird watching collects limited-edition art prints from contemporary artists. Sarah is an avid mountain climber who has scaled several peaks. Everyone in the room is an avid mountain climber who has scaled several peaks if they collects limited-edition art prints from contemporary artists and vice versa. Everyone in the room does not practice yoga or collects limited-edition art prints from contemporary artists. Sarah dreamt that "not everyone in the room enjoys snowboarding if they practices kickboxing". Everyone outside the room practices kickboxing if they does not enjoy bird watching and vice versa. Everyone in the room mentors a youth basketball team on weekends, practices kickboxing and can play the harmonica if they does practice yoga. Someone anywhere reads mystery novels. Sarah enjoys snowboarding. Everyone in the room is not an avid mountain climber who has scaled several peaks or enjoys bird watching. Sarah practices kickboxing. Everyone in the room mentors a youth basketball team on weekends if and only if they collects limited-edition art prints from contemporary artists.

Sarah dreamt that "Sarah does practice yoga".

entailment

room(sarah)&(![X]:(room(X)=>(X='sarah')))& ((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(sarah))=>(~?[X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))<=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X)))))))& ((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(sarah))=>(collects_limited-edition_art_prints_from_contemporary_artists(sarah)))& (reads_mystery_novels(sarah))& (![X]:(room(X)=>(((enjoys_bird_watching(X))=>(does_not_practice_yoga(X))))))& (![X]:(room(X)=>(((does_not_practice_kickboxing(X))<=(does_not_enjoy_snowboarding(X))))))& (collects_limited-edition_art_prints_from_contemporary_artists(sarah))& (![X]:(room(X)=>(((does_not_own_a_3D_printer(X))<=>(enjoys_snowboarding(X))))))& (![X]:(~room(X)=>(reads_mystery_novels(X))))& (![X]:(room(X)=>(((enjoys_bird_watching(X))=>(collects_limited-edition_art_prints_from_contemporary_artists(X))))))& (is_an_avid_mountain_climber_who_has_scaled_several_peaks(sarah))& (![X]:(room(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))<=>(collects_limited-edition_art_prints_from_contemporary_artists(X))))))& (![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))|(does_not_practice_yoga(X))))))& ((sarah_dream=>(~![X]:(room(X)=>(((practices_kickboxing(X))=>(enjoys_snowboarding(X))))))))& (![X]:(~room(X)=>(((practices_kickboxing(X))<=>(does_not_enjoy_bird_watching(X))))))& (![X]:(room(X)=>(((does_practice_yoga(X))=>(((mentors_a_youth_basketball_team_on_weekends(X))&(practices_kickboxing(X))&(can_play_the_harmonica(X))))))))& (?[X]:(anywhere(X)&(reads_mystery_novels(X))))& (enjoys_snowboarding(sarah))& (![X]:(room(X)=>(((enjoys_bird_watching(X))|(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))& (practices_kickboxing(sarah))& (![X]:(room(X)=>(((mentors_a_youth_basketball_team_on_weekends(X))<=>(collects_limited-edition_art_prints_from_contemporary_artists(X))))))

room(sarah)&(![X]:(room(X)=>(X='sarah')))& (sarah_dream=>(does_practice_yoga(sarah)))

% SZS status Unsatisfiable for 1293190359523633501406530 % SZS output start Proof for 1293190359523633501406530 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 57. mary_dream => ~! [X0] : (room(X0) => (predb(X0) => predc(X0))) [input p13] 61. predc(mary) [input p17] 65. ~((mary_dream => predi(mary)) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 67. ~(~mary_dream & ! [X0] : (room(X0) => mary = X0) & room(mary)) [pure predicate removal 65] 147. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 156. ? [X0] : ((~predc(X0) & predb(X0)) & room(X0)) | ~mary_dream [ennf transformation 57] 157. ? [X0] : (~predc(X0) & predb(X0) & room(X0)) | ~mary_dream [flattening 156] 162. mary_dream | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 67] 168. ? [X0] : (~predc(X0) & predb(X0) & room(X0)) => (~predc(sK0) & predb(sK0) & room(sK0)) [choice axiom] 169. (~predc(sK0) & predb(sK0) & room(sK0)) | ~mary_dream [skolemisation 157,168] 172. ? [X0] : (mary != X0 & room(X0)) => (mary != sK1 & room(sK1)) [choice axiom] 173. mary_dream | (mary != sK1 & room(sK1)) | ~room(mary) [skolemisation 162,172] 254. room(mary) [cnf transformation 147] 255. ~room(X0) | mary = X0 [cnf transformation 147] 268. room(sK0) | ~mary_dream [cnf transformation 169] 270. ~predc(sK0) | ~mary_dream [cnf transformation 169] 273. predc(mary) [cnf transformation 61] 278. mary_dream | room(sK1) | ~room(mary) [cnf transformation 173] 279. mary_dream | mary != sK1 | ~room(mary) [cnf transformation 173] 303. 6 <=> mary_dream [avatar definition] 307. 7 <=> predc(sK0) [avatar definition] 309. ~predc(sK0) <- (~7) [avatar component clause 307] 310. ~6 | ~7 [avatar split clause 270,307,303] 317. 9 <=> room(sK0) [avatar definition] 319. room(sK0) <- (9) [avatar component clause 317] 320. ~6 | 9 [avatar split clause 268,317,303] 321. mary_dream | mary != sK1 [subsumption resolution 279,254] 323. 10 <=> mary = sK1 [avatar definition] 325. mary != sK1 <- (~10) [avatar component clause 323] 326. ~10 | 6 [avatar split clause 321,303,323] 327. mary_dream | room(sK1) [subsumption resolution 278,254] 329. 11 <=> room(sK1) [avatar definition] 331. room(sK1) <- (11) [avatar component clause 329] 332. 11 | 6 [avatar split clause 327,303,329] 338. mary = sK0 <- (9) [resolution 255,319] 361. ~predc(mary) <- (~7, 9) [forward demodulation 309,338] 362. $false <- (~7, 9) [subsumption resolution 361,273] 363. 7 | ~9 [avatar contradiction clause 362] 365. mary = sK1 <- (11) [resolution 331,255] 366. $false <- (~10, 11) [subsumption resolution 365,325] 367. 10 | ~11 [avatar contradiction clause 366] 368. $false [avatar sat refutation 310,320,326,332,363,367] % SZS output end Proof for 1293190359523633501406530 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Dwight is the only person in the room. If “Dwight creates bespoke furniture pieces from reclaimed wood” then “Dwight owns a microscope”. If “Dwight owns a microscope” then “Dwight can play the flute”. If “Dwight is a client of LVMH” then “everyone outside the room who practices digital art is not an avid hiker”. If “someone in the room hosts regular game nights featuring complex strategy games” then “only one person in the room hosts regular game nights featuring complex strategy games, is a client of LVMH or creates bespoke furniture pieces from reclaimed wood”. If “Dwight practices digital art” then “Dwight who hosts a popular podcast about emerging technologies practices digital art”. Either “Dwight does not have a saltwater aquarium, is a night owl or does not practice digital art” or “Dwight enjoys virtual reality gaming” but not both. Either “Dwight mentors a youth basketball team on weekends” or “Dwight enjoys virtual reality gaming” but not both. Either “Dwight plays the violin” or “Dwight hosts regular game nights featuring complex strategy games” but not both. Either “Dwight can play the flute” or “it is not the case that “Dwight is a client of Costco”” but not both. Dwight enjoys virtual reality gaming. Dwight practices digital art. Dwight is an avid hiker. Dwight can play the flute. Only one person in the room enjoys logic puzzles. Dwight hosts a popular podcast about emerging technologies. Dwight enjoys writing detailed reviews of new and classic board games. Dwight has a saltwater aquarium. Dwight regularly contributes to tech forums and online communities. Everyone in the room who regularly contributes to tech forums and online communities has a vast collection of first-edition science fiction novels.

Dwight is a client of LVMH.

neutral

room(dwight)&(![X]:(room(X)=>(X='dwight')))& ((creates_bespoke_furniture_pieces_from_reclaimed_wood(dwight))=>(owns_a_microscope(dwight)))& ((owns_a_microscope(dwight))=>(can_play_the_flute(dwight)))& ((is_a_client_of_LVMH(dwight))=>(![X]:(~room(X)=>(((practices_digital_art(X))=>(is_not_an_avid_hiker(X)))))))& ((?[X]:(room(X)&(hosts_regular_game_nights_featuring_complex_strategy_games(X))))=>(((?[X]:(room(X)&((hosts_regular_game_nights_featuring_complex_strategy_games(X))|(is_a_client_of_LVMH(X))|(creates_bespoke_furniture_pieces_from_reclaimed_wood(X)))))&(![X,Y]:((room(X)&room(Y)&(((hosts_regular_game_nights_featuring_complex_strategy_games(X))|(is_a_client_of_LVMH(X))|(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))&(((hosts_regular_game_nights_featuring_complex_strategy_games(Y))|(is_a_client_of_LVMH(Y))|(creates_bespoke_furniture_pieces_from_reclaimed_wood(Y)))))=>(X=Y))))))& ((practices_digital_art(dwight))=>((hosts_a_popular_podcast_about_emerging_technologies(dwight))&(practices_digital_art(dwight))))& ((((does_not_have_a_saltwater_aquarium(dwight))|(is_a_night_owl(dwight))|(does_not_practice_digital_art(dwight))))<~>(enjoys_virtual_reality_gaming(dwight)))& ((mentors_a_youth_basketball_team_on_weekends(dwight))<~>(enjoys_virtual_reality_gaming(dwight)))& ((plays_the_violin(dwight))<~>(hosts_regular_game_nights_featuring_complex_strategy_games(dwight)))& ((can_play_the_flute(dwight))<~>(~(is_a_client_of_Costco(dwight))))& (enjoys_virtual_reality_gaming(dwight))& (practices_digital_art(dwight))& (is_an_avid_hiker(dwight))& (can_play_the_flute(dwight))& (((?[X]:(room(X)&enjoys_logic_puzzles(X)))&(![X,Y]:((room(X)&room(Y)&(enjoys_logic_puzzles(X))&(enjoys_logic_puzzles(Y)))=>(X=Y)))))& (hosts_a_popular_podcast_about_emerging_technologies(dwight))& (enjoys_writing_detailed_reviews_of_new_and_classic_board_games(dwight))& (has_a_saltwater_aquarium(dwight))& (regularly_contributes_to_tech_forums_and_online_communities(dwight))& (![X]:(room(X)=>(((regularly_contributes_to_tech_forums_and_online_communities(X))=>(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))

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

Lee, Stephen are the only persons in the room. If “everyone in the room does not regularly goes on multi-day backpacking trips in national parks or reads mystery novels” then “Lee reads mystery novels”. If “Lee reads mystery novels” then “everyone outside the room reads mystery novels if they practices digital art”. If “everyone outside the room does not regularly goes on multi-day backpacking trips in national parks or reads mystery novels” then “everyone in the room who does not regularly goes on multi-day backpacking trips in national parks collects rare minerals”. If “everyone in the room uses a Windows laptop or does not read mystery novels” then “Lee enjoys stargazing”. If “everyone in the room does not have a specialized collection of handmade artisan pottery or does not practice yoga” then “not everyone in the room regularly goes on multi-day backpacking trips in national parks if they does not have a specialized collection of handmade artisan pottery”. Stephen regularly goes on multi-day backpacking trips in national parks, enjoys windsurfing or does not regularly goes on multi-day backpacking trips in national parks. Someone in the room is an expert in identifying and foraging wild edible plants. Everyone in the room who regularly goes on multi-day backpacking trips in national parks enjoys windsurfing. Everyone in the room who is an expert in identifying and foraging wild edible plants collects rare minerals. Everyone in the room regularly goes on multi-day backpacking trips in national parks or has a specialized collection of handmade artisan pottery or both if they collects rare minerals.

Lee enjoys stargazing.

neutral

room(lee)&room(stephen)&(![X]:(room(X)=>(X='lee'|X='stephen')))& (((![X]:(room(X)=>(((reads_mystery_novels(X))|(does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))=>(reads_mystery_novels(lee)))& ((reads_mystery_novels(lee))=>(![X]:(~room(X)=>(((practices_digital_art(X))=>(reads_mystery_novels(X))))))))& ((![X]:(~room(X)=>(((reads_mystery_novels(X))|(does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))=>(![X]:(room(X)=>(((does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))=>(collects_rare_minerals(X)))))))& ((![X]:(room(X)=>(((does_not_read_mystery_novels(X))|(uses_a_Windows_laptop(X))))))=>(enjoys_stargazing(lee)))& ((![X]:(room(X)=>(((does_not_practice_yoga(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))=>(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X)))))))& (((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(stephen))|(enjoys_windsurfing(stephen))|(does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(stephen))))& (?[X]:(room(X)&(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))& (![X]:(room(X)=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))=>(enjoys_windsurfing(X))))))& (![X]:(room(X)=>(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))=>(collects_rare_minerals(X))))))& (![X]:(room(X)=>(((collects_rare_minerals(X))=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))|(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))))

room(lee)&room(stephen)&(![X]:(room(X)=>(X='lee'|X='stephen')))& enjoys_stargazing(lee)

Lisa, David, Helen, Christopher, John are the only persons in the room. If “it is not the case that “Richard and John hate each other”” then “Richard and John hate each other”. If “Richard and John hate each other” then “if someone is hated by Richard then he/she is a quiet european”. “Richard and Helen hate each other” only if “George and David hate each other”. “Richard and Lisa hate each other” only if “it is not the case that “it is not the case that “it is not the case that “Richard and David like each other””””. “It is not the case that “it is not the case that “it is not the case that “George and Helen hate each other”””” only if “David who is a brave european, is a curious person and is old is a humble european”. If “it is not the case that “Richard and John hate each other”” then “George and Helen like each other”.

Helen is happy.

entailment

room(lisa)&room(david)&room(helen)&room(christopher)&room(john)&(![X]:(room(X)=>(X='lisa'|X='david'|X='helen'|X='christopher'|X='john')))& (((~((hate(richard,john) & hate(john,richard))))=>((hate(richard,john) & hate(john,richard))))& (((hate(richard,john) & hate(john,richard)))=>((![X]:((hate(X,richard))=>(quiet(X)&european(X)))))))& (((hate(richard,helen) & hate(helen,richard)))=>((hate(george,david) & hate(david,george))))& (((hate(richard,lisa) & hate(lisa,richard)))=>(~(~(~((like(richard,david) & like(david,richard)))))))& ((~(~(~((hate(george,helen) & hate(helen,george))))))=>((((brave(david)&european(david))&(curious(david)&person(david))&(old(david))))&(humble(david)&european(david))))& (((~((hate(richard,john) & hate(john,richard))))=>((like(george,helen) & like(helen,george))))& (((like(george,helen) & like(helen,george)))=>((![X]:((quiet(X)&european(X))=>(wise(X)&person(X)))))))& ((~((hate(george,lisa) & hate(lisa,george))))=>((calm(david)&person(david))&(((kind(david)&tourist(david))&(brave(david)&tourist(david))&(happy(david)&european(david))))))& ((~(~((hate(george,john) & hate(john,george)))))=>(~((like(george,david) & like(david,george)))))& (((~(~((hate(richard,john) & hate(john,richard)))))=>((like(george,john) & like(john,george))))& (((like(george,john) & like(john,george)))=>((![X]:((brave(X)&tourist(X))=>(patient(X)&tourist(X)))))))& (~((like(george,lisa) & like(lisa,george))))& ((![X]:((brave(X)&tourist(X))=>(patient(X)&tourist(X)))))& (![X]:((room(X)&(X!=helen))=>quieter(X,helen)))& (~(~((hate(richard,john) & hate(john,richard)))))& ((like(lisa,richard))&(calm(lisa)&tourist(lisa)))& ((![X]:((creative(X)&european(X))=>(quiet(X)&european(X)))))& ((wise(helen)&tourist(helen))&(strong(helen)&person(helen)))& ((like(richard,christopher) & like(christopher,richard)))& ((![X]:((funny(X))=>(curious(X)&person(X)))))& ((![X]:((humble(X)&european(X))=>(funny(X)&tourist(X)))))& (~((hate(george,lisa) & hate(lisa,george))))& ((![X]:((((curious(X))<~>(quiet(X)&european(X))))=>(tall(X)&tourist(X)))))& ((hate(richard,john) & hate(john,richard)))& ((![X]:((wise(X)&tourist(X))=>(happy(X)))))& ((![X]:((generous(X)&european(X))=>(calm(X)&european(X)))))& ((like(richard,helen) & like(helen,richard)))& ((![X]:((patient(X)&tourist(X))=>(happy(X)&european(X)))))& ((((funny(john)&person(john))<~>(generous(john)&person(john))))&(patient(john)&european(john)))

room(lisa)&room(david)&room(helen)&room(christopher)&room(john)&(![X]:(room(X)=>(X='lisa'|X='david'|X='helen'|X='christopher'|X='john')))& happy(helen)

% SZS status Unsatisfiable for 8720484514115727460835113 % SZS output start Proof for 8720484514115727460835113 44. european(john) & patient(john) & ((person(john) & funny(john)) <~> (person(john) & generous(john))) & ! [X0] : ((tourist(X0) & patient(X0)) => (european(X0) & happy(X0))) & like(fred,lucy) & like(lucy,fred) & ! [X0] : ((european(X0) & generous(X0)) => (european(X0) & calm(X0))) & ! [X0] : ((tourist(X0) & wise(X0)) => happy(X0)) & hate(john,lucy) & hate(lucy,john) & ! [X0] : ((curious(X0) <~> (european(X0) & quiet(X0))) => (tourist(X0) & tall(X0))) & ~(hate(mary,susan) & hate(susan,mary)) & ! [X0] : ((european(X0) & humble(X0)) => (tourist(X0) & funny(X0))) & ! [X0] : (funny(X0) => (person(X0) & curious(X0))) & like(alice,lucy) & like(lucy,alice) & person(fred) & strong(fred) & tourist(fred) & wise(fred) & ! [X0] : ((european(X0) & creative(X0)) => (european(X0) & quiet(X0))) & tourist(mary) & calm(mary) & like(mary,lucy) & ~~(hate(john,lucy) & hate(lucy,john)) & ! [X0] : ((fred != X0 & room(X0)) => quieter(X0,fred)) & ! [X0] : ((tourist(X0) & brave(X0)) => (tourist(X0) & patient(X0))) & ~(like(mary,susan) & like(susan,mary)) & ((like(john,susan) & like(susan,john)) => ! [X0] : ((tourist(X0) & brave(X0)) => (tourist(X0) & patient(X0)))) & (~~(hate(john,lucy) & hate(lucy,john)) => (like(john,susan) & like(susan,john))) & (~~(hate(john,susan) & hate(susan,john)) => ~(like(paul,susan) & like(susan,paul))) & (~(hate(mary,susan) & hate(susan,mary)) => (european(paul) & happy(paul) & tourist(paul) & brave(paul) & tourist(paul) & kind(paul) & person(paul) & calm(paul))) & ((like(fred,susan) & like(susan,fred)) => ! [X0] : ((european(X0) & quiet(X0)) => (person(X0) & wise(X0)))) & (~(hate(john,lucy) & hate(lucy,john)) => (like(fred,susan) & like(susan,fred))) & (~~~(hate(fred,susan) & hate(susan,fred)) => (european(paul) & humble(paul) & old(paul) & person(paul) & curious(paul) & european(paul) & brave(paul))) & ((hate(mary,lucy) & hate(lucy,mary)) => ~~~(like(paul,lucy) & like(lucy,paul))) & ((hate(fred,lucy) & hate(lucy,fred)) => (hate(paul,susan) & hate(susan,paul))) & ((hate(john,lucy) & hate(lucy,john)) => ! [X0] : (hate(X0,lucy) => (european(X0) & quiet(X0)))) & (~(hate(john,lucy) & hate(lucy,john)) => (hate(john,lucy) & hate(lucy,john))) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 45. ~(happy(fred) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 46. european(john) & patient(john) & ((person(john) & funny(john)) <~> (person(john) & generous(john))) & ! [X0] : ((tourist(X0) & patient(X0)) => (european(X0) & happy(X0))) & like(fred,lucy) & like(lucy,fred) & ! [X1] : ((european(X1) & generous(X1)) => (european(X1) & calm(X1))) & ! [X2] : ((tourist(X2) & wise(X2)) => happy(X2)) & hate(john,lucy) & hate(lucy,john) & ! [X3] : ((curious(X3) <~> (european(X3) & quiet(X3))) => (tourist(X3) & tall(X3))) & ~(hate(mary,susan) & hate(susan,mary)) & ! [X4] : ((european(X4) & humble(X4)) => (tourist(X4) & funny(X4))) & ! [X5] : (funny(X5) => (person(X5) & curious(X5))) & like(alice,lucy) & like(lucy,alice) & person(fred) & strong(fred) & tourist(fred) & wise(fred) & ! [X6] : ((european(X6) & creative(X6)) => (european(X6) & quiet(X6))) & tourist(mary) & calm(mary) & like(mary,lucy) & ~~(hate(john,lucy) & hate(lucy,john)) & ! [X7] : ((fred != X7 & room(X7)) => quieter(X7,fred)) & ! [X8] : ((tourist(X8) & brave(X8)) => (tourist(X8) & patient(X8))) & ~(like(mary,susan) & like(susan,mary)) & ((like(john,susan) & like(susan,john)) => ! [X9] : ((tourist(X9) & brave(X9)) => (tourist(X9) & patient(X9)))) & (~~(hate(john,lucy) & hate(lucy,john)) => (like(john,susan) & like(susan,john))) & (~~(hate(john,susan) & hate(susan,john)) => ~(like(paul,susan) & like(susan,paul))) & (~(hate(mary,susan) & hate(susan,mary)) => (european(paul) & happy(paul) & tourist(paul) & brave(paul) & tourist(paul) & kind(paul) & person(paul) & calm(paul))) & ((like(fred,susan) & like(susan,fred)) => ! [X10] : ((european(X10) & quiet(X10)) => (person(X10) & wise(X10)))) & (~(hate(john,lucy) & hate(lucy,john)) => (like(fred,susan) & like(susan,fred))) & (~~~(hate(fred,susan) & hate(susan,fred)) => (european(paul) & humble(paul) & old(paul) & person(paul) & curious(paul) & european(paul) & brave(paul))) & ((hate(mary,lucy) & hate(lucy,mary)) => ~~~(like(paul,lucy) & like(lucy,paul))) & ((hate(fred,lucy) & hate(lucy,fred)) => (hate(paul,susan) & hate(susan,paul))) & ((hate(john,lucy) & hate(lucy,john)) => ! [X11] : (hate(X11,lucy) => (european(X11) & quiet(X11)))) & (~(hate(john,lucy) & hate(lucy,john)) => (hate(john,lucy) & hate(lucy,john))) & ! [X12] : (room(X12) => (john = X12 | alice = X12 | fred = X12 | paul = X12 | mary = X12)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 44] 47. european(john) & patient(john) & ((person(john) & funny(john)) <~> (person(john) & generous(john))) & ! [X0] : ((tourist(X0) & patient(X0)) => (european(X0) & happy(X0))) & like(fred,lucy) & like(lucy,fred) & ! [X1] : ((european(X1) & generous(X1)) => (european(X1) & calm(X1))) & ! [X2] : ((tourist(X2) & wise(X2)) => happy(X2)) & hate(john,lucy) & hate(lucy,john) & ! [X3] : ((curious(X3) <~> (european(X3) & quiet(X3))) => (tourist(X3) & tall(X3))) & ~(hate(mary,susan) & hate(susan,mary)) & ! [X4] : ((european(X4) & humble(X4)) => (tourist(X4) & funny(X4))) & ! [X5] : (funny(X5) => (person(X5) & curious(X5))) & like(alice,lucy) & like(lucy,alice) & person(fred) & strong(fred) & tourist(fred) & wise(fred) & ! [X6] : ((european(X6) & creative(X6)) => (european(X6) & quiet(X6))) & tourist(mary) & calm(mary) & like(mary,lucy) & (hate(john,lucy) & hate(lucy,john)) & ! [X7] : ((fred != X7 & room(X7)) => quieter(X7,fred)) & ! [X8] : ((tourist(X8) & brave(X8)) => (tourist(X8) & patient(X8))) & ~(like(mary,susan) & like(susan,mary)) & ((like(john,susan) & like(susan,john)) => ! [X9] : ((tourist(X9) & brave(X9)) => (tourist(X9) & patient(X9)))) & ((hate(john,lucy) & hate(lucy,john)) => (like(john,susan) & like(susan,john))) & ((hate(john,susan) & hate(susan,john)) => ~(like(paul,susan) & like(susan,paul))) & (~(hate(mary,susan) & hate(susan,mary)) => (european(paul) & happy(paul) & tourist(paul) & brave(paul) & tourist(paul) & kind(paul) & person(paul) & calm(paul))) & ((like(fred,susan) & like(susan,fred)) => ! [X10] : ((european(X10) & quiet(X10)) => (person(X10) & wise(X10)))) & (~(hate(john,lucy) & hate(lucy,john)) => (like(fred,susan) & like(susan,fred))) & (~(hate(fred,susan) & hate(susan,fred)) => (european(paul) & humble(paul) & old(paul) & person(paul) & curious(paul) & european(paul) & brave(paul))) & ((hate(mary,lucy) & hate(lucy,mary)) => ~(like(paul,lucy) & like(lucy,paul))) & ((hate(fred,lucy) & hate(lucy,fred)) => (hate(paul,susan) & hate(susan,paul))) & ((hate(john,lucy) & hate(lucy,john)) => ! [X11] : (hate(X11,lucy) => (european(X11) & quiet(X11)))) & (~(hate(john,lucy) & hate(lucy,john)) => (hate(john,lucy) & hate(lucy,john))) & ! [X12] : (room(X12) => (john = X12 | alice = X12 | fred = X12 | paul = X12 | mary = X12)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 46] 48. hate(john,lucy) & hate(lucy,john) & european(john) & patient(john) & ((person(john) & funny(john)) <~> (person(john) & generous(john))) & ! [X0] : ((tourist(X0) & patient(X0)) => (european(X0) & happy(X0))) & like(fred,lucy) & like(lucy,fred) & ! [X1] : ((european(X1) & generous(X1)) => (european(X1) & calm(X1))) & ! [X2] : ((tourist(X2) & wise(X2)) => happy(X2)) & hate(john,lucy) & hate(lucy,john) & ! [X3] : ((curious(X3) <~> (european(X3) & quiet(X3))) => tourist(X3)) & ~(hate(mary,susan) & hate(susan,mary)) & ! [X4] : ((european(X4) & humble(X4)) => (tourist(X4) & funny(X4))) & ! [X5] : (funny(X5) => (person(X5) & curious(X5))) & like(alice,lucy) & like(lucy,alice) & person(fred) & strong(fred) & tourist(fred) & wise(fred) & ! [X6] : ((european(X6) & creative(X6)) => (european(X6) & quiet(X6))) & tourist(mary) & calm(mary) & like(mary,lucy) & ! [X7] : ((fred != X7 & room(X7)) => quieter(X7,fred)) & ! [X8] : ((tourist(X8) & brave(X8)) => (tourist(X8) & patient(X8))) & ~(like(mary,susan) & like(susan,mary)) & ((like(john,susan) & like(susan,john)) => ! [X9] : ((tourist(X9) & brave(X9)) => (tourist(X9) & patient(X9)))) & ((hate(john,lucy) & hate(lucy,john)) => (like(john,susan) & like(susan,john))) & ((hate(john,susan) & hate(susan,john)) => ~(like(paul,susan) & like(susan,paul))) & (~(hate(mary,susan) & hate(susan,mary)) => (european(paul) & happy(paul) & tourist(paul) & brave(paul) & tourist(paul) & kind(paul) & person(paul) & calm(paul))) & ((like(fred,susan) & like(susan,fred)) => ! [X10] : ((european(X10) & quiet(X10)) => (person(X10) & wise(X10)))) & (~(hate(john,lucy) & hate(lucy,john)) => (like(fred,susan) & like(susan,fred))) & (~(hate(fred,susan) & hate(susan,fred)) => (european(paul) & humble(paul) & old(paul) & person(paul) & curious(paul) & european(paul) & brave(paul))) & ((hate(mary,lucy) & hate(lucy,mary)) => ~(like(paul,lucy) & like(lucy,paul))) & ((hate(fred,lucy) & hate(lucy,fred)) => (hate(paul,susan) & hate(susan,paul))) & ((hate(john,lucy) & hate(lucy,john)) => ! [X11] : (hate(X11,lucy) => (european(X11) & quiet(X11)))) & (~(hate(john,lucy) & hate(lucy,john)) => (hate(john,lucy) & hate(lucy,john))) & ! [X12] : (room(X12) => (john = X12 | alice = X12 | fred = X12 | paul = X12 | mary = X12)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 47] 49. hate(john,lucy) & hate(lucy,john) & european(john) & patient(john) & ((person(john) & funny(john)) <~> (person(john) & generous(john))) & ! [X0] : ((tourist(X0) & patient(X0)) => (european(X0) & happy(X0))) & like(fred,lucy) & like(lucy,fred) & ! [X1] : ((european(X1) & generous(X1)) => (european(X1) & calm(X1))) & ! [X2] : ((tourist(X2) & wise(X2)) => happy(X2)) & hate(john,lucy) & hate(lucy,john) & ! [X3] : ((curious(X3) <~> (european(X3) & quiet(X3))) => tourist(X3)) & ~(hate(mary,susan) & hate(susan,mary)) & ! [X4] : ((european(X4) & humble(X4)) => (tourist(X4) & funny(X4))) & ! [X5] : (funny(X5) => (person(X5) & curious(X5))) & like(alice,lucy) & like(lucy,alice) & person(fred) & tourist(fred) & wise(fred) & ! [X6] : ((european(X6) & creative(X6)) => (european(X6) & quiet(X6))) & tourist(mary) & calm(mary) & like(mary,lucy) & ! [X7] : ((fred != X7 & room(X7)) => quieter(X7,fred)) & ! [X8] : ((tourist(X8) & brave(X8)) => (tourist(X8) & patient(X8))) & ~(like(mary,susan) & like(susan,mary)) & ((like(john,susan) & like(susan,john)) => ! [X9] : ((tourist(X9) & brave(X9)) => (tourist(X9) & patient(X9)))) & ((hate(john,lucy) & hate(lucy,john)) => (like(john,susan) & like(susan,john))) & ((hate(john,susan) & hate(susan,john)) => ~(like(paul,susan) & like(susan,paul))) & (~(hate(mary,susan) & hate(susan,mary)) => (european(paul) & happy(paul) & tourist(paul) & brave(paul) & tourist(paul) & kind(paul) & person(paul) & calm(paul))) & ((like(fred,susan) & like(susan,fred)) => ! [X10] : ((european(X10) & quiet(X10)) => (person(X10) & wise(X10)))) & (~(hate(john,lucy) & hate(lucy,john)) => (like(fred,susan) & like(susan,fred))) & (~(hate(fred,susan) & hate(susan,fred)) => (european(paul) & humble(paul) & old(paul) & person(paul) & curious(paul) & european(paul) & brave(paul))) & ((hate(mary,lucy) & hate(lucy,mary)) => ~(like(paul,lucy) & like(lucy,paul))) & ((hate(fred,lucy) & hate(lucy,fred)) => (hate(paul,susan) & hate(susan,paul))) & ((hate(john,lucy) & hate(lucy,john)) => ! [X11] : (hate(X11,lucy) => (european(X11) & quiet(X11)))) & (~(hate(john,lucy) & hate(lucy,john)) => (hate(john,lucy) & hate(lucy,john))) & ! [X12] : (room(X12) => (john = X12 | alice = X12 | fred = X12 | paul = X12 | mary = X12)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 48] 50. hate(john,lucy) & hate(lucy,john) & european(john) & patient(john) & ((person(john) & funny(john)) <~> (person(john) & generous(john))) & ! [X0] : ((tourist(X0) & patient(X0)) => (european(X0) & happy(X0))) & like(fred,lucy) & like(lucy,fred) & ! [X1] : ((european(X1) & generous(X1)) => (european(X1) & calm(X1))) & ! [X2] : ((tourist(X2) & wise(X2)) => happy(X2)) & hate(john,lucy) & hate(lucy,john) & ! [X3] : ((curious(X3) <~> (european(X3) & quiet(X3))) => tourist(X3)) & ~(hate(mary,susan) & hate(susan,mary)) & ! [X4] : ((european(X4) & humble(X4)) => (tourist(X4) & funny(X4))) & ! [X5] : (funny(X5) => (person(X5) & curious(X5))) & like(alice,lucy) & like(lucy,alice) & person(fred) & tourist(fred) & wise(fred) & tourist(mary) & calm(mary) & like(mary,lucy) & ! [X7] : ((fred != X7 & room(X7)) => quieter(X7,fred)) & ! [X8] : ((tourist(X8) & brave(X8)) => (tourist(X8) & patient(X8))) & ~(like(mary,susan) & like(susan,mary)) & ((like(john,susan) & like(susan,john)) => ! [X9] : ((tourist(X9) & brave(X9)) => (tourist(X9) & patient(X9)))) & ((hate(john,lucy) & hate(lucy,john)) => (like(john,susan) & like(susan,john))) & ((hate(john,susan) & hate(susan,john)) => ~(like(paul,susan) & like(susan,paul))) & (~(hate(mary,susan) & hate(susan,mary)) => (european(paul) & happy(paul) & tourist(paul) & brave(paul) & tourist(paul) & kind(paul) & person(paul) & calm(paul))) & ((like(fred,susan) & like(susan,fred)) => ! [X10] : ((european(X10) & quiet(X10)) => (person(X10) & wise(X10)))) & (~(hate(john,lucy) & hate(lucy,john)) => (like(fred,susan) & like(susan,fred))) & (~(hate(fred,susan) & hate(susan,fred)) => (european(paul) & humble(paul) & old(paul) & person(paul) & curious(paul) & european(paul) & brave(paul))) & ((hate(mary,lucy) & hate(lucy,mary)) => ~(like(paul,lucy) & like(lucy,paul))) & ((hate(fred,lucy) & hate(lucy,fred)) => (hate(paul,susan) & hate(susan,paul))) & ((hate(john,lucy) & hate(lucy,john)) => ! [X11] : (hate(X11,lucy) => (european(X11) & quiet(X11)))) & (~(hate(john,lucy) & hate(lucy,john)) => (hate(john,lucy) & hate(lucy,john))) & ! [X12] : (room(X12) => (john = X12 | alice = X12 | fred = X12 | paul = X12 | mary = X12)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 49] 51. hate(john,lucy) & hate(lucy,john) & european(john) & patient(john) & ((person(john) & funny(john)) <~> (person(john) & generous(john))) & ! [X0] : ((tourist(X0) & patient(X0)) => (european(X0) & happy(X0))) & like(fred,lucy) & like(lucy,fred) & ! [X1] : ((european(X1) & generous(X1)) => (european(X1) & calm(X1))) & ! [X2] : ((tourist(X2) & wise(X2)) => happy(X2)) & hate(john,lucy) & hate(lucy,john) & ! [X3] : ((curious(X3) <~> (european(X3) & quiet(X3))) => tourist(X3)) & ~(hate(mary,susan) & hate(susan,mary)) & ! [X4] : ((european(X4) & humble(X4)) => (tourist(X4) & funny(X4))) & ! [X5] : (funny(X5) => (person(X5) & curious(X5))) & like(alice,lucy) & like(lucy,alice) & person(fred) & tourist(fred) & wise(fred) & tourist(mary) & calm(mary) & like(mary,lucy) & ! [X7] : ((fred != X7 & room(X7)) => quieter(X7,fred)) & ! [X8] : ((tourist(X8) & brave(X8)) => (tourist(X8) & patient(X8))) & ~(like(mary,susan) & like(susan,mary)) & ((like(john,susan) & like(susan,john)) => ! [X9] : ((tourist(X9) & brave(X9)) => (tourist(X9) & patient(X9)))) & ((hate(john,lucy) & hate(lucy,john)) => (like(john,susan) & like(susan,john))) & ((hate(john,susan) & hate(susan,john)) => ~(like(paul,susan) & like(susan,paul))) & (~(hate(mary,susan) & hate(susan,mary)) => (european(paul) & happy(paul) & tourist(paul) & brave(paul) & tourist(paul) & person(paul) & calm(paul))) & ((like(fred,susan) & like(susan,fred)) => ! [X10] : ((european(X10) & quiet(X10)) => (person(X10) & wise(X10)))) & (~(hate(john,lucy) & hate(lucy,john)) => (like(fred,susan) & like(susan,fred))) & (~(hate(fred,susan) & hate(susan,fred)) => (european(paul) & humble(paul) & old(paul) & person(paul) & curious(paul) & european(paul) & brave(paul))) & ((hate(mary,lucy) & hate(lucy,mary)) => ~(like(paul,lucy) & like(lucy,paul))) & ((hate(fred,lucy) & hate(lucy,fred)) => (hate(paul,susan) & hate(susan,paul))) & ((hate(john,lucy) & hate(lucy,john)) => ! [X11] : (hate(X11,lucy) => (european(X11) & quiet(X11)))) & (~(hate(john,lucy) & hate(lucy,john)) => (hate(john,lucy) & hate(lucy,john))) & ! [X12] : (room(X12) => (john = X12 | alice = X12 | fred = X12 | paul = X12 | mary = X12)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 50] 52. hate(john,lucy) & hate(lucy,john) & european(john) & patient(john) & ((person(john) & funny(john)) <~> (person(john) & generous(john))) & ! [X0] : ((tourist(X0) & patient(X0)) => (european(X0) & happy(X0))) & like(fred,lucy) & like(lucy,fred) & ! [X1] : ((european(X1) & generous(X1)) => european(X1)) & ! [X2] : ((tourist(X2) & wise(X2)) => happy(X2)) & hate(john,lucy) & hate(lucy,john) & ! [X3] : ((curious(X3) <~> (european(X3) & quiet(X3))) => tourist(X3)) & ~(hate(mary,susan) & hate(susan,mary)) & ! [X4] : ((european(X4) & humble(X4)) => (tourist(X4) & funny(X4))) & ! [X5] : (funny(X5) => (person(X5) & curious(X5))) & like(alice,lucy) & like(lucy,alice) & person(fred) & tourist(fred) & wise(fred) & tourist(mary) & like(mary,lucy) & ! [X7] : ((fred != X7 & room(X7)) => quieter(X7,fred)) & ! [X8] : ((tourist(X8) & brave(X8)) => (tourist(X8) & patient(X8))) & ~(like(mary,susan) & like(susan,mary)) & ((like(john,susan) & like(susan,john)) => ! [X9] : ((tourist(X9) & brave(X9)) => (tourist(X9) & patient(X9)))) & ((hate(john,lucy) & hate(lucy,john)) => (like(john,susan) & like(susan,john))) & ((hate(john,susan) & hate(susan,john)) => ~(like(paul,susan) & like(susan,paul))) & (~(hate(mary,susan) & hate(susan,mary)) => (european(paul) & happy(paul) & tourist(paul) & brave(paul) & tourist(paul) & person(paul))) & ((like(fred,susan) & like(susan,fred)) => ! [X10] : ((european(X10) & quiet(X10)) => (person(X10) & wise(X10)))) & (~(hate(john,lucy) & hate(lucy,john)) => (like(fred,susan) & like(susan,fred))) & (~(hate(fred,susan) & hate(susan,fred)) => (european(paul) & humble(paul) & old(paul) & person(paul) & curious(paul) & european(paul) & brave(paul))) & ((hate(mary,lucy) & hate(lucy,mary)) => ~(like(paul,lucy) & like(lucy,paul))) & ((hate(fred,lucy) & hate(lucy,fred)) => (hate(paul,susan) & hate(susan,paul))) & ((hate(john,lucy) & hate(lucy,john)) => ! [X11] : (hate(X11,lucy) => (european(X11) & quiet(X11)))) & (~(hate(john,lucy) & hate(lucy,john)) => (hate(john,lucy) & hate(lucy,john))) & ! [X12] : (room(X12) => (john = X12 | alice = X12 | fred = X12 | paul = X12 | mary = X12)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 51] 127. hate(john,lucy) & hate(lucy,john) & european(john) & patient(john) & ((person(john) & funny(john)) <~> (person(john) & generous(john))) & ! [X0] : ((european(X0) & happy(X0)) | (~tourist(X0) | ~patient(X0))) & like(fred,lucy) & like(lucy,fred) & ! [X1] : (european(X1) | (~european(X1) | ~generous(X1))) & ! [X2] : (happy(X2) | (~tourist(X2) | ~wise(X2))) & hate(john,lucy) & hate(lucy,john) & ! [X3] : (tourist(X3) | (curious(X3) <=> (european(X3) & quiet(X3)))) & (~hate(mary,susan) | ~hate(susan,mary)) & ! [X4] : ((tourist(X4) & funny(X4)) | (~european(X4) | ~humble(X4))) & ! [X5] : ((person(X5) & curious(X5)) | ~funny(X5)) & like(alice,lucy) & like(lucy,alice) & person(fred) & tourist(fred) & wise(fred) & tourist(mary) & like(mary,lucy) & ! [X7] : (quieter(X7,fred) | (fred = X7 | ~room(X7))) & ! [X8] : ((tourist(X8) & patient(X8)) | (~tourist(X8) | ~brave(X8))) & (~like(mary,susan) | ~like(susan,mary)) & (! [X9] : ((tourist(X9) & patient(X9)) | (~tourist(X9) | ~brave(X9))) | (~like(john,susan) | ~like(susan,john))) & ((like(john,susan) & like(susan,john)) | (~hate(john,lucy) | ~hate(lucy,john))) & ((~like(paul,susan) | ~like(susan,paul)) | (~hate(john,susan) | ~hate(susan,john))) & ((european(paul) & happy(paul) & tourist(paul) & brave(paul) & tourist(paul) & person(paul)) | (hate(mary,susan) & hate(susan,mary))) & (! [X10] : ((person(X10) & wise(X10)) | (~european(X10) | ~quiet(X10))) | (~like(fred,susan) | ~like(susan,fred))) & ((like(fred,susan) & like(susan,fred)) | (hate(john,lucy) & hate(lucy,john))) & ((european(paul) & humble(paul) & old(paul) & person(paul) & curious(paul) & european(paul) & brave(paul)) | (hate(fred,susan) & hate(susan,fred))) & ((~like(paul,lucy) | ~like(lucy,paul)) | (~hate(mary,lucy) | ~hate(lucy,mary))) & ((hate(paul,susan) & hate(susan,paul)) | (~hate(fred,lucy) | ~hate(lucy,fred))) & (! [X11] : ((european(X11) & quiet(X11)) | ~hate(X11,lucy)) | (~hate(john,lucy) | ~hate(lucy,john))) & ((hate(john,lucy) & hate(lucy,john)) | (hate(john,lucy) & hate(lucy,john))) & ! [X12] : ((john = X12 | alice = X12 | fred = X12 | paul = X12 | mary = X12) | ~room(X12)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 52] 128. hate(john,lucy) & hate(lucy,john) & european(john) & patient(john) & ((person(john) & funny(john)) <~> (person(john) & generous(john))) & ! [X0] : ((european(X0) & happy(X0)) | ~tourist(X0) | ~patient(X0)) & like(fred,lucy) & like(lucy,fred) & ! [X1] : (european(X1) | ~european(X1) | ~generous(X1)) & ! [X2] : (happy(X2) | ~tourist(X2) | ~wise(X2)) & hate(john,lucy) & hate(lucy,john) & ! [X3] : (tourist(X3) | (curious(X3) <=> (european(X3) & quiet(X3)))) & (~hate(mary,susan) | ~hate(susan,mary)) & ! [X4] : ((tourist(X4) & funny(X4)) | ~european(X4) | ~humble(X4)) & ! [X5] : ((person(X5) & curious(X5)) | ~funny(X5)) & like(alice,lucy) & like(lucy,alice) & person(fred) & tourist(fred) & wise(fred) & tourist(mary) & like(mary,lucy) & ! [X7] : (quieter(X7,fred) | fred = X7 | ~room(X7)) & ! [X8] : ((tourist(X8) & patient(X8)) | ~tourist(X8) | ~brave(X8)) & (~like(mary,susan) | ~like(susan,mary)) & (! [X9] : ((tourist(X9) & patient(X9)) | ~tourist(X9) | ~brave(X9)) | ~like(john,susan) | ~like(susan,john)) & ((like(john,susan) & like(susan,john)) | ~hate(john,lucy) | ~hate(lucy,john)) & (~like(paul,susan) | ~like(susan,paul) | ~hate(john,susan) | ~hate(susan,john)) & ((european(paul) & happy(paul) & tourist(paul) & brave(paul) & tourist(paul) & person(paul)) | (hate(mary,susan) & hate(susan,mary))) & (! [X10] : ((person(X10) & wise(X10)) | ~european(X10) | ~quiet(X10)) | ~like(fred,susan) | ~like(susan,fred)) & ((like(fred,susan) & like(susan,fred)) | (hate(john,lucy) & hate(lucy,john))) & ((european(paul) & humble(paul) & old(paul) & person(paul) & curious(paul) & european(paul) & brave(paul)) | (hate(fred,susan) & hate(susan,fred))) & (~like(paul,lucy) | ~like(lucy,paul) | ~hate(mary,lucy) | ~hate(lucy,mary)) & ((hate(paul,susan) & hate(susan,paul)) | ~hate(fred,lucy) | ~hate(lucy,fred)) & (! [X11] : ((european(X11) & quiet(X11)) | ~hate(X11,lucy)) | ~hate(john,lucy) | ~hate(lucy,john)) & ((hate(john,lucy) & hate(lucy,john)) | (hate(john,lucy) & hate(lucy,john))) & ! [X12] : (john = X12 | alice = X12 | fred = X12 | paul = X12 | mary = X12 | ~room(X12)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 127] 129. ~happy(fred) | ? [X0] : ((john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 45] 130. ~happy(fred) | ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 129] 131. (european(paul) & humble(paul) & old(paul) & person(paul) & curious(paul) & european(paul) & brave(paul)) | ~sP0 [predicate definition introduction] 132. (european(paul) & happy(paul) & tourist(paul) & brave(paul) & tourist(paul) & person(paul)) | ~sP1 [predicate definition introduction] 133. hate(john,lucy) & hate(lucy,john) & european(john) & patient(john) & ((person(john) & funny(john)) <~> (person(john) & generous(john))) & ! [X0] : ((european(X0) & happy(X0)) | ~tourist(X0) | ~patient(X0)) & like(fred,lucy) & like(lucy,fred) & ! [X1] : (european(X1) | ~european(X1) | ~generous(X1)) & ! [X2] : (happy(X2) | ~tourist(X2) | ~wise(X2)) & hate(john,lucy) & hate(lucy,john) & ! [X3] : (tourist(X3) | (curious(X3) <=> (european(X3) & quiet(X3)))) & (~hate(mary,susan) | ~hate(susan,mary)) & ! [X4] : ((tourist(X4) & funny(X4)) | ~european(X4) | ~humble(X4)) & ! [X5] : ((person(X5) & curious(X5)) | ~funny(X5)) & like(alice,lucy) & like(lucy,alice) & person(fred) & tourist(fred) & wise(fred) & tourist(mary) & like(mary,lucy) & ! [X7] : (quieter(X7,fred) | fred = X7 | ~room(X7)) & ! [X8] : ((tourist(X8) & patient(X8)) | ~tourist(X8) | ~brave(X8)) & (~like(mary,susan) | ~like(susan,mary)) & (! [X9] : ((tourist(X9) & patient(X9)) | ~tourist(X9) | ~brave(X9)) | ~like(john,susan) | ~like(susan,john)) & ((like(john,susan) & like(susan,john)) | ~hate(john,lucy) | ~hate(lucy,john)) & (~like(paul,susan) | ~like(susan,paul) | ~hate(john,susan) | ~hate(susan,john)) & (sP1 | (hate(mary,susan) & hate(susan,mary))) & (! [X10] : ((person(X10) & wise(X10)) | ~european(X10) | ~quiet(X10)) | ~like(fred,susan) | ~like(susan,fred)) & ((like(fred,susan) & like(susan,fred)) | (hate(john,lucy) & hate(lucy,john))) & (sP0 | (hate(fred,susan) & hate(susan,fred))) & (~like(paul,lucy) | ~like(lucy,paul) | ~hate(mary,lucy) | ~hate(lucy,mary)) & ((hate(paul,susan) & hate(susan,paul)) | ~hate(fred,lucy) | ~hate(lucy,fred)) & (! [X11] : ((european(X11) & quiet(X11)) | ~hate(X11,lucy)) | ~hate(john,lucy) | ~hate(lucy,john)) & ((hate(john,lucy) & hate(lucy,john)) | (hate(john,lucy) & hate(lucy,john))) & ! [X12] : (john = X12 | alice = X12 | fred = X12 | paul = X12 | mary = X12 | ~room(X12)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [definition folding 128,132,131] 137. hate(john,lucy) & hate(lucy,john) & european(john) & patient(john) & (((~person(john) | ~generous(john)) | (~person(john) | ~funny(john))) & ((person(john) & generous(john)) | (person(john) & funny(john)))) & ! [X0] : ((european(X0) & happy(X0)) | ~tourist(X0) | ~patient(X0)) & like(fred,lucy) & like(lucy,fred) & ! [X1] : (european(X1) | ~european(X1) | ~generous(X1)) & ! [X2] : (happy(X2) | ~tourist(X2) | ~wise(X2)) & hate(john,lucy) & hate(lucy,john) & ! [X3] : (tourist(X3) | ((curious(X3) | (~european(X3) | ~quiet(X3))) & ((european(X3) & quiet(X3)) | ~curious(X3)))) & (~hate(mary,susan) | ~hate(susan,mary)) & ! [X4] : ((tourist(X4) & funny(X4)) | ~european(X4) | ~humble(X4)) & ! [X5] : ((person(X5) & curious(X5)) | ~funny(X5)) & like(alice,lucy) & like(lucy,alice) & person(fred) & tourist(fred) & wise(fred) & tourist(mary) & like(mary,lucy) & ! [X7] : (quieter(X7,fred) | fred = X7 | ~room(X7)) & ! [X8] : ((tourist(X8) & patient(X8)) | ~tourist(X8) | ~brave(X8)) & (~like(mary,susan) | ~like(susan,mary)) & (! [X9] : ((tourist(X9) & patient(X9)) | ~tourist(X9) | ~brave(X9)) | ~like(john,susan) | ~like(susan,john)) & ((like(john,susan) & like(susan,john)) | ~hate(john,lucy) | ~hate(lucy,john)) & (~like(paul,susan) | ~like(susan,paul) | ~hate(john,susan) | ~hate(susan,john)) & (sP1 | (hate(mary,susan) & hate(susan,mary))) & (! [X10] : ((person(X10) & wise(X10)) | ~european(X10) | ~quiet(X10)) | ~like(fred,susan) | ~like(susan,fred)) & ((like(fred,susan) & like(susan,fred)) | (hate(john,lucy) & hate(lucy,john))) & (sP0 | (hate(fred,susan) & hate(susan,fred))) & (~like(paul,lucy) | ~like(lucy,paul) | ~hate(mary,lucy) | ~hate(lucy,mary)) & ((hate(paul,susan) & hate(susan,paul)) | ~hate(fred,lucy) | ~hate(lucy,fred)) & (! [X11] : ((european(X11) & quiet(X11)) | ~hate(X11,lucy)) | ~hate(john,lucy) | ~hate(lucy,john)) & ((hate(john,lucy) & hate(lucy,john)) | (hate(john,lucy) & hate(lucy,john))) & ! [X12] : (john = X12 | alice = X12 | fred = X12 | paul = X12 | mary = X12 | ~room(X12)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [nnf transformation 133] 138. hate(john,lucy) & hate(lucy,john) & european(john) & patient(john) & (~person(john) | ~generous(john) | ~person(john) | ~funny(john)) & ((person(john) & generous(john)) | (person(john) & funny(john))) & ! [X0] : ((european(X0) & happy(X0)) | ~tourist(X0) | ~patient(X0)) & like(fred,lucy) & like(lucy,fred) & ! [X1] : (european(X1) | ~european(X1) | ~generous(X1)) & ! [X2] : (happy(X2) | ~tourist(X2) | ~wise(X2)) & hate(john,lucy) & hate(lucy,john) & ! [X3] : (tourist(X3) | ((curious(X3) | ~european(X3) | ~quiet(X3)) & ((european(X3) & quiet(X3)) | ~curious(X3)))) & (~hate(mary,susan) | ~hate(susan,mary)) & ! [X4] : ((tourist(X4) & funny(X4)) | ~european(X4) | ~humble(X4)) & ! [X5] : ((person(X5) & curious(X5)) | ~funny(X5)) & like(alice,lucy) & like(lucy,alice) & person(fred) & tourist(fred) & wise(fred) & tourist(mary) & like(mary,lucy) & ! [X7] : (quieter(X7,fred) | fred = X7 | ~room(X7)) & ! [X8] : ((tourist(X8) & patient(X8)) | ~tourist(X8) | ~brave(X8)) & (~like(mary,susan) | ~like(susan,mary)) & (! [X9] : ((tourist(X9) & patient(X9)) | ~tourist(X9) | ~brave(X9)) | ~like(john,susan) | ~like(susan,john)) & ((like(john,susan) & like(susan,john)) | ~hate(john,lucy) | ~hate(lucy,john)) & (~like(paul,susan) | ~like(susan,paul) | ~hate(john,susan) | ~hate(susan,john)) & (sP1 | (hate(mary,susan) & hate(susan,mary))) & (! [X10] : ((person(X10) & wise(X10)) | ~european(X10) | ~quiet(X10)) | ~like(fred,susan) | ~like(susan,fred)) & ((like(fred,susan) & like(susan,fred)) | (hate(john,lucy) & hate(lucy,john))) & (sP0 | (hate(fred,susan) & hate(susan,fred))) & (~like(paul,lucy) | ~like(lucy,paul) | ~hate(mary,lucy) | ~hate(lucy,mary)) & ((hate(paul,susan) & hate(susan,paul)) | ~hate(fred,lucy) | ~hate(lucy,fred)) & (! [X11] : ((european(X11) & quiet(X11)) | ~hate(X11,lucy)) | ~hate(john,lucy) | ~hate(lucy,john)) & ((hate(john,lucy) & hate(lucy,john)) | (hate(john,lucy) & hate(lucy,john))) & ! [X12] : (john = X12 | alice = X12 | fred = X12 | paul = X12 | mary = X12 | ~room(X12)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 137] 139. hate(john,lucy) & hate(lucy,john) & european(john) & patient(john) & (~person(john) | ~generous(john) | ~person(john) | ~funny(john)) & ((person(john) & generous(john)) | (person(john) & funny(john))) & ! [X0] : ((european(X0) & happy(X0)) | ~tourist(X0) | ~patient(X0)) & like(fred,lucy) & like(lucy,fred) & ! [X1] : (european(X1) | ~european(X1) | ~generous(X1)) & ! [X2] : (happy(X2) | ~tourist(X2) | ~wise(X2)) & hate(john,lucy) & hate(lucy,john) & ! [X3] : (tourist(X3) | ((curious(X3) | ~european(X3) | ~quiet(X3)) & ((european(X3) & quiet(X3)) | ~curious(X3)))) & (~hate(mary,susan) | ~hate(susan,mary)) & ! [X4] : ((tourist(X4) & funny(X4)) | ~european(X4) | ~humble(X4)) & ! [X5] : ((person(X5) & curious(X5)) | ~funny(X5)) & like(alice,lucy) & like(lucy,alice) & person(fred) & tourist(fred) & wise(fred) & tourist(mary) & like(mary,lucy) & ! [X6] : (quieter(X6,fred) | fred = X6 | ~room(X6)) & ! [X7] : ((tourist(X7) & patient(X7)) | ~tourist(X7) | ~brave(X7)) & (~like(mary,susan) | ~like(susan,mary)) & (! [X8] : ((tourist(X8) & patient(X8)) | ~tourist(X8) | ~brave(X8)) | ~like(john,susan) | ~like(susan,john)) & ((like(john,susan) & like(susan,john)) | ~hate(john,lucy) | ~hate(lucy,john)) & (~like(paul,susan) | ~like(susan,paul) | ~hate(john,susan) | ~hate(susan,john)) & (sP1 | (hate(mary,susan) & hate(susan,mary))) & (! [X9] : ((person(X9) & wise(X9)) | ~european(X9) | ~quiet(X9)) | ~like(fred,susan) | ~like(susan,fred)) & ((like(fred,susan) & like(susan,fred)) | (hate(john,lucy) & hate(lucy,john))) & (sP0 | (hate(fred,susan) & hate(susan,fred))) & (~like(paul,lucy) | ~like(lucy,paul) | ~hate(mary,lucy) | ~hate(lucy,mary)) & ((hate(paul,susan) & hate(susan,paul)) | ~hate(fred,lucy) | ~hate(lucy,fred)) & (! [X10] : ((european(X10) & quiet(X10)) | ~hate(X10,lucy)) | ~hate(john,lucy) | ~hate(lucy,john)) & ((hate(john,lucy) & hate(lucy,john)) | (hate(john,lucy) & hate(lucy,john))) & ! [X11] : (john = X11 | alice = X11 | fred = X11 | paul = X11 | mary = X11 | ~room(X11)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 138] 140. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK2 & alice != sK2 & fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 141. ~happy(fred) | (john != sK2 & alice != sK2 & fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 130,140] 239. room(mary) [cnf transformation 139] 240. room(paul) [cnf transformation 139] 241. room(fred) [cnf transformation 139] 242. room(alice) [cnf transformation 139] 243. room(john) [cnf transformation 139] 244. ~room(X11) | alice = X11 | fred = X11 | paul = X11 | mary = X11 | john = X11 [cnf transformation 139] 275. wise(fred) [cnf transformation 139] 276. tourist(fred) [cnf transformation 139] 290. ~wise(X2) | ~tourist(X2) | happy(X2) [cnf transformation 139] 305. ~happy(fred) | room(sK2) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 141] 306. ~happy(fred) | mary != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 141] 307. ~happy(fred) | paul != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 141] 308. ~happy(fred) | fred != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 141] 309. ~happy(fred) | alice != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 141] 310. ~happy(fred) | john != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 141] 487. ~happy(fred) | john != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 310,243] 488. ~happy(fred) | john != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 487,242] 489. ~happy(fred) | john != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 488,241] 490. ~happy(fred) | john != sK2 | ~room(mary) [subsumption resolution 489,240] 491. ~happy(fred) | john != sK2 [subsumption resolution 490,239] 493. 35 <=> john = sK2 [avatar definition] 495. john != sK2 <- (~35) [avatar component clause 493] 497. 36 <=> happy(fred) [avatar definition] 500. ~35 | ~36 [avatar split clause 491,497,493] 501. ~happy(fred) | alice != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 309,243] 502. ~happy(fred) | alice != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 501,242] 503. ~happy(fred) | alice != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 502,241] 504. ~happy(fred) | alice != sK2 | ~room(mary) [subsumption resolution 503,240] 505. ~happy(fred) | alice != sK2 [subsumption resolution 504,239] 507. 37 <=> alice = sK2 [avatar definition] 509. alice != sK2 <- (~37) [avatar component clause 507] 510. ~37 | ~36 [avatar split clause 505,497,507] 511. ~happy(fred) | fred != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 308,243] 512. ~happy(fred) | fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 511,242] 513. ~happy(fred) | fred != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 512,241] 514. ~happy(fred) | fred != sK2 | ~room(mary) [subsumption resolution 513,240] 515. ~happy(fred) | fred != sK2 [subsumption resolution 514,239] 517. 38 <=> fred = sK2 [avatar definition] 519. fred != sK2 <- (~38) [avatar component clause 517] 520. ~38 | ~36 [avatar split clause 515,497,517] 521. ~happy(fred) | paul != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 307,243] 522. ~happy(fred) | paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 521,242] 523. ~happy(fred) | paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 522,241] 524. ~happy(fred) | paul != sK2 | ~room(mary) [subsumption resolution 523,240] 525. ~happy(fred) | paul != sK2 [subsumption resolution 524,239] 527. 39 <=> paul = sK2 [avatar definition] 529. paul != sK2 <- (~39) [avatar component clause 527] 530. ~39 | ~36 [avatar split clause 525,497,527] 531. ~happy(fred) | mary != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 306,243] 532. ~happy(fred) | mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 531,242] 533. ~happy(fred) | mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 532,241] 534. ~happy(fred) | mary != sK2 | ~room(mary) [subsumption resolution 533,240] 535. ~happy(fred) | mary != sK2 [subsumption resolution 534,239] 537. 40 <=> mary = sK2 [avatar definition] 539. mary != sK2 <- (~40) [avatar component clause 537] 540. ~40 | ~36 [avatar split clause 535,497,537] 541. ~happy(fred) | room(sK2) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 305,243] 542. ~happy(fred) | room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 541,242] 543. ~happy(fred) | room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 542,241] 544. ~happy(fred) | room(sK2) | ~room(mary) [subsumption resolution 543,240] 545. ~happy(fred) | room(sK2) [subsumption resolution 544,239] 547. 41 <=> room(sK2) [avatar definition] 549. room(sK2) <- (41) [avatar component clause 547] 550. 41 | ~36 [avatar split clause 545,497,547] 571. ~tourist(fred) | happy(fred) [resolution 290,275] 572. happy(fred) [subsumption resolution 571,276] 575. 36 [avatar split clause 572,497] 686. alice = sK2 | fred = sK2 | paul = sK2 | mary = sK2 | john = sK2 <- (41) [resolution 244,549] 687. fred = sK2 | paul = sK2 | mary = sK2 | john = sK2 <- (~37, 41) [subsumption resolution 686,509] 688. paul = sK2 | mary = sK2 | john = sK2 <- (~37, ~38, 41) [subsumption resolution 687,519] 689. mary = sK2 | john = sK2 <- (~37, ~38, ~39, 41) [subsumption resolution 688,529] 690. john = sK2 <- (~37, ~38, ~39, ~40, 41) [subsumption resolution 689,539] 691. $false <- (~35, ~37, ~38, ~39, ~40, 41) [subsumption resolution 690,495] 692. 35 | 37 | 38 | 39 | 40 | ~41 [avatar contradiction clause 691] 693. $false [avatar sat refutation 500,510,520,530,540,550,575,692] % SZS output end Proof for 8720484514115727460835113 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.023 s % ------------------------------ % ------------------------------

Elizabeth is the only person in the room. If “everyone in the room does not enjoy fishing or collects action figures” then “at least one person in the room has a tattoo”. If “at least one person in the room has a tattoo” then “if someone enjoys fishing then he/she does not enjoy making ceramics and vice versa”. Everyone outside the room collects action figures if they enjoys making ceramics and enjoys fishing. Everyone in the room enjoys making ceramics if they collects action figures.

Not everyone in the room collects action figures.

neutral

room(elizabeth)&(![X]:(room(X)=>(X='elizabeth')))& (((![X]:(room(X)=>(((collects_action_figures(X))|(does_not_enjoy_fishing(X))))))=>(((?[X]:(room(X)&has_a_tattoo(X))))))& ((((?[X]:(room(X)&has_a_tattoo(X)))))=>((![X]:((enjoys_fishing(X))<=>(does_not_enjoy_making_ceramics(X)))))))& (![X]:(~room(X)=>(((((enjoys_making_ceramics(X))&(enjoys_fishing(X))))=>(collects_action_figures(X))))))& (![X]:(room(X)=>(((collects_action_figures(X))=>(enjoys_making_ceramics(X))))))

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

Connie is the only person in the room. If “everyone in the room enjoys bird watching or does not enjoy virtual reality gaming” then “Connie neither collects rare minerals nor practices pilates”. “If someone either enjoys virtual reality gaming or is a cybersecurity expert but not both then he/she streams on Twitch” if “Connie enjoys bird watching”. Either “Connie uses contact lenses” or “Connie practices pilates” but not both. Either “Connie practices and performs acrobatic dance routines” or “everyone in the room collects rare minerals or does not practice pilates” but not both. If someone is a dedicated advocate for digital privacy and encryption then he/she either enjoys landscape photography or makes homemade pastries but not both and vice versa. Everyone in the room who practices tai chi enjoys origami. If someone makes homemade pastries then he/she practices and performs acrobatic dance routines. Connie is an expert in identifying and foraging wild edible plants. Connie collects rare and antique scientific instruments. Everyone in the room who is an expert in identifying and foraging wild edible plants enjoys kayaking. It is not the case that “it is not the case that “Connie collects rare and antique scientific instruments””. Connie makes homemade pastries. Connie is a tea enthusiast. Connie hosts regular game nights featuring complex strategy games. Connie is an enthusiastic bird watcher who travels for rare sightings. Connie neither enjoys landscape photography nor knows morse code. Connie either is a tea enthusiast or enjoys snowboarding but not both. Connie is a coffee connoisseur.

Connie enjoys bird watching.

contradiction

room(connie)&(![X]:(room(X)=>(X='connie')))& ((![X]:(room(X)=>(((does_not_enjoy_virtual_reality_gaming(X))|(enjoys_bird_watching(X))))))=>(~((collects_rare_minerals(connie))|(practices_pilates(connie)))))& ((enjoys_bird_watching(connie))=>((![X]:((((enjoys_virtual_reality_gaming(X))<~>(is_a_cybersecurity_expert(X))))=>(streams_on_Twitch(X))))))& ((uses_contact_lenses(connie))<~>(practices_pilates(connie)))& ((practices_and_performs_acrobatic_dance_routines(connie))<~>(![X]:(room(X)=>(((does_not_practice_pilates(X))|(collects_rare_minerals(X)))))))& ((![X]:((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))<=>(((enjoys_landscape_photography(X))<~>(makes_homemade_pastries(X)))))))& (![X]:(room(X)=>(((practices_tai_chi(X))=>(enjoys_origami(X))))))& ((![X]:((makes_homemade_pastries(X))=>(practices_and_performs_acrobatic_dance_routines(X)))))& (is_an_expert_in_identifying_and_foraging_wild_edible_plants(connie))& (collects_rare_and_antique_scientific_instruments(connie))& (![X]:(room(X)=>(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))=>(enjoys_kayaking(X))))))& (~(~(collects_rare_and_antique_scientific_instruments(connie))))& (makes_homemade_pastries(connie))& (is_a_tea_enthusiast(connie))& (hosts_regular_game_nights_featuring_complex_strategy_games(connie))& (is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(connie))& (~((enjoys_landscape_photography(connie))|(knows_morse_code(connie))))& (((is_a_tea_enthusiast(connie))<~>(enjoys_snowboarding(connie))))& (is_a_coffee_connoisseur(connie))

room(connie)&(![X]:(room(X)=>(X='connie')))& enjoys_bird_watching(connie)

% SZS status Unsatisfiable for 5227253844762348239419963 % SZS output start Proof for 5227253844762348239419963 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 45. ! [X0] : (room(X0) => (predm(X0) | ~prede(X0))) => ~(predq(mary) | predb(mary)) [input p1] 48. predp(mary) <~> ! [X0] : (room(X0) => (predb(X0) | ~predq(X0))) [input p4] 51. ! [X0] : (predw(X0) => predp(X0)) [input p7] 56. predw(mary) [input p12] 63. predm(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 75. ! [X0] : (room(X0) => predm(X0)) => ~(predq(mary) | predb(mary)) [pure predicate removal 45] 148. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 149. (~predq(mary) & ~predb(mary)) | ? [X0] : (~predm(X0) & room(X0)) [ennf transformation 75] 150. predp(mary) <~> ! [X0] : ((predb(X0) | ~predq(X0)) | ~room(X0)) [ennf transformation 48] 151. predp(mary) <~> ! [X0] : (predb(X0) | ~predq(X0) | ~room(X0)) [flattening 150] 152. ! [X0] : (predp(X0) | ~predw(X0)) [ennf transformation 51] 153. predm(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 63] 155. ? [X0] : (~predm(X0) & room(X0)) => (~predm(sK0) & room(sK0)) [choice axiom] 156. (~predq(mary) & ~predb(mary)) | (~predm(sK0) & room(sK0)) [skolemisation 149,155] 158. (? [X0] : (~predb(X0) & predq(X0) & room(X0)) | ~predp(mary)) & (! [X0] : (predb(X0) | ~predq(X0) | ~room(X0)) | predp(mary)) [nnf transformation 151] 159. (? [X0] : (~predb(X0) & predq(X0) & room(X0)) | ~predp(mary)) & (! [X1] : (predb(X1) | ~predq(X1) | ~room(X1)) | predp(mary)) [rectify 158] 160. ? [X0] : (~predb(X0) & predq(X0) & room(X0)) => (~predb(sK1) & predq(sK1) & room(sK1)) [choice axiom] 161. ((~predb(sK1) & predq(sK1) & room(sK1)) | ~predp(mary)) & (! [X1] : (predb(X1) | ~predq(X1) | ~room(X1)) | predp(mary)) [skolemisation 159,160] 244. ~room(X0) | mary = X0 [cnf transformation 148] 247. ~predq(mary) | room(sK0) [cnf transformation 156] 248. ~predq(mary) | ~predm(sK0) [cnf transformation 156] 252. room(sK1) | ~predp(mary) [cnf transformation 161] 253. predq(sK1) | ~predp(mary) [cnf transformation 161] 255. ~predw(X0) | predp(X0) [cnf transformation 152] 256. predw(mary) [cnf transformation 56] 262. predm(mary) [cnf transformation 153] 264. 1 <=> predm(sK0) [avatar definition] 266. ~predm(sK0) <- (~1) [avatar component clause 264] 268. 2 <=> predq(mary) [avatar definition] 271. ~1 | ~2 [avatar split clause 248,268,264] 273. 3 <=> room(sK0) [avatar definition] 275. room(sK0) <- (3) [avatar component clause 273] 276. 3 | ~2 [avatar split clause 247,268,273] 290. 6 <=> predp(mary) [avatar definition] 299. 8 <=> predq(sK1) [avatar definition] 301. predq(sK1) <- (8) [avatar component clause 299] 302. ~6 | 8 [avatar split clause 253,299,290] 304. 9 <=> room(sK1) [avatar definition] 306. room(sK1) <- (9) [avatar component clause 304] 307. ~6 | 9 [avatar split clause 252,304,290] 313. predp(mary) [resolution 255,256] 315. mary = sK0 <- (3) [resolution 244,275] 316. mary = sK1 <- (9) [resolution 244,306] 317. ~predm(mary) <- (~1, 3) [backward demodulation 266,315] 319. $false <- (~1, 3) [subsumption resolution 317,262] 320. 1 | ~3 [avatar contradiction clause 319] 322. predq(mary) <- (8, 9) [backward demodulation 301,316] 325. 2 | ~8 | ~9 [avatar split clause 322,304,299,268] 326. 6 [avatar split clause 313,290] 328. $false [avatar sat refutation 271,276,302,307,320,325,326] % SZS output end Proof for 5227253844762348239419963 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Barbara is the only person in the room. Everyone in the room who enjoys coding in Python or owns an extensive assortment of vintage comic book memorabilia or both enjoys coding in Python. If someone enjoys coding in Python then he/she is allergic to anything and vice versa. Barbara does not enjoy salsa dancing or enjoys stargazing or both. Barbara who competes in national level swimming championships enjoys salsa dancing or enjoys stargazing or both. Barbara competes in national level swimming championships. Barbara who has a saltwater aquarium maintains a large, organic vegetable garden year-round or competes in national level swimming championships or both. Barbara owns an extensive assortment of vintage comic book memorabilia.

Barbara drives a hybrid car, enjoys stargazing and enjoys making ceramics.

neutral

room(barbara)&(![X]:(room(X)=>(X='barbara')))& (![X]:(room(X)=>(((((enjoys_coding_in_Python(X))|(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))=>(enjoys_coding_in_Python(X))))))& ((![X]:((enjoys_coding_in_Python(X))<=>(is_allergic_to_anything(X)))))& (((does_not_enjoy_salsa_dancing(barbara))|(enjoys_stargazing(barbara))))& ((competes_in_national_level_swimming_championships(barbara))&(((enjoys_salsa_dancing(barbara))|(enjoys_stargazing(barbara)))))& (competes_in_national_level_swimming_championships(barbara))& ((has_a_saltwater_aquarium(barbara))&(((maintains_a_large,_organic_vegetable_garden_year-round(barbara))|(competes_in_national_level_swimming_championships(barbara)))))& (owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(barbara))& (((?[X]:(room(X)&drives_a_hybrid_car(X)))))& (![X]:(room(X)=>(((enjoys_stargazing(X))=>(collects_historical_artifacts_related_to_ancient_civilizations(X))))))& (![X]:(room(X)=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))|(does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))))))& (![X]:(room(X)=>(((enjoys_coding_in_Python(X))<=(does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))))))& (enjoys_origami(barbara))& (has_a_specialized_collection_of_handmade_artisan_pottery(barbara))& (![X]:(room(X)=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))=>(((drives_a_hybrid_car(X))|(enjoys_making_ceramics(X))))))))& (![X]:(~room(X)=>(((((enjoys_salsa_dancing(X))<~>(enjoys_stargazing(X))))=>(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))))& (![X]:(anywhere(X)=>(((((enjoys_origami(X))<~>(collects_historical_artifacts_related_to_ancient_civilizations(X))))=>(is_allergic_to_anything(X))))))& (![X]:(room(X)=>(((is_allergic_to_anything(X))=>(collects_historical_artifacts_related_to_ancient_civilizations(X))))))& (![X]:(~room(X)=>(((((enjoys_origami(X))&(has_a_specialized_collection_of_handmade_artisan_pottery(X))))<=(is_a_Linux_enthusiast(X))))))& (![X]:(room(X)=>(((does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))|(competes_in_national_level_swimming_championships(X))))))

room(barbara)&(![X]:(room(X)=>(X='barbara')))& ((drives_a_hybrid_car(barbara))&(enjoys_stargazing(barbara))&(enjoys_making_ceramics(barbara)))

Mark, Edna, Clyde, Jason are the only persons in the room. Mark has a specialized collection of handmade artisan pottery. Everyone outside the room who enjoys rooftop gardening writes and illustrates their own graphic novels. Everyone in the room who has a specialized collection of handmade artisan pottery writes and illustrates their own graphic novels. If someone neither writes and illustrates their own graphic novels nor enjoys rooftop gardening then he/she either enjoys rooftop gardening or has a specialized collection of handmade artisan pottery but not both. Everyone in the room does not enjoy windsurfing or enjoys rooftop gardening. Mark enjoys cross-country skiing. Everyone in the room who either writes and illustrates their own graphic novels or enjoys cross-country skiing but not both enjoys cross-country skiing. Mark writes and illustrates their own graphic novels. Mark enjoys rooftop gardening. Everyone in the room owns a significant collection of rare gemstones and minerals if and only if they neither writes and illustrates their own graphic novels nor enjoys rooftop gardening. Mark enjoys windsurfing. Everyone in the room who neither owns a significant collection of rare gemstones and minerals nor has a specialized collection of handmade artisan pottery writes and illustrates their own graphic novels. Everyone in the room writes and illustrates their own graphic novels only if they owns a significant collection of rare gemstones and minerals or writes and illustrates their own graphic novels or both.

Clyde enjoys cross-country skiing.

entailment

room(mark)&room(edna)&room(clyde)&room(jason)&(![X]:(room(X)=>(X='mark'|X='edna'|X='clyde'|X='jason')))& (has_a_specialized_collection_of_handmade_artisan_pottery(mark))& (![X]:(~room(X)=>(((enjoys_rooftop_gardening(X))=>(writes_and_illustrates_their_own_graphic_novels(X))))))& (![X]:(room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))=>(writes_and_illustrates_their_own_graphic_novels(X))))))& ((![X]:((~((writes_and_illustrates_their_own_graphic_novels(X))|(enjoys_rooftop_gardening(X))))=>(((enjoys_rooftop_gardening(X))<~>(has_a_specialized_collection_of_handmade_artisan_pottery(X)))))))& (![X]:(room(X)=>(((enjoys_rooftop_gardening(X))|(does_not_enjoy_windsurfing(X))))))& (enjoys_cross-country_skiing(mark))& (![X]:(room(X)=>(((((writes_and_illustrates_their_own_graphic_novels(X))<~>(enjoys_cross-country_skiing(X))))=>(enjoys_cross-country_skiing(X))))))& (writes_and_illustrates_their_own_graphic_novels(mark))& (enjoys_rooftop_gardening(mark))& (![X]:(room(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))<=>(~((writes_and_illustrates_their_own_graphic_novels(X))|(enjoys_rooftop_gardening(X))))))))& (enjoys_windsurfing(mark))& (![X]:(room(X)=>(((~((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))|(has_a_specialized_collection_of_handmade_artisan_pottery(X))))=>(writes_and_illustrates_their_own_graphic_novels(X))))))& (![X]:(room(X)=>(((((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))|(writes_and_illustrates_their_own_graphic_novels(X))))<=(writes_and_illustrates_their_own_graphic_novels(X))))))

room(mark)&room(edna)&room(clyde)&room(jason)&(![X]:(room(X)=>(X='mark'|X='edna'|X='clyde'|X='jason')))& enjoys_cross-country_skiing(clyde)

% SZS status Unsatisfiable for 3114302095192892124439788 % SZS output start Proof for 3114302095192892124439788 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 47. ! [X0] : (room(X0) => (preda(X0) => predc(X0))) [input p3] 48. ! [X0] : (~(predf(X0) | predc(X0)) => (predf(X0) <~> preda(X0))) [input p4] 51. ! [X0] : (room(X0) => ((predc(X0) <~> predb(X0)) => predb(X0))) [input p7] 54. ! [X0] : (room(X0) => (predd(X0) <=> ~(predf(X0) | predc(X0)))) [input p10] 56. ! [X0] : (room(X0) => (~(preda(X0) | predd(X0)) => predc(X0))) [input p12] 58. ~(predb(fred) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 131. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 132. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 131] 135. ! [X0] : ((predc(X0) | ~preda(X0)) | ~room(X0)) [ennf transformation 47] 136. ! [X0] : (predc(X0) | ~preda(X0) | ~room(X0)) [flattening 135] 137. ! [X0] : ((predf(X0) <~> preda(X0)) | (predf(X0) | predc(X0))) [ennf transformation 48] 138. ! [X0] : ((predf(X0) <~> preda(X0)) | predf(X0) | predc(X0)) [flattening 137] 141. ! [X0] : ((predb(X0) | (predc(X0) <=> predb(X0))) | ~room(X0)) [ennf transformation 51] 142. ! [X0] : (predb(X0) | (predc(X0) <=> predb(X0)) | ~room(X0)) [flattening 141] 143. ! [X0] : ((predd(X0) <=> (~predf(X0) & ~predc(X0))) | ~room(X0)) [ennf transformation 54] 144. ! [X0] : ((predc(X0) | (preda(X0) | predd(X0))) | ~room(X0)) [ennf transformation 56] 145. ! [X0] : (predc(X0) | preda(X0) | predd(X0) | ~room(X0)) [flattening 144] 148. ~predb(fred) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 58] 149. ~predb(fred) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 148] 151. ! [X0] : (((~preda(X0) | ~predf(X0)) & (preda(X0) | predf(X0))) | predf(X0) | predc(X0)) [nnf transformation 138] 152. ! [X0] : (predb(X0) | ((predc(X0) | ~predb(X0)) & (predb(X0) | ~predc(X0))) | ~room(X0)) [nnf transformation 142] 153. ! [X0] : (((predd(X0) | (predf(X0) | predc(X0))) & ((~predf(X0) & ~predc(X0)) | ~predd(X0))) | ~room(X0)) [nnf transformation 143] 154. ! [X0] : (((predd(X0) | predf(X0) | predc(X0)) & ((~predf(X0) & ~predc(X0)) | ~predd(X0))) | ~room(X0)) [flattening 153] 155. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK0 & fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) [choice axiom] 156. ~predb(fred) | (alice != sK0 & fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 149,155] 237. room(mary) [cnf transformation 132] 238. room(paul) [cnf transformation 132] 239. room(fred) [cnf transformation 132] 240. room(alice) [cnf transformation 132] 241. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 132] 244. ~preda(X0) | predc(X0) | ~room(X0) [cnf transformation 136] 245. preda(X0) | predf(X0) | predf(X0) | predc(X0) [cnf transformation 151] 249. predb(X0) | predb(X0) | ~predc(X0) | ~room(X0) [cnf transformation 152] 254. ~predd(X0) | ~predf(X0) | ~room(X0) [cnf transformation 154] 257. predc(X0) | preda(X0) | predd(X0) | ~room(X0) [cnf transformation 145] 259. ~predb(fred) | room(sK0) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 156] 260. ~predb(fred) | mary != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 156] 261. ~predb(fred) | paul != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 156] 262. ~predb(fred) | fred != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 156] 263. ~predb(fred) | alice != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 156] 264. ~predc(X0) | predb(X0) | ~room(X0) [duplicate literal removal 249] 265. predc(X0) | predf(X0) | preda(X0) [duplicate literal removal 245] 266. ~room(X0) | predd(X0) | predc(X0) [subsumption resolution 257,244] 267. ~predb(fred) | alice != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 263,240] 268. ~predb(fred) | alice != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 267,239] 269. ~predb(fred) | alice != sK0 | ~room(mary) [subsumption resolution 268,238] 270. ~predb(fred) | alice != sK0 [subsumption resolution 269,237] 272. 1 <=> alice = sK0 [avatar definition] 274. alice != sK0 <- (~1) [avatar component clause 272] 276. 2 <=> predb(fred) [avatar definition] 279. ~1 | ~2 [avatar split clause 270,276,272] 280. ~predb(fred) | fred != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 262,240] 281. ~predb(fred) | fred != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 280,239] 282. ~predb(fred) | fred != sK0 | ~room(mary) [subsumption resolution 281,238] 283. ~predb(fred) | fred != sK0 [subsumption resolution 282,237] 285. 3 <=> fred = sK0 [avatar definition] 287. fred != sK0 <- (~3) [avatar component clause 285] 288. ~3 | ~2 [avatar split clause 283,276,285] 289. ~predb(fred) | paul != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 261,240] 290. ~predb(fred) | paul != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 289,239] 291. ~predb(fred) | paul != sK0 | ~room(mary) [subsumption resolution 290,238] 292. ~predb(fred) | paul != sK0 [subsumption resolution 291,237] 294. 4 <=> paul = sK0 [avatar definition] 296. paul != sK0 <- (~4) [avatar component clause 294] 297. ~4 | ~2 [avatar split clause 292,276,294] 298. ~predb(fred) | mary != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 260,240] 299. ~predb(fred) | mary != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 298,239] 300. ~predb(fred) | mary != sK0 | ~room(mary) [subsumption resolution 299,238] 301. ~predb(fred) | mary != sK0 [subsumption resolution 300,237] 303. 5 <=> mary = sK0 [avatar definition] 305. mary != sK0 <- (~5) [avatar component clause 303] 306. ~5 | ~2 [avatar split clause 301,276,303] 307. ~predb(fred) | room(sK0) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 259,240] 308. ~predb(fred) | room(sK0) | ~room(paul) | ~room(mary) [subsumption resolution 307,239] 309. ~predb(fred) | room(sK0) | ~room(mary) [subsumption resolution 308,238] 310. ~predb(fred) | room(sK0) [subsumption resolution 309,237] 312. 6 <=> room(sK0) [avatar definition] 314. room(sK0) <- (6) [avatar component clause 312] 315. 6 | ~2 [avatar split clause 310,276,312] 323. predd(fred) | predc(fred) [resolution 266,239] 335. 9 <=> predc(fred) [avatar definition] 336. ~predc(fred) <- (~9) [avatar component clause 335] 337. predc(fred) <- (9) [avatar component clause 335] 339. 10 <=> predd(fred) [avatar definition] 341. predd(fred) <- (10) [avatar component clause 339] 342. 9 | 10 [avatar split clause 323,339,335] 358. predb(fred) | ~room(fred) <- (9) [resolution 337,264] 362. predb(fred) <- (9) [subsumption resolution 358,239] 363. 2 | ~9 [avatar split clause 362,335,276] 381. 16 <=> predf(fred) [avatar definition] 385. predf(fred) | preda(fred) <- (~9) [resolution 336,265] 387. 17 <=> preda(fred) [avatar definition] 389. preda(fred) <- (17) [avatar component clause 387] 390. 17 | 16 | 9 [avatar split clause 385,335,381,387] 394. ~predf(fred) | ~room(fred) <- (10) [resolution 341,254] 396. ~predf(fred) <- (10) [subsumption resolution 394,239] 397. ~16 | ~10 [avatar split clause 396,339,381] 419. predc(fred) | ~room(fred) <- (17) [resolution 389,244] 420. ~room(fred) <- (~9, 17) [subsumption resolution 419,336] 421. $false <- (~9, 17) [subsumption resolution 420,239] 422. 9 | ~17 [avatar contradiction clause 421] 473. fred = sK0 | paul = sK0 | mary = sK0 | alice = sK0 <- (6) [resolution 241,314] 474. paul = sK0 | mary = sK0 | alice = sK0 <- (~3, 6) [subsumption resolution 473,287] 475. mary = sK0 | alice = sK0 <- (~3, ~4, 6) [subsumption resolution 474,296] 476. alice = sK0 <- (~3, ~4, ~5, 6) [subsumption resolution 475,305] 477. $false <- (~1, ~3, ~4, ~5, 6) [subsumption resolution 476,274] 478. 1 | 3 | 4 | 5 | ~6 [avatar contradiction clause 477] 479. $false [avatar sat refutation 279,288,297,306,315,342,363,390,397,422,478] % SZS output end Proof for 3114302095192892124439788 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 “no one in the room practices pilates” then “everyone in the room can play the guitar if they makes intricate hand-cut paper art for exhibitions”. Either “everyone in the room enjoys stargazing or does not practice pilates” or “everyone in the room makes intricate hand-cut paper art for exhibitions or cannot play the guitar” but not both. If “everyone anywhere is a certified yoga instructor teaching classes weekly or does not make intricate hand-cut paper art for exhibitions” then “everyone in the room makes intricate hand-cut paper art for exhibitions if they enjoys stargazing”. Everyone in the room does not practice pilates. Everyone in the room enjoys stargazing or is not a certified yoga instructor teaching classes weekly. Everyone in the room who enjoys stargazing cannot play the guitar and participates in citizen science projects related to wildlife monitoring. Everyone in the room who cannot play the guitar and participates in citizen science projects related to wildlife monitoring can play the guitar. Everyone in the room who practices pilates does not participate in citizen science projects related to wildlife monitoring.

Everyone outside the room does not practice pilates.

neutral

(there_is_a_room)& ((~?[X]:(room(X)=>(practices_pilates(X))))=>(![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))=>(can_play_the_guitar(X)))))))& ((![X]:(room(X)=>(((does_not_practice_pilates(X))|(enjoys_stargazing(X))))))<~>(![X]:(room(X)=>(((cannot_play_the_guitar(X))|(makes_intricate_hand-cut_paper_art_for_exhibitions(X)))))))& ((![X]:(anywhere(X)=>(((does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))|(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))=>(![X]:(room(X)=>(((enjoys_stargazing(X))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X)))))))& (![X]:(room(X)=>(does_not_practice_pilates(X))))& (![X]:(room(X)=>(((is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))|(enjoys_stargazing(X))))))& (![X]:(room(X)=>(((enjoys_stargazing(X))=>(((cannot_play_the_guitar(X))&(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))))& (![X]:(room(X)=>(((((cannot_play_the_guitar(X))&(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))=>(can_play_the_guitar(X))))))& (![X]:(room(X)=>(((practices_pilates(X))=>(does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))

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

Ida, Joseph, Tommie, Cynthia, Michael are the only persons in the room. If 'Ida hosts regular game nights featuring complex strategy games' then 'Ida either is not allergic to anything or knows morse code but not both'. If 'Ida does not have a saltwater aquarium' then 'more than one person in the room builds model airplanes'. If 'at least one person in the room creates YouTube content' then 'Ida enjoys wildlife photography'. If 'Ida has a vast collection of first-edition science fiction novels' then 'Ida is not a certified yoga instructor teaching classes weekly'. If 'Ida enjoys skydiving' then 'Ida does not have lived in exactly three countries'. Either 'Ida plays as a goalkeeper for a local amateur soccer team' or 'Ida is a certified yoga instructor teaching classes weekly, mentors a youth basketball team on weekends and practices digital art' but not both. Ida practices graffiti art. Ida has a saltwater aquarium. Ida builds model airplanes, has lived in exactly three countries or owns an extensive assortment of vintage comic book memorabilia. At least one person in the room is allergic to anything. Ida mentors a youth basketball team on weekends. It is not the case that 'Ida plays as a goalkeeper for a local amateur soccer team'. If someone has a saltwater aquarium and creates YouTube content then he/she practices tai chi. If someone is not an avid mountain climber who has scaled several peaks then he/she creates YouTube content and vice versa. If someone owns an extensive assortment of vintage comic book memorabilia then he/she does not have lived in exactly three countries and vice versa. Ida owns an extensive assortment of vintage comic book memorabilia. Ida enjoys kayaking and exploring remote waterways. More than one person in the room enjoys skydiving. It is true that 'if someone is an avid mountain climber who has scaled several peaks then he/she neither does not enjoy mountain biking nor hosts regular game nights featuring complex strategy games'.

Ida neither mentors a youth basketball team on weekends nor creates YouTube content.

contradiction

room(ida)&room(joseph)&room(tommie)&room(cynthia)&room(michael)&(![X]:(room(X)=>(X='ida'|X='joseph'|X='tommie'|X='cynthia'|X='michael')))& ((hosts_regular_game_nights_featuring_complex_strategy_games(ida))=>(((is_not_allergic_to_anything(ida))<~>(knows_morse_code(ida)))))& ((does_not_have_a_saltwater_aquarium(ida))=>((?[X,Y]:(room(X)&room(Y)&(builds_model_airplanes(X)&builds_model_airplanes(Y))&(X!=Y)))))& ((((?[X]:(room(X)&creates_YouTube_content(X)))))=>(enjoys_wildlife_photography(ida)))& ((has_a_vast_collection_of_first-edition_science_fiction_novels(ida))=>(is_not_a_certified_yoga_instructor_teaching_classes_weekly(ida)))& ((enjoys_skydiving(ida))=>(does_not_have_lived_in_exactly_three_countries(ida)))& ((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(ida))<~>(((is_a_certified_yoga_instructor_teaching_classes_weekly(ida))&(mentors_a_youth_basketball_team_on_weekends(ida))&(practices_digital_art(ida)))))& (practices_graffiti_art(ida))& (has_a_saltwater_aquarium(ida))& (((builds_model_airplanes(ida))|(has_lived_in_exactly_three_countries(ida))|(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(ida))))& (((?[X]:(room(X)&is_allergic_to_anything(X)))))& (mentors_a_youth_basketball_team_on_weekends(ida))& (~(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(ida)))& ((![X]:((((has_a_saltwater_aquarium(X))&(creates_YouTube_content(X))))=>(practices_tai_chi(X)))))& ((![X]:((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))<=>(creates_YouTube_content(X)))))& ((![X]:((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))<=>(does_not_have_lived_in_exactly_three_countries(X)))))& (owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(ida))& (enjoys_kayaking_and_exploring_remote_waterways(ida))& ((?[X,Y]:(room(X)&room(Y)&(enjoys_skydiving(X)&enjoys_skydiving(Y))&(X!=Y))))& ((![X]:((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(~((does_not_enjoy_mountain_biking(X))|(hosts_regular_game_nights_featuring_complex_strategy_games(X)))))))

room(ida)&room(joseph)&room(tommie)&room(cynthia)&room(michael)&(![X]:(room(X)=>(X='ida'|X='joseph'|X='tommie'|X='cynthia'|X='michael')))& ~((mentors_a_youth_basketball_team_on_weekends(ida))|(creates_YouTube_content(ida)))

% SZS status Unsatisfiable for 7091706117675116708167362 % SZS output start Proof for 7091706117675116708167362 55. predw(mary) [input p11] 64. ~(predo(mary) | predw(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] 83. ~predw(mary) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 64] 159. ~predw(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 83] 160. ~predw(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 159] 259. predw(mary) [cnf transformation 55] 270. ~predw(mary) [cnf transformation 160] 280. 3 <=> predw(mary) [avatar definition] 291. 3 [avatar split clause 259,280] 293. ~3 [avatar split clause 270,280] 294. $false [avatar sat refutation 291,293] % SZS output end Proof for 7091706117675116708167362 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Petra, Diane are the only persons in the room. Either “at least one person in the room is a calm person” or “Florence is richer than Diane” but not both. If “someone anywhere either is richer than Florence or is a generous old person but not both” then “everyone in the room neither is a old brave person nor is a quiet person if they is a calm strong person”. “Petra is older than Kimberly” if “Diane is a humble calm person” and vice versa.

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(petra)&room(diane)&(![X]:(room(X)=>(X='petra'|X='diane')))& ((((?[X]:(room(X)&calm(X)&person(X)))))<~>(richer(diane,florence)))& ((?[X]:(anywhere(X)&(((richer(florence,X))<~>(generous(X)&old(X)&person(X))))))=>(![X]:(room(X)=>(((calm(X)&strong(X)&person(X))=>(~((old(X)&brave(X)&person(X))|(quiet(X)&person(X)))))))))& ((humble(diane)&calm(diane)&person(diane))<=>(older(kimberly,petra)))& ((quiet(petra)&patient(petra)&person(petra))=>(calm(petra)&person(petra)))& ((calm(diane))<~>(generous(petra)))& ((quiet(diane))=>(older(kimberly,petra)))& ((richer(diane,eleanor))=>(![X]:(patient(X)=>quiet(X))))& ((quieter(eleanor,diane))=>(((~(patient(diane)&wise(diane)&curious(diane)&person(diane)))<~>(quieter(eleanor,diane)))))& (![X]:(room(X)=>(((quieter(kimberly,X))=>(older(florence,X))))))& (~(brave(petra)&humble(petra)&funny(petra)&patient(petra)&person(petra)))& (![X]:(room(X)=>(((older(florence,X))=>(quieter(florence,X))))))& (~quiet(petra)&~patient(petra))& (older(eleanor,petra))& (![X]:(humble(X)=>quiet(X)))& (~![X]:(anywhere(X)=>(((older(florence,X))=>(((tall(X)&person(X))&(strong(X)&funny(X)&calm(X)&person(X))&(older(florence,X))))))))& (![X]:(room(X)=>(((older(kimberly,X))<=>(~strong(X)&~old(X)&~quiet(X))))))& (~(strong(petra)&kind(petra)&person(petra)))& (~(generous(diane)&quiet(diane)&creative(diane)&strong(diane)&person(diane)))

room(petra)&room(diane)&(![X]:(room(X)=>(X='petra'|X='diane')))& ~(~(~((?[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))))))

Nelle, Florence, Alfonso are the only persons in the room. “Not everyone in the room is not a funny person” if “everyone in the room is a quiet person” and vice versa. Everyone in the room is not a wise person. Not everyone in the room is a wise person. Not everyone outside the room is a humble person. Everyone outside the room is a creative person, is a funny person and is not old. If someone is a humble person then he/she is not a happy person and vice versa. Everyone in the room is a happy person. Everyone in the room is a kind person. Everyone in the room is a patient person. Everyone in the room is a quiet person. More than one person anywhere is a old person. Everyone in the room is not a brave person. It is true that “everyone outside the room is not a generous person”. Not everyone in the room is not a funny person. If someone is not a humble person then he/she is not tall and vice versa.

All brave persons are funny.

entailment

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

room(nelle)&room(florence)&room(alfonso)&(![X]:(room(X)=>(X='nelle'|X='florence'|X='alfonso')))& ![X]:(brave(X)=>funny(X))

% SZS status Unsatisfiable for 3583672168273416436982634 % SZS output start Proof for 3583672168273416436982634 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 49. ! [X0] : (~room(X0) => (~old(X0) & person(X0) & funny(X0) & person(X0) & creative(X0))) [input p5] 50. ! [X0] : ((person(X0) & humble(X0)) <=> ~(person(X0) & happy(X0))) [input p6] 56. ! [X0] : (room(X0) => ~(person(X0) & brave(X0))) [input p12] 60. ~(! [X0] : (brave(X0) => funny(X0)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 62. ~(! [X0] : (brave(X0) => funny(X0)) & ! [X1] : (room(X1) => (fred = X1 | paul = X1 | mary = X1)) & room(fred) & room(paul) & room(mary)) [rectify 60] 66. ! [X0] : (~room(X0) => (~old(X0) & person(X0) & funny(X0) & person(X0))) [pure predicate removal 49] 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] 148. ! [X0] : ((~old(X0) & person(X0) & funny(X0) & person(X0)) | room(X0)) [ennf transformation 66] 149. ! [X0] : ((person(X0) & humble(X0)) <=> (~person(X0) | ~happy(X0))) [ennf transformation 50] 154. ! [X0] : ((~person(X0) | ~brave(X0)) | ~room(X0)) [ennf transformation 56] 155. ! [X0] : (~person(X0) | ~brave(X0) | ~room(X0)) [flattening 154] 158. ? [X0] : (~funny(X0) & brave(X0)) | ? [X1] : ((fred != X1 & paul != X1 & mary != X1) & room(X1)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 62] 159. ? [X0] : (~funny(X0) & brave(X0)) | ? [X1] : (fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 158] 170. ! [X0] : (((person(X0) & humble(X0)) | (person(X0) & happy(X0))) & ((~person(X0) | ~happy(X0)) | (~person(X0) | ~humble(X0)))) [nnf transformation 149] 171. ! [X0] : (((person(X0) & humble(X0)) | (person(X0) & happy(X0))) & (~person(X0) | ~happy(X0) | ~person(X0) | ~humble(X0))) [flattening 170] 176. ? [X0] : (~funny(X0) & brave(X0)) => (~funny(sK7) & brave(sK7)) [choice axiom] 177. ? [X1] : (fred != X1 & paul != X1 & mary != X1 & room(X1)) => (fred != sK8 & paul != sK8 & mary != sK8 & room(sK8)) [choice axiom] 178. (~funny(sK7) & brave(sK7)) | (fred != sK8 & paul != sK8 & mary != sK8 & room(sK8)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 159,177,176] 259. room(mary) [cnf transformation 143] 260. room(paul) [cnf transformation 143] 261. room(fred) [cnf transformation 143] 262. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 143] 275. funny(X0) | room(X0) [cnf transformation 148] 282. person(X0) | person(X0) [cnf transformation 171] 294. ~person(X0) | ~brave(X0) | ~room(X0) [cnf transformation 155] 298. brave(sK7) | room(sK8) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178] 299. brave(sK7) | mary != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178] 300. brave(sK7) | paul != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178] 301. brave(sK7) | fred != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178] 302. ~funny(sK7) | room(sK8) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178] 303. ~funny(sK7) | mary != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178] 304. ~funny(sK7) | paul != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178] 305. ~funny(sK7) | fred != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 178] 307. person(X0) [duplicate literal removal 282] 360. ~brave(X0) | ~room(X0) [subsumption resolution 294,307] 361. ~funny(sK7) | fred != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 305,261] 362. ~funny(sK7) | fred != sK8 | ~room(mary) [subsumption resolution 361,260] 363. ~funny(sK7) | fred != sK8 [subsumption resolution 362,259] 365. 12 <=> fred = sK8 [avatar definition] 367. fred != sK8 <- (~12) [avatar component clause 365] 369. 13 <=> funny(sK7) [avatar definition] 371. ~funny(sK7) <- (~13) [avatar component clause 369] 372. ~12 | ~13 [avatar split clause 363,369,365] 373. ~funny(sK7) | paul != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 304,261] 374. ~funny(sK7) | paul != sK8 | ~room(mary) [subsumption resolution 373,260] 375. ~funny(sK7) | paul != sK8 [subsumption resolution 374,259] 377. 14 <=> paul = sK8 [avatar definition] 379. paul != sK8 <- (~14) [avatar component clause 377] 380. ~14 | ~13 [avatar split clause 375,369,377] 381. ~funny(sK7) | mary != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 303,261] 382. ~funny(sK7) | mary != sK8 | ~room(mary) [subsumption resolution 381,260] 383. ~funny(sK7) | mary != sK8 [subsumption resolution 382,259] 385. 15 <=> mary = sK8 [avatar definition] 387. mary != sK8 <- (~15) [avatar component clause 385] 388. ~15 | ~13 [avatar split clause 383,369,385] 389. ~funny(sK7) | room(sK8) | ~room(paul) | ~room(mary) [subsumption resolution 302,261] 390. ~funny(sK7) | room(sK8) | ~room(mary) [subsumption resolution 389,260] 391. ~funny(sK7) | room(sK8) [subsumption resolution 390,259] 393. 16 <=> room(sK8) [avatar definition] 395. room(sK8) <- (16) [avatar component clause 393] 396. 16 | ~13 [avatar split clause 391,369,393] 397. brave(sK7) | fred != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 301,261] 398. brave(sK7) | fred != sK8 | ~room(mary) [subsumption resolution 397,260] 399. brave(sK7) | fred != sK8 [subsumption resolution 398,259] 401. 17 <=> brave(sK7) [avatar definition] 403. brave(sK7) <- (17) [avatar component clause 401] 404. ~12 | 17 [avatar split clause 399,401,365] 405. brave(sK7) | paul != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 300,261] 406. brave(sK7) | paul != sK8 | ~room(mary) [subsumption resolution 405,260] 407. brave(sK7) | paul != sK8 [subsumption resolution 406,259] 408. ~14 | 17 [avatar split clause 407,401,377] 409. brave(sK7) | mary != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 299,261] 410. brave(sK7) | mary != sK8 | ~room(mary) [subsumption resolution 409,260] 411. brave(sK7) | mary != sK8 [subsumption resolution 410,259] 412. ~15 | 17 [avatar split clause 411,401,385] 413. brave(sK7) | room(sK8) | ~room(paul) | ~room(mary) [subsumption resolution 298,261] 414. brave(sK7) | room(sK8) | ~room(mary) [subsumption resolution 413,260] 415. brave(sK7) | room(sK8) [subsumption resolution 414,259] 416. 16 | 17 [avatar split clause 415,401,393] 417. room(sK7) <- (~13) [resolution 275,371] 504. paul = sK7 | mary = sK7 | fred = sK7 <- (~13) [resolution 262,417] 505. paul = sK8 | mary = sK8 | fred = sK8 <- (16) [resolution 262,395] 572. 33 <=> fred = sK7 [avatar definition] 574. fred = sK7 <- (33) [avatar component clause 572] 576. 34 <=> mary = sK7 [avatar definition] 578. mary = sK7 <- (34) [avatar component clause 576] 580. 35 <=> paul = sK7 [avatar definition] 582. paul = sK7 <- (35) [avatar component clause 580] 583. 33 | 34 | 35 | 13 [avatar split clause 504,369,580,576,572] 584. mary = sK8 | fred = sK8 <- (~14, 16) [subsumption resolution 505,379] 585. fred = sK8 <- (~14, ~15, 16) [subsumption resolution 584,387] 586. $false <- (~12, ~14, ~15, 16) [subsumption resolution 585,367] 587. 12 | 14 | 15 | ~16 [avatar contradiction clause 586] 624. brave(mary) <- (17, 34) [backward demodulation 403,578] 656. ~room(mary) <- (17, 34) [resolution 624,360] 657. $false <- (17, 34) [subsumption resolution 656,259] 658. ~17 | ~34 [avatar contradiction clause 657] 660. brave(paul) <- (17, 35) [backward demodulation 403,582] 668. ~room(paul) <- (17, 35) [resolution 660,360] 669. $false <- (17, 35) [subsumption resolution 668,260] 670. ~17 | ~35 [avatar contradiction clause 669] 672. brave(fred) <- (17, 33) [backward demodulation 403,574] 689. ~room(fred) <- (17, 33) [resolution 672,360] 690. $false <- (17, 33) [subsumption resolution 689,261] 691. ~17 | ~33 [avatar contradiction clause 690] 692. $false [avatar sat refutation 372,380,388,396,404,408,412,416,583,587,658,670,691] % SZS output end Proof for 3583672168273416436982634 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.040 s % ------------------------------ % ------------------------------

There is a room. If “everyone in the room does not enjoy rooftop gardening or owns a telescope” then “everyone in the room does not enjoy rooftop gardening only if they is a scotch connoisseur”. If “everyone in the room cannot play the piano or builds model airplanes” then “everyone in the room cannot play the piano only if they is a drone photographer”. If “everyone in the room does not practice tai chi or is a drone photographer” then “everyone in the room who does not practice tai chi enjoys making ceramics”. If “everyone in the room does not enjoy watercolor painting or collects action figures” then “everyone in the room does not enjoy watercolor painting only if they collects action figures, owns a telescope or practices tai chi”. Not everyone in the room collects action figures, owns a telescope or practices tai chi only if they can play the piano. Everyone in the room who can play the piano enjoys rooftop gardening, practices tai chi or does not enjoy watercolor painting. No one in the room streams on Twitch if they enjoys rooftop gardening, practices tai chi or does not enjoy watercolor painting. Everyone in the room does not stream on Twitch or plays the violin. More than one person in the room builds model airplanes. If someone either owns a telescope or is a scotch connoisseur but not both then he/she does not enjoy watercolor painting and vice versa. Everyone in the room streams on Twitch, plays the violin and collects antique clocks only if they can play the piano. Everyone in the room composes and performs experimental electronic music if they builds model airplanes, practices tai chi or collects action figures. Everyone anywhere who streams on Twitch and does not own a telescope regularly contributes to tech forums and online communities. Everyone in the room is a scotch connoisseur if they regularly contributes to tech forums and online communities. Everyone in the room enjoys rooftop gardening if they is a scotch connoisseur.

Everyone in the room builds model airplanes.

neutral

(there_is_a_room)& ((![X]:(room(X)=>(((owns_a_telescope(X))|(does_not_enjoy_rooftop_gardening(X))))))=>(![X]:(room(X)=>(((is_a_scotch_connoisseur(X))<=(does_not_enjoy_rooftop_gardening(X)))))))& ((![X]:(room(X)=>(((builds_model_airplanes(X))|(cannot_play_the_piano(X))))))=>(![X]:(room(X)=>(((is_a_drone_photographer(X))<=(cannot_play_the_piano(X)))))))& ((![X]:(room(X)=>(((is_a_drone_photographer(X))|(does_not_practice_tai_chi(X))))))=>(![X]:(room(X)=>(((does_not_practice_tai_chi(X))=>(enjoys_making_ceramics(X)))))))& ((![X]:(room(X)=>(((collects_action_figures(X))|(does_not_enjoy_watercolor_painting(X))))))=>(![X]:(room(X)=>(((((collects_action_figures(X))|(owns_a_telescope(X))|(practices_tai_chi(X))))<=(does_not_enjoy_watercolor_painting(X)))))))& (~![X]:(room(X)=>(((can_play_the_piano(X))<=(((collects_action_figures(X))|(owns_a_telescope(X))|(practices_tai_chi(X))))))))& (![X]:(room(X)=>(((can_play_the_piano(X))=>(((enjoys_rooftop_gardening(X))|(practices_tai_chi(X))|(does_not_enjoy_watercolor_painting(X))))))))& (~?[X]:(room(X)=>(((((enjoys_rooftop_gardening(X))|(practices_tai_chi(X))|(does_not_enjoy_watercolor_painting(X))))=>(streams_on_Twitch(X))))))& (![X]:(room(X)=>(((plays_the_violin(X))|(does_not_stream_on_Twitch(X))))))& ((?[X,Y]:(room(X)&room(Y)&(builds_model_airplanes(X)&builds_model_airplanes(Y))&(X!=Y))))& ((![X]:((((owns_a_telescope(X))<~>(is_a_scotch_connoisseur(X))))<=>(does_not_enjoy_watercolor_painting(X)))))& (![X]:(room(X)=>(((can_play_the_piano(X))<=(((streams_on_Twitch(X))&(plays_the_violin(X))&(collects_antique_clocks(X))))))))& (![X]:(room(X)=>(((((builds_model_airplanes(X))|(practices_tai_chi(X))|(collects_action_figures(X))))=>(composes_and_performs_experimental_electronic_music(X))))))& (![X]:(anywhere(X)=>(((((streams_on_Twitch(X))&(does_not_own_a_telescope(X))))=>(regularly_contributes_to_tech_forums_and_online_communities(X))))))& (![X]:(room(X)=>(((regularly_contributes_to_tech_forums_and_online_communities(X))=>(is_a_scotch_connoisseur(X))))))& (![X]:(room(X)=>(((is_a_scotch_connoisseur(X))=>(enjoys_rooftop_gardening(X))))))& (![X]:(room(X)=>(((enjoys_rooftop_gardening(X))=>(is_a_drone_photographer(X))))))& (![X]:(room(X)=>(((is_a_drone_photographer(X))=>(enjoys_making_ceramics(X))))))& (~![X]:(room(X)=>(((has_a_piercing(X))&(practices_tai_chi(X))&(streams_on_Twitch(X))))))& ((?[X,Y]:(room(X)&room(Y)&(owns_a_telescope(X)&owns_a_telescope(Y))&(X!=Y))))& (![X]:(room(X)=>(((composes_and_performs_experimental_electronic_music(X))<=(((builds_model_airplanes(X))|(collects_action_figures(X))))))))& (![X]:(room(X)=>(((streams_on_Twitch(X))=>(is_a_scotch_connoisseur(X))))))& (![X]:(room(X)=>(((enjoys_watercolor_painting(X))=>(enjoys_rooftop_gardening(X))))))& (((?[X]:(room(X)&enjoys_watercolor_painting(X)))))& (![X]:(room(X)=>(((((streams_on_Twitch(X))&(regularly_contributes_to_tech_forums_and_online_communities(X))))<=(((does_not_enjoy_watercolor_painting(X))<~>(regularly_contributes_to_tech_forums_and_online_communities(X))))))))& (![X]:(room(X)=>(((((streams_on_Twitch(X))&(regularly_contributes_to_tech_forums_and_online_communities(X))))=>(collects_action_figures(X))))))& (![X]:(room(X)=>(((((is_a_scotch_connoisseur(X))<~>(practices_tai_chi(X))))<=(collects_action_figures(X))))))

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

Maryann, Sylvia, Patricia are the only persons in the room. If it is not the case that Sylvia is a old person and is quieter than Ashley then Maryann is kind. If Ashley is quieter than Sylvia then Patricia who is richer than Minerva and is strong is richer than Ashley, is quieter than Ashley or is richer than Minerva. If Maryann is quieter than Minerva then Maryann who is older than Ashley is richer than Minerva and is richer than Ashley. If Ashley is older than Sylvia then if someone is older than Ashley then he/she is older than Minerva. Sylvia who is quieter than Minerva is richer than Ashley. Maryann who is older than Minerva is quieter than Ashley. Maryann is quieter than Minerva. Patricia and Maryann are not a generous old persons. Everyone in the room who is richer than Ashley is quieter than Ashley. Only one person in the room is quiet. Not everyone in the room who is older than Ashley is quieter than Ashley. Maryann and Sylvia are richer than Ashley. Someone in the room is older than Ashley.

Patricia is older than Ashley.

entailment

room(maryannann)&room(sylvia)&room(patricia)&(![X]:(room(X)=>(X='maryannann'|X='sylvia'|X='patricia')))& ((~(((old(sylvia)&person(sylvia))&(quieter(ashley,sylvia)))))=>(kind(maryannann)))& ((quieter(sylvia,ashley))=>((((richer(minerva,patricia))&(strong(patricia))))&(((richer(ashley,patricia))|(quieter(ashley,patricia))|(richer(minerva,patricia))))))& ((quieter(minerva,maryannann))=>((older(ashley,maryannann))&(((richer(minerva,maryannann))&(richer(ashley,maryannann))))))& ((older(sylvia,ashley))=>((![X]:((older(ashley,X))=>(older(minerva,X))))))& ((quieter(minerva,sylvia))&(richer(ashley,sylvia)))& ((older(minerva,maryannann))&(quieter(ashley,maryannann)))& (quieter(minerva,maryannann))& (~(generous(patricia)&old(patricia)&person(patricia))&~(generous(maryannann)&old(maryannann)&person(maryannann)))& (![X]:(room(X)=>(((richer(ashley,X))=>(quieter(ashley,X))))))& (((?[X]:(room(X)&quiet(X)))&(![X,Y]:((room(X)&room(Y)&(quiet(X))&(quiet(Y)))=>(X=Y)))))& (~![X]:(room(X)=>(((older(ashley,X))=>(quieter(ashley,X))))))& (richer(ashley,maryannann)&richer(ashley,sylvia))& (?[X]:(room(X)&(older(ashley,X))))

room(maryannann)&room(sylvia)&room(patricia)&(![X]:(room(X)=>(X='maryannann'|X='sylvia'|X='patricia')))& older(ashley,patricia)

% SZS status Unsatisfiable for 6933334692130738749236044 % SZS output start Proof for 6933334692130738749236044 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 49. richer(alice,paul) & quieter(john,paul) [input p5] 50. quieter(alice,mary) & older(john,mary) [input p6] 53. ! [X0] : (room(X0) => (richer(alice,X0) => quieter(alice,X0))) [input p9] 55. ~! [X0] : (room(X0) => (older(alice,X0) => quieter(alice,X0))) [input p11] 58. ~(older(alice,fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 136. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 137. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 136] 141. ! [X0] : ((quieter(alice,X0) | ~richer(alice,X0)) | ~room(X0)) [ennf transformation 53] 142. ! [X0] : (quieter(alice,X0) | ~richer(alice,X0) | ~room(X0)) [flattening 141] 145. ? [X0] : ((~quieter(alice,X0) & older(alice,X0)) & room(X0)) [ennf transformation 55] 146. ? [X0] : (~quieter(alice,X0) & older(alice,X0) & room(X0)) [flattening 145] 147. ~older(alice,fred) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 58] 148. ~older(alice,fred) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 147] 152. ? [X0] : (~quieter(alice,X0) & older(alice,X0) & room(X0)) => (~quieter(alice,sK1) & older(alice,sK1) & room(sK1)) [choice axiom] 153. ~quieter(alice,sK1) & older(alice,sK1) & room(sK1) [skolemisation 146,152] 156. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) [choice axiom] 157. ~older(alice,fred) | (fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 148,156] 238. room(mary) [cnf transformation 137] 239. room(paul) [cnf transformation 137] 240. room(fred) [cnf transformation 137] 241. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 137] 249. richer(alice,paul) [cnf transformation 49] 251. quieter(alice,mary) [cnf transformation 50] 253. ~richer(alice,X0) | quieter(alice,X0) | ~room(X0) [cnf transformation 142] 257. room(sK1) [cnf transformation 153] 258. older(alice,sK1) [cnf transformation 153] 259. ~quieter(alice,sK1) [cnf transformation 153] 264. ~older(alice,fred) | room(sK3) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 157] 265. ~older(alice,fred) | mary != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 157] 266. ~older(alice,fred) | paul != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 157] 267. ~older(alice,fred) | fred != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 157] 315. ~older(alice,fred) | fred != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 267,240] 316. ~older(alice,fred) | fred != sK3 | ~room(mary) [subsumption resolution 315,239] 317. ~older(alice,fred) | fred != sK3 [subsumption resolution 316,238] 319. 11 <=> fred = sK3 [avatar definition] 323. 12 <=> older(alice,fred) [avatar definition] 325. ~older(alice,fred) <- (~12) [avatar component clause 323] 326. ~11 | ~12 [avatar split clause 317,323,319] 327. ~older(alice,fred) | paul != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 266,240] 328. ~older(alice,fred) | paul != sK3 | ~room(mary) [subsumption resolution 327,239] 329. ~older(alice,fred) | paul != sK3 [subsumption resolution 328,238] 331. 13 <=> paul = sK3 [avatar definition] 333. paul != sK3 <- (~13) [avatar component clause 331] 334. ~13 | ~12 [avatar split clause 329,323,331] 335. ~older(alice,fred) | mary != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 265,240] 336. ~older(alice,fred) | mary != sK3 | ~room(mary) [subsumption resolution 335,239] 337. ~older(alice,fred) | mary != sK3 [subsumption resolution 336,238] 339. 14 <=> mary = sK3 [avatar definition] 341. mary != sK3 <- (~14) [avatar component clause 339] 342. ~14 | ~12 [avatar split clause 337,323,339] 343. ~older(alice,fred) | room(sK3) | ~room(paul) | ~room(mary) [subsumption resolution 264,240] 344. ~older(alice,fred) | room(sK3) | ~room(mary) [subsumption resolution 343,239] 345. ~older(alice,fred) | room(sK3) [subsumption resolution 344,238] 347. 15 <=> room(sK3) [avatar definition] 349. room(sK3) <- (15) [avatar component clause 347] 350. 15 | ~12 [avatar split clause 345,323,347] 351. quieter(alice,paul) | ~room(paul) [resolution 253,249] 353. quieter(alice,paul) [subsumption resolution 351,239] 664. paul = sK3 | mary = sK3 | fred = sK3 <- (15) [resolution 349,241] 665. mary = sK3 | fred = sK3 <- (~13, 15) [subsumption resolution 664,333] 666. fred = sK3 <- (~13, ~14, 15) [subsumption resolution 665,341] 669. 11 | 13 | 14 | ~15 [avatar split clause 666,347,339,331,319] 682. paul = sK1 | mary = sK1 | fred = sK1 [resolution 257,241] 684. 46 <=> fred = sK1 [avatar definition] 686. fred = sK1 <- (46) [avatar component clause 684] 688. 47 <=> mary = sK1 [avatar definition] 690. mary = sK1 <- (47) [avatar component clause 688] 692. 48 <=> paul = sK1 [avatar definition] 694. paul = sK1 <- (48) [avatar component clause 692] 695. 46 | 47 | 48 [avatar split clause 682,692,688,684] 701. ~quieter(alice,mary) <- (47) [backward demodulation 259,690] 702. $false <- (47) [subsumption resolution 701,251] 703. ~47 [avatar contradiction clause 702] 705. older(alice,fred) <- (46) [backward demodulation 258,686] 710. $false <- (~12, 46) [subsumption resolution 705,325] 711. 12 | ~46 [avatar contradiction clause 710] 715. ~quieter(alice,paul) <- (48) [backward demodulation 259,694] 719. $false <- (48) [subsumption resolution 715,353] 720. ~48 [avatar contradiction clause 719] 722. $false [avatar sat refutation 326,334,342,350,669,695,703,711,720] % SZS output end Proof for 6933334692130738749236044 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.022 s % ------------------------------ % ------------------------------

James, Doyle are the only persons in the room. Doyle does not like Noella. Someone in the room does not hate Noella. James does not hate Brenda or is not liked by Noella or both. Doyle and Noella hate each other. Someone in the room does not like Noella. At least one person in the room is not liked by Noella. It is not the case that “James is not liked by Noella”. Someone in the room does not hate Brenda. James does not like Noella.

James is liked by Brenda.

neutral

room(james)&room(doyle)&(![X]:(room(X)=>(X='james'|X='doyle')))& (~like(noella,doyle))& (?[X]:(room(X)&(~hate(noella,X))))& (((~hate(brenda,james))|(~like(james,noella))))& ((hate(doyle,noella) & hate(noella,doyle)))& (?[X]:(room(X)&(~like(noella,X))))& (((?[X]:(room(X)&~like(X,noella)))))& (~(~like(james,noella)))& (?[X]:(room(X)&(~hate(brenda,X))))& (~like(noella,james))

room(james)&room(doyle)&(![X]:(room(X)=>(X='james'|X='doyle')))& like(james,brenda)

There is a room. Everyone in the room is not hated by Mike. If someone neither is liked by Jeanne nor is hated by Jeanne then he/she is not liked by Jeanne, hates Jeanne or is not hated by Mike.

Everyone in the room likes Jeanne.

neutral

(there_is_a_room)& (![X]:(room(X)=>(~hate(X,mike))))& ((![X]:((~((like(X,jeanne))|(hate(X,jeanne))))=>(((~like(X,jeanne))|(hate(jeanne,X))|(~hate(X,mike)))))))& ((?[X,Y]:(room(X)&room(Y)&(~hate(X,jeanne)&~hate(Y,jeanne))&(X!=Y))))& ((![X]:((((like(X,jeanne))|(hate(X,jeanne))|(like(jeanne,X))))=>(((like(X,jeanne))|(~like(X,jeanne)))))))& (![X]:(room(X)=>(((like(X,mike))|(hate(mike,X))|(~hate(X,mike))))))& (~![X]:(anywhere(X)=>(((like(X,jeanne))|(hate(jeanne,X))))))& (![X]:(room(X)=>(~like(X,jeanne))))& (((?[X]:(room(X)&like(jeanne,X)))))& (![X]:(~room(X)=>(((hate(X,jeanne))|(like(mike,X))))))& (![X]:(room(X)=>(((~like(X,jeanne))|(hate(mike,X))))))

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

Felicia is the only person in the room. If "Felicia is a creative tall brave european" then "Felicia is a client of Jonas". If "someone in the room participates in citizen science projects related to wildlife monitoring" then "Felicia practices digital art". If "Felicia is curious" then "Felicia is the least old in the room". If "Felicia is a sibling of David" then "Felicia enjoys cross-country skiing". If "David is a sibling of Felicia" then "it is not the case that "Felicia is not passionate about collecting and restoring classic cars"". If someone does not host a popular podcast about emerging technologies then he/she knows morse code. All kind person is strong. Felicia is a client of David. Felicia is not passionate about collecting and restoring classic cars. All wise person is curious. Felicia is the least poor anywhere. All patient person is old. Someone anywhere is not a quiet european. All tall person is generous. It is not the case that "Felicia is not a tall generous person".

Felicia is old.

neutral

room(felicia)&(![X]:(room(X)=>(X='felicia')))& ((creative(felicia)&tall(felicia)&brave(felicia)&european(felicia))=>(client(jonas,felicia)))& ((?[X]:(room(X)&(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))=>(practices_digital_art(felicia)))& ((curious(felicia))=>(![X]:((room(X)&(X!=felicia))=>older(felicia,X))))& ((sibling(david,felicia))=>(enjoys_cross-country_skiing(felicia)))& ((sibling(felicia,david))=>(~(is_not_passionate_about_collecting_and_restoring_classic_cars(felicia))))& ((![X]:((does_not_host_a_popular_podcast_about_emerging_technologies(X))=>(knows_morse_code(X)))))& (![X]:(kind(X)=>strong(X)))& (client(david,felicia))& (is_not_passionate_about_collecting_and_restoring_classic_cars(felicia))& (![X]:(wise(X)=>curious(X)))& (![X]:((anywhere(X)&(X!=felicia))=>poorer(felicia,X)))& (![X]:(patient(X)=>old(X)))& (?[X]:(anywhere(X)&(~(quiet(X)&european(X)))))& (![X]:(tall(X)=>generous(X)))& (~(~(tall(felicia)&generous(felicia)&person(felicia))))& (client(ronald,felicia))& ((![X]:((~(patient(X)&european(X)))=>(does_not_enjoy_cross-country_skiing(X)))))& (enjoys_kayaking_and_exploring_remote_waterways(felicia))& (~(creative(felicia)&brave(felicia)&tall(felicia)&tourist(felicia)))& (quiet(felicia))& (quieter(felicia,michelle))& (?[X]:(room(X)&(does_not_collect_foreign_coins(X))))& (enjoys_stand-up_paddleboarding(felicia))& (enjoys_macrame(felicia))

room(felicia)&(![X]:(room(X)=>(X='felicia')))& old(felicia)

Rena is the only person in the room. “No one outside the room who is not a Linux enthusiast enjoys virtual reality gaming” unless “everyone in the room is a certified yoga instructor teaching classes weekly or does not participate in citizen science projects related to wildlife monitoring”. Everyone in the room neither does practice yoga nor hosts a popular podcast about emerging technologies if they is a certified yoga instructor teaching classes weekly. Rena who does practice yoga is an active member of a local robotics club.

Rena participates in citizen science projects related to wildlife monitoring.

contradiction

room(rena)&(![X]:(room(X)=>(X='rena')))& ((![X]:(room(X)=>(((does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))))))=>(![X]:(room(X)=>(((is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(uses_an_ios_phone(X)))))))& (~(![X]:(room(X)=>(((does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))=>(~?[X]:(~room(X)=>(((is_not_a_Linux_enthusiast(X))=>(enjoys_virtual_reality_gaming(X)))))))& ((![X]:(room(X)=>(((does_not_practice_digital_art(X))|(does_not_know_morse_code(X))))))=>(![X]:(room(X)=>(((enjoys_windsurfing(X))<=(does_not_know_morse_code(X)))))))& ((![X]:(room(X)=>(((is_not_an_active_member_of_a_local_robotics_club(X))|(does_not_enjoy_logic_puzzles(X))))))=>(((collects_comic_books(rena))&(enjoys_logic_puzzles(rena))&(does_not_own_a_television(rena)))))& (![X]:(room(X)=>(((does_not_enjoy_logic_puzzles(X))=>(~((is_not_a_professional_photographer_specializing_in_portrait_photography(X))|(uses_an_ios_phone(X))))))))& (![X]:(room(X)=>(((~((is_not_a_professional_photographer_specializing_in_portrait_photography(X))|(uses_an_ios_phone(X))))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& (![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(~((does_practice_yoga(X))|(hosts_a_popular_podcast_about_emerging_technologies(X))))))))& (![X]:(~room(X)=>(((collects_rare_minerals(X))=>(has_completed_a_triathlon(X))))))& (enjoys_logic_puzzles(rena))& ((does_practice_yoga(rena))&(is_an_active_member_of_a_local_robotics_club(rena)))& (![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))=>(((collects_rare_minerals(X))&(is_a_professional_photographer_specializing_in_portrait_photography(X))&(enjoys_stand-up_paddleboarding(X))))))))& (![X]:(~room(X)=>(((((collects_rare_minerals(X))&(is_a_professional_photographer_specializing_in_portrait_photography(X))&(enjoys_stand-up_paddleboarding(X))))=>(~((practices_digital_art(X))|(uses_an_ios_phone(X))))))))& (is_a_client_of_Meta(rena))& (![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))=>(collects_historical_artifacts_related_to_ancient_civilizations(X))))))& (![X]:(room(X)=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))|(does_not_collect_rare_minerals(X))))))& (![X]:(room(X)=>(((does_not_collect_rare_minerals(X))=>(does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))))))& (![X]:(room(X)=>(((does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))=>(hosts_a_popular_podcast_about_emerging_technologies(X))))))& (![X]:(room(X)=>(((has_a_saltwater_aquarium(X))<=(hosts_a_popular_podcast_about_emerging_technologies(X))))))& (![X]:(room(X)=>(((does_not_have_completed_a_triathlon(X))=>(has_completed_a_triathlon(X))))))

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

% SZS status Unsatisfiable for 5963169771524940592229161 % SZS output start Proof for 5963169771524940592229161 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 46. ~! [X0] : (room(X0) => (predr(X0) | ~predy(X0))) => ~? [X0] : (~room(X0) => (~predp(X0) => predo(X0))) [input p2] 51. ! [X0] : (room(X0) => (predr(X0) => ~(predn(X0) | predx(X0)))) [input p7] 54. predv(mary) & predx(mary) [input p10] 64. predy(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 66. ~! [X0] : (room(X0) => (predr(X0) | ~predy(X0))) => ~? [X1] : (~room(X1) => (~predp(X1) => predo(X1))) [rectify 46] 78. predx(mary) [pure predicate removal 54] 81. ~! [X0] : (room(X0) => (predr(X0) | ~predy(X0))) => ~? [X1] : (~room(X1) => ~~predp(X1)) [pure predicate removal 66] 82. ~! [X0] : (room(X0) => (predr(X0) | ~predy(X0))) => ~? [X1] : ~~room(X1) [pure predicate removal 81] 155. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 158. ! [X1] : ~room(X1) | ! [X0] : ((predr(X0) | ~predy(X0)) | ~room(X0)) [ennf transformation 82] 159. ! [X1] : ~room(X1) | ! [X0] : (predr(X0) | ~predy(X0) | ~room(X0)) [flattening 158] 162. ! [X0] : (((~predn(X0) & ~predx(X0)) | ~predr(X0)) | ~room(X0)) [ennf transformation 51] 163. ! [X0] : ((~predn(X0) & ~predx(X0)) | ~predr(X0) | ~room(X0)) [flattening 162] 174. predy(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 64] 179. ! [X0] : ~room(X0) | ! [X1] : (predr(X1) | ~predy(X1) | ~room(X1)) [rectify 159] 260. room(mary) [cnf transformation 155] 265. ~room(X0) | predr(X1) | ~predy(X1) | ~room(X1) [cnf transformation 179] 267. ~predx(X0) | ~predr(X0) | ~room(X0) [cnf transformation 163] 269. predx(mary) [cnf transformation 78] 279. predy(mary) [cnf transformation 174] 299. 5 <=> ! [X1] : (predr(X1) | ~room(X1) | ~predy(X1)) [avatar definition] 300. ~predy(X1) | ~room(X1) | predr(X1) <- (5) [avatar component clause 299] 302. 6 <=> ! [X0] : ~room(X0) [avatar definition] 303. ~room(X0) <- (6) [avatar component clause 302] 304. 5 | 6 [avatar split clause 265,302,299] 306. ~predr(mary) | ~room(mary) [resolution 267,269] 307. ~predr(mary) [subsumption resolution 306,260] 321. ~room(mary) | predr(mary) <- (5) [resolution 300,279] 322. predr(mary) <- (5) [subsumption resolution 321,260] 323. $false <- (5) [subsumption resolution 322,307] 324. ~5 [avatar contradiction clause 323] 325. $false <- (6) [resolution 303,260] 326. ~6 [avatar contradiction clause 325] 327. $false [avatar sat refutation 304,324,326] % SZS output end Proof for 5963169771524940592229161 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Ida, Mark, Eugene, Rosemary are the only persons in the room. “No kind person is creative” if “Mark and Eugene are respectively old and wise”. All curious persons are creative. Mark and Eugene are richer than Allen. All happy persons are curious. If someone is richer than Allen then he/she is happy.

Eugene is creative.

entailment

room(ida)&room(mark)&room(eugene)&room(rosemary)&(![X]:(room(X)=>(X='ida'|X='mark'|X='eugene'|X='rosemary')))& (((old(mark))&(wise(eugene)))=>(~?[X]:(kind(X)=>creative(X))))& (((patient(mark))&(wise(rosemary)))=>((![X]:((richer(allen,X))=>(quieter(allen,X))))))& (((funny(ida))&(generous(rosemary)))<=>(quieter(ida,allen)))& ((older(allen,rosemary)&older(allen,ida))=>(older(allen,rosemary)&older(allen,eugene)))& ((((richer(allen,rosemary))<~>(quieter(allen,rosemary)))&((richer(allen,eugene))<~>(quieter(allen,eugene))))<=>((happy(eugene))&(tall(ida))))& (![X]:(curious(X)=>creative(X)))& (old(ida)&old(rosemary))& (~?[X]:(generous(X)=>kind(X)))& (~?[X]:(funny(X)=>brave(X)))& (![X]:(patient(X)=>creative(X)))& (richer(allen,mark)&richer(allen,eugene))& ((happy(mark))&(curious(rosemary)))& ((![X]:((older(allen,X))=>(richer(allen,X)))))& ((ida_dream=>(older(allen,eugene)&older(allen,rosemary))))& (![X]:(humble(X)=>calm(X)))& (![X]:(happy(X)=>curious(X)))& ((![X]:((richer(allen,X))=>(older(allen,X)))))& (![X]:(old(X)=>curious(X)))& ((![X]:((richer(allen,X))=>(happy(X)))))& (![X]:((~room(X)&(X!=mark))=>richer(X,mark)))& (![X]:((room(X)&(X!=eugene))=>richer(X,eugene)))& (![X]:(old(X)=>generous(X)))

room(ida)&room(mark)&room(eugene)&room(rosemary)&(![X]:(room(X)=>(X='ida'|X='mark'|X='eugene'|X='rosemary')))& creative(eugene)

% SZS status Unsatisfiable for 360480288623520431447185 % SZS output start Proof for 360480288623520431447185 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 50. ! [X0] : (curious(X0) => creative(X0)) [input p6] 55. richer(john,fred) & richer(john,paul) [input p11] 60. ! [X0] : (happy(X0) => curious(X0)) [input p16] 63. ! [X0] : (richer(john,X0) => happy(X0)) [input p19] 67. ~(creative(fred) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 147. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 148. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 147] 151. ! [X0] : (creative(X0) | ~curious(X0)) [ennf transformation 50] 155. ! [X0] : (curious(X0) | ~happy(X0)) [ennf transformation 60] 158. ! [X0] : (happy(X0) | ~richer(john,X0)) [ennf transformation 63] 164. ~creative(fred) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 67] 165. ~creative(fred) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 164] 175. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK1 & fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) [choice axiom] 176. ~creative(fred) | (alice != sK1 & fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 165,175] 257. room(mary) [cnf transformation 148] 258. room(paul) [cnf transformation 148] 259. room(fred) [cnf transformation 148] 260. room(alice) [cnf transformation 148] 261. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 148] 278. ~curious(X0) | creative(X0) [cnf transformation 151] 284. richer(john,fred) [cnf transformation 55] 288. ~happy(X0) | curious(X0) [cnf transformation 155] 291. ~richer(john,X0) | happy(X0) [cnf transformation 158] 295. ~creative(fred) | room(sK1) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 176] 296. ~creative(fred) | mary != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 176] 297. ~creative(fred) | paul != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 176] 298. ~creative(fred) | fred != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 176] 299. ~creative(fred) | alice != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 176] 341. 10 <=> richer(john,fred) [avatar definition] 343. richer(john,fred) <- (10) [avatar component clause 341] 357. 12 <=> happy(fred) [avatar definition] 358. happy(fred) <- (12) [avatar component clause 357] 367. 10 [avatar split clause 284,341] 368. ~creative(fred) | alice != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 299,260] 369. ~creative(fred) | alice != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 368,259] 370. ~creative(fred) | alice != sK1 | ~room(mary) [subsumption resolution 369,258] 371. ~creative(fred) | alice != sK1 [subsumption resolution 370,257] 373. 14 <=> alice = sK1 [avatar definition] 375. alice != sK1 <- (~14) [avatar component clause 373] 377. 15 <=> creative(fred) [avatar definition] 380. ~14 | ~15 [avatar split clause 371,377,373] 381. ~creative(fred) | fred != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 298,260] 382. ~creative(fred) | fred != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 381,259] 383. ~creative(fred) | fred != sK1 | ~room(mary) [subsumption resolution 382,258] 384. ~creative(fred) | fred != sK1 [subsumption resolution 383,257] 386. 16 <=> fred = sK1 [avatar definition] 388. fred != sK1 <- (~16) [avatar component clause 386] 389. ~16 | ~15 [avatar split clause 384,377,386] 390. ~creative(fred) | paul != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 297,260] 391. ~creative(fred) | paul != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 390,259] 392. ~creative(fred) | paul != sK1 | ~room(mary) [subsumption resolution 391,258] 393. ~creative(fred) | paul != sK1 [subsumption resolution 392,257] 395. 17 <=> paul = sK1 [avatar definition] 397. paul != sK1 <- (~17) [avatar component clause 395] 398. ~17 | ~15 [avatar split clause 393,377,395] 399. ~creative(fred) | mary != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 296,260] 400. ~creative(fred) | mary != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 399,259] 401. ~creative(fred) | mary != sK1 | ~room(mary) [subsumption resolution 400,258] 402. ~creative(fred) | mary != sK1 [subsumption resolution 401,257] 404. 18 <=> mary = sK1 [avatar definition] 406. mary != sK1 <- (~18) [avatar component clause 404] 407. ~18 | ~15 [avatar split clause 402,377,404] 408. ~creative(fred) | room(sK1) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 295,260] 409. ~creative(fred) | room(sK1) | ~room(paul) | ~room(mary) [subsumption resolution 408,259] 410. ~creative(fred) | room(sK1) | ~room(mary) [subsumption resolution 409,258] 411. ~creative(fred) | room(sK1) [subsumption resolution 410,257] 413. 19 <=> room(sK1) [avatar definition] 415. room(sK1) <- (19) [avatar component clause 413] 416. 19 | ~15 [avatar split clause 411,377,413] 428. happy(fred) <- (10) [resolution 291,343] 431. 12 | ~10 [avatar split clause 428,341,357] 432. curious(fred) <- (12) [resolution 358,288] 433. creative(fred) <- (12) [resolution 432,278] 436. 15 | ~12 [avatar split clause 433,357,377] 693. fred = sK1 | paul = sK1 | mary = sK1 | alice = sK1 <- (19) [resolution 261,415] 694. paul = sK1 | mary = sK1 | alice = sK1 <- (~16, 19) [subsumption resolution 693,388] 695. mary = sK1 | alice = sK1 <- (~16, ~17, 19) [subsumption resolution 694,397] 696. alice = sK1 <- (~16, ~17, ~18, 19) [subsumption resolution 695,406] 697. $false <- (~14, ~16, ~17, ~18, 19) [subsumption resolution 696,375] 698. 14 | 16 | 17 | 18 | ~19 [avatar contradiction clause 697] 699. $false [avatar sat refutation 367,380,389,398,407,416,431,436,698] % SZS output end Proof for 360480288623520431447185 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.028 s % ------------------------------ % ------------------------------

Ethan, Larry, Jason, William, Leann are the only persons in the room. “Someone in the room is not a certified scuba diver with advanced underwater photography skills and collects historical artifacts related to ancient civilizations” if “everyone in the room is not a certified scuba diver with advanced underwater photography skills or bakes bread at home”. “Everyone in the room is not a certified scuba diver with advanced underwater photography skills or does not collect historical artifacts related to ancient civilizations” only if “everyone anywhere does not work as a freelance web developer specializing in e-commerce sites”. Everyone in the room is not a certified scuba diver with advanced underwater photography skills. Someone in the room is not a scotch connoisseur. Everyone in the room does not maintain a personal blog focused on cybersecurity tips. Someone in the room is a scotch connoisseur.

Not everyone in the room is a scotch connoisseur.

entailment

room(ethan)&room(larry)&room(jason)&room(william)&room(leann)&(![X]:(room(X)=>(X='ethan'|X='larry'|X='jason'|X='william'|X='leann')))& ((![X]:(room(X)=>(((bakes_bread_at_home(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))&(collects_historical_artifacts_related_to_ancient_civilizations(X)))))))& ((![X]:(room(X)=>(((does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))|(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))=>(![X]:(anywhere(X)=>(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X)))))& (![X]:(room(X)=>(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))& (?[X]:(room(X)&(is_not_a_scotch_connoisseur(X))))& (![X]:(room(X)=>(does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))))& (?[X]:(room(X)&(is_a_scotch_connoisseur(X))))

room(ethan)&room(larry)&room(jason)&room(william)&room(leann)&(![X]:(room(X)=>(X='ethan'|X='larry'|X='jason'|X='william'|X='leann')))& ~![X]:(room(X)=>(is_a_scotch_connoisseur(X)))

% SZS status Unsatisfiable for 578270165502729871582897 % SZS output start Proof for 578270165502729871582897 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] : (~predj(X0) & room(X0)) [input p4] 51. ~(~! [X0] : (room(X0) => predj(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] 54. ~(~! [X0] : (room(X0) => predj(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 51] 131. ! [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] 132. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 131] 135. ! [X0] : (predj(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 54] 136. ! [X0] : (predj(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 135] 142. ? [X0] : (~predj(X0) & room(X0)) => (~predj(sK2) & room(sK2)) [choice axiom] 143. ~predj(sK2) & room(sK2) [skolemisation 48,142] 146. ? [X1] : (john != X1 & alice != X1 & fred != X1 & paul != X1 & mary != X1 & room(X1)) => (john != sK4 & alice != sK4 & fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) [choice axiom] 147. ! [X0] : (predj(X0) | ~room(X0)) | (john != sK4 & alice != sK4 & fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 136,146] 228. room(mary) [cnf transformation 132] 229. room(paul) [cnf transformation 132] 230. room(fred) [cnf transformation 132] 231. room(alice) [cnf transformation 132] 232. room(john) [cnf transformation 132] 233. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 132] 239. room(sK2) [cnf transformation 143] 240. ~predj(sK2) [cnf transformation 143] 243. predj(X0) | ~room(X0) | room(sK4) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 147] 244. predj(X0) | ~room(X0) | mary != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 147] 245. predj(X0) | ~room(X0) | paul != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 147] 246. predj(X0) | ~room(X0) | fred != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 147] 247. predj(X0) | ~room(X0) | alice != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 147] 248. predj(X0) | ~room(X0) | john != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 147] 269. predj(X0) | ~room(X0) | john != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 248,232] 270. predj(X0) | ~room(X0) | john != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 269,231] 271. predj(X0) | ~room(X0) | john != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 270,230] 272. predj(X0) | ~room(X0) | john != sK4 | ~room(mary) [subsumption resolution 271,229] 273. predj(X0) | ~room(X0) | john != sK4 [subsumption resolution 272,228] 275. 5 <=> john = sK4 [avatar definition] 277. john != sK4 <- (~5) [avatar component clause 275] 279. 6 <=> ! [X0] : (predj(X0) | ~room(X0)) [avatar definition] 280. ~room(X0) | predj(X0) <- (6) [avatar component clause 279] 281. ~5 | 6 [avatar split clause 273,279,275] 282. predj(X0) | ~room(X0) | alice != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 247,232] 283. predj(X0) | ~room(X0) | alice != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 282,231] 284. predj(X0) | ~room(X0) | alice != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 283,230] 285. predj(X0) | ~room(X0) | alice != sK4 | ~room(mary) [subsumption resolution 284,229] 286. predj(X0) | ~room(X0) | alice != sK4 [subsumption resolution 285,228] 288. 7 <=> alice = sK4 [avatar definition] 290. alice != sK4 <- (~7) [avatar component clause 288] 291. ~7 | 6 [avatar split clause 286,279,288] 292. predj(X0) | ~room(X0) | fred != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 246,232] 293. predj(X0) | ~room(X0) | fred != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 292,231] 294. predj(X0) | ~room(X0) | fred != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 293,230] 295. predj(X0) | ~room(X0) | fred != sK4 | ~room(mary) [subsumption resolution 294,229] 296. predj(X0) | ~room(X0) | fred != sK4 [subsumption resolution 295,228] 298. 8 <=> fred = sK4 [avatar definition] 300. fred != sK4 <- (~8) [avatar component clause 298] 301. ~8 | 6 [avatar split clause 296,279,298] 302. predj(X0) | ~room(X0) | paul != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 245,232] 303. predj(X0) | ~room(X0) | paul != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 302,231] 304. predj(X0) | ~room(X0) | paul != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 303,230] 305. predj(X0) | ~room(X0) | paul != sK4 | ~room(mary) [subsumption resolution 304,229] 306. predj(X0) | ~room(X0) | paul != sK4 [subsumption resolution 305,228] 308. 9 <=> paul = sK4 [avatar definition] 310. paul != sK4 <- (~9) [avatar component clause 308] 311. ~9 | 6 [avatar split clause 306,279,308] 312. predj(X0) | ~room(X0) | mary != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 244,232] 313. predj(X0) | ~room(X0) | mary != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 312,231] 314. predj(X0) | ~room(X0) | mary != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 313,230] 315. predj(X0) | ~room(X0) | mary != sK4 | ~room(mary) [subsumption resolution 314,229] 316. predj(X0) | ~room(X0) | mary != sK4 [subsumption resolution 315,228] 318. 10 <=> mary = sK4 [avatar definition] 320. mary != sK4 <- (~10) [avatar component clause 318] 321. ~10 | 6 [avatar split clause 316,279,318] 322. predj(X0) | ~room(X0) | room(sK4) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 243,232] 323. predj(X0) | ~room(X0) | room(sK4) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 322,231] 324. predj(X0) | ~room(X0) | room(sK4) | ~room(paul) | ~room(mary) [subsumption resolution 323,230] 325. predj(X0) | ~room(X0) | room(sK4) | ~room(mary) [subsumption resolution 324,229] 326. predj(X0) | ~room(X0) | room(sK4) [subsumption resolution 325,228] 328. 11 <=> room(sK4) [avatar definition] 330. room(sK4) <- (11) [avatar component clause 328] 331. 11 | 6 [avatar split clause 326,279,328] 338. predj(sK2) <- (6) [resolution 280,239] 340. $false <- (6) [subsumption resolution 338,240] 341. ~6 [avatar contradiction clause 340] 392. alice = sK4 | fred = sK4 | paul = sK4 | mary = sK4 | john = sK4 <- (11) [resolution 233,330] 456. fred = sK4 | paul = sK4 | mary = sK4 | john = sK4 <- (~7, 11) [subsumption resolution 392,290] 457. paul = sK4 | mary = sK4 | john = sK4 <- (~7, ~8, 11) [subsumption resolution 456,300] 458. mary = sK4 | john = sK4 <- (~7, ~8, ~9, 11) [subsumption resolution 457,310] 459. john = sK4 <- (~7, ~8, ~9, ~10, 11) [subsumption resolution 458,320] 460. $false <- (~5, ~7, ~8, ~9, ~10, 11) [subsumption resolution 459,277] 461. 5 | 7 | 8 | 9 | 10 | ~11 [avatar contradiction clause 460] 462. $false [avatar sat refutation 281,291,301,311,321,331,341,461] % SZS output end Proof for 578270165502729871582897 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Melissa is the only person in the room. “Melissa enjoys origami” if “everyone in the room enjoys origami or does not enjoy kayaking” and vice versa. If “Melissa is a craft beer aficionado” then “everyone in the room maintains a large, organic vegetable garden year-round”. “Everyone in the room does not maintain a large, organic vegetable garden year-round or has a specialized collection of handmade artisan pottery” if “everyone in the room does not practice kickboxing or does not enjoy logic puzzles” and vice versa. “Melissa does not enjoy kayaking” if “Melissa practices and performs acrobatic dance routines, practices kickboxing or collects rare minerals”. If “Melissa practices kickboxing” then “everyone in the room is not a Linux enthusiast and uses an ios phone if they hosts regular game nights featuring complex strategy games”. If someone writes and illustrates their own graphic novels then he/she does not enjoy logic puzzles or enjoys logic puzzles or both. Melissa has a piercing. Everyone in the room maintains a large, organic vegetable garden year-round. Melissa enjoys origami. Everyone in the room is not a Linux enthusiast and uses an ios phone if they hosts regular game nights featuring complex strategy games. Everyone in the room does not enjoy camping and organizing outdoor survival workshops if they does not have a piercing. Everyone in the room who does not enjoy camping and organizing outdoor survival workshops neither hosts regular game nights featuring complex strategy games nor collects luxury watches. Not everyone anywhere who is not an enthusiastic bird watcher who travels for rare sightings is a Linux enthusiast. Melissa dreamt that “someone in the room enjoys making ceramics”. Everyone in the room has a specialized collection of handmade artisan pottery if they collects luxury watches or uses an ios phone or both and vice versa. Everyone in the room uses an ios phone if they collects luxury watches or uses an ios phone or both.

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

entailment

room(melissa)&(![X]:(room(X)=>(X='melissa')))& ((![X]:(room(X)=>(((does_not_enjoy_kayaking(X))|(enjoys_origami(X))))))<=>(enjoys_origami(melissa)))& ((is_a_craft_beer_aficionado(melissa))=>(![X]:(room(X)=>(maintains_a_large,_organic_vegetable_garden_year-round(X)))))& ((![X]:(room(X)=>(((does_not_enjoy_logic_puzzles(X))|(does_not_practice_kickboxing(X))))))<=>(![X]:(room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))|(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X)))))))& ((((practices_and_performs_acrobatic_dance_routines(melissa))|(practices_kickboxing(melissa))|(collects_rare_minerals(melissa))))=>(does_not_enjoy_kayaking(melissa)))& ((practices_kickboxing(melissa))=>(![X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(((is_not_a_Linux_enthusiast(X))&(uses_an_ios_phone(X)))))))))& ((![X]:((writes_and_illustrates_their_own_graphic_novels(X))=>(((does_not_enjoy_logic_puzzles(X))|(enjoys_logic_puzzles(X)))))))& (has_a_piercing(melissa))& (![X]:(room(X)=>(maintains_a_large,_organic_vegetable_garden_year-round(X))))& (enjoys_origami(melissa))& (![X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(((is_not_a_Linux_enthusiast(X))&(uses_an_ios_phone(X))))))))& (![X]:(room(X)=>(((does_not_have_a_piercing(X))=>(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))))))& (![X]:(room(X)=>(((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))=>(~((hosts_regular_game_nights_featuring_complex_strategy_games(X))|(collects_luxury_watches(X))))))))& (~![X]:(anywhere(X)=>(((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(is_a_Linux_enthusiast(X))))))& ((melissa_dream=>(?[X]:(room(X)&(enjoys_making_ceramics(X))))))& (![X]:(room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))<=>(((collects_luxury_watches(X))|(uses_an_ios_phone(X))))))))& (![X]:(room(X)=>(((((collects_luxury_watches(X))|(uses_an_ios_phone(X))))=>(uses_an_ios_phone(X))))))& (does_enjoy_mountain_biking(melissa))& ((((does_not_collect_rare_minerals(melissa))&(enjoys_salsa_dancing(melissa))&(is_a_wine_connoisseur(melissa))))&(((enjoys_making_ceramics(melissa))|(enjoys_logic_puzzles(melissa))|(collects_luxury_watches(melissa)))))& (![X]:(anywhere(X)=>(((((maintains_a_large,_organic_vegetable_garden_year-round(X))&(does_not_enjoy_mountain_biking(X))))=>(collects_modern_art(X))))))& (develops_open-source_software_projects_in_their_free_time(melissa))& ((does_not_enjoy_kayaking(melissa))&(does_not_collect_modern_art(melissa)))& (![X]:(~room(X)=>(((watches_fantasy_movies(X))=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))|(enjoys_logic_puzzles(X))|(collects_luxury_watches(X))))))))& (((practices_and_performs_acrobatic_dance_routines(melissa))|(collects_luxury_watches(melissa))|(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(melissa))))

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

% SZS status Unsatisfiable for 6583153119626461350518457 % SZS output start Proof for 6583153119626461350518457 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 52. ! [X0] : (room(X0) => predy(X0)) [input p8] 68. ~(predy(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 165. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 171. ! [X0] : (predy(X0) | ~room(X0)) [ennf transformation 52] 176. ~predy(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 68] 191. ? [X0] : (mary != X0 & room(X0)) => (mary != sK4 & room(sK4)) [choice axiom] 192. ~predy(mary) | (mary != sK4 & room(sK4)) | ~room(mary) [skolemisation 176,191] 273. room(mary) [cnf transformation 165] 274. ~room(X0) | mary = X0 [cnf transformation 165] 287. ~room(X0) | predy(X0) [cnf transformation 171] 297. ~predy(mary) | room(sK4) | ~room(mary) [cnf transformation 192] 298. ~predy(mary) | mary != sK4 | ~room(mary) [cnf transformation 192] 383. ~predy(mary) | mary != sK4 [subsumption resolution 298,273] 385. 19 <=> mary = sK4 [avatar definition] 387. mary != sK4 <- (~19) [avatar component clause 385] 389. 20 <=> predy(mary) [avatar definition] 392. ~19 | ~20 [avatar split clause 383,389,385] 393. ~predy(mary) | room(sK4) [subsumption resolution 297,273] 395. 21 <=> room(sK4) [avatar definition] 397. room(sK4) <- (21) [avatar component clause 395] 398. 21 | ~20 [avatar split clause 393,389,395] 400. predy(mary) [resolution 287,273] 403. 20 [avatar split clause 400,389] 408. mary = sK4 <- (21) [resolution 274,397] 409. $false <- (~19, 21) [subsumption resolution 408,387] 410. 19 | ~21 [avatar contradiction clause 409] 411. $false [avatar sat refutation 392,398,403,410] % SZS output end Proof for 6583153119626461350518457 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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. Everyone in the room either is not generous or is a kind person but not both. Everyone in the room is a curious person. No one in the room is patient. Not everyone in the room is a kind person.

Not everyone in the room is a generous person.

entailment

(there_is_a_room)& ((![X]:((((generous(X)&person(X))|(~funny(X))|(humble(X)&person(X))))<=>(((curious(X)&person(X))|(humble(X)&person(X))|(~strong(X)))))))& (![X]:(funny(X)=>kind(X)))& (?[X,Y]:((((wise(X)&person(X))<~>(funny(X)&person(X))))&(kind(Y)&person(Y))&(older(X,Y))))& (![X]:(room(X)=>(((~generous(X))<~>(kind(X)&person(X))))))& (![X]:(room(X)=>(curious(X)&person(X))))& (~?[X]:(room(X)=>(patient(X))))& (~![X]:(room(X)=>(kind(X)&person(X))))& (![X]:(room(X)=>(strong(X)&person(X))))& (![X]:(room(X)=>(brave(X)&person(X))))

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

% SZS status Unsatisfiable for 4817530662743877422631801 % SZS output start Proof for 4817530662743877422631801 44. there_is_a_room [input p0] 48. ! [X0] : (room(X0) => (~generous(X0) <~> (person(X0) & kind(X0)))) [input p4] 49. ! [X0] : (room(X0) => (person(X0) & curious(X0))) [input p5] 50. ~? [X0] : (room(X0) => patient(X0)) [input p6] 51. ~! [X0] : (room(X0) => (person(X0) & kind(X0))) [input p7] 54. ~(~! [X0] : (room(X0) => (person(X0) & generous(X0))) & there_is_a_room) [input hypothesis] 56. ~? [X0] : ~room(X0) [pure predicate removal 50] 130. ! [X0] : ((~generous(X0) <~> (person(X0) & kind(X0))) | ~room(X0)) [ennf transformation 48] 131. ! [X0] : ((person(X0) & curious(X0)) | ~room(X0)) [ennf transformation 49] 132. ! [X0] : room(X0) [ennf transformation 56] 133. ? [X0] : ((~person(X0) | ~kind(X0)) & room(X0)) [ennf transformation 51] 136. ! [X0] : ((person(X0) & generous(X0)) | ~room(X0)) | ~there_is_a_room [ennf transformation 54] 148. ! [X0] : ((((~person(X0) | ~kind(X0)) | generous(X0)) & ((person(X0) & kind(X0)) | ~generous(X0))) | ~room(X0)) [nnf transformation 130] 149. ! [X0] : (((~person(X0) | ~kind(X0) | generous(X0)) & ((person(X0) & kind(X0)) | ~generous(X0))) | ~room(X0)) [flattening 148] 150. ? [X0] : ((~person(X0) | ~kind(X0)) & room(X0)) => ((~person(sK3) | ~kind(sK3)) & room(sK3)) [choice axiom] 151. (~person(sK3) | ~kind(sK3)) & room(sK3) [skolemisation 133,150] 232. there_is_a_room [cnf transformation 44] 256. ~room(X0) | ~generous(X0) | kind(X0) [cnf transformation 149] 260. ~room(X0) | person(X0) [cnf transformation 131] 261. room(X0) [cnf transformation 132] 263. ~person(sK3) | ~kind(sK3) [cnf transformation 151] 267. generous(X0) | ~room(X0) | ~there_is_a_room [cnf transformation 136] 291. 4 <=> kind(sK3) [avatar definition] 293. ~kind(sK3) <- (~4) [avatar component clause 291] 295. 5 <=> person(sK3) [avatar definition] 297. ~person(sK3) <- (~5) [avatar component clause 295] 298. ~4 | ~5 [avatar split clause 263,295,291] 300. generous(X0) | ~there_is_a_room [subsumption resolution 267,261] 301. generous(X0) [subsumption resolution 300,232] 304. person(X0) [resolution 260,261] 305. $false <- (~5) [resolution 304,297] 306. 5 [avatar contradiction clause 305] 310. ~generous(X0) | kind(X0) [resolution 256,261] 311. kind(X0) [subsumption resolution 310,301] 313. $false <- (~4) [resolution 311,293] 314. 4 [avatar contradiction clause 313] 315. $false [avatar sat refutation 298,306,314] % SZS output end Proof for 4817530662743877422631801 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.020 s % ------------------------------ % ------------------------------

Ingrid, Jose are the only persons in the room. 'Salvador and Jose like each other' if 'Jose is younger than Salvador' and vice versa. If 'Jose is not wise' then 'all calm persons are tall'. If 'someone outside the room is curious' then 'Ingrid and Jose are older than Marcy'. Mario is younger than Ingrid. All patient persons are humble. Jose is the quietest anywhere. Ingrid is the least old in the room.

Salvador is quieter than Jose.

contradiction

room(ingrid)&room(jose)&(![X]:(room(X)=>(X='ingrid'|X='jose')))& ((younger(salvador,jose))<=>((like(salvador,jose) & like(jose,salvador))))& ((~wise(jose))=>(![X]:(calm(X)=>tall(X))))& ((?[X]:(~room(X)&(curious(X))))=>(older(marcy,ingrid)&older(marcy,jose)))& (younger(ingrid,mario))& (![X]:(patient(X)=>humble(X)))& (![X]:((anywhere(X)&(X!=jose))=>quieter(X,jose)))& (![X]:((room(X)&(X!=ingrid))=>older(ingrid,X)))& ((hate(jose,mario) & hate(mario,jose)))& (is_a_night_owl(ingrid))& (![X]:(creative(X)=>humble(X)))& ((funny(ingrid))&(patient(jose)))& (~?[X]:(calm(X)=>creative(X)))& (~hate(ingrid,kathleen)&~hate(jose,kathleen))& (![X]:(brave(X)=>wise(X)))

room(ingrid)&room(jose)&(![X]:(room(X)=>(X='ingrid'|X='jose')))& quieter(jose,salvador)

% SZS status Unsatisfiable for 7199625113371023494985668 % SZS output start Proof for 7199625113371023494985668 5. ! [X0] : anywhere(X0) [input b4] 14. ! [X0,X1] : (X0 != X1 => (quieter(X0,X1) => ~quieter(X1,X0))) [input b13] 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 50. ! [X0] : ((paul != X0 & anywhere(X0)) => quieter(X0,paul)) [input p6] 59. quieter(paul,john) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 90. ! [X0,X1] : ((~quieter(X1,X0) | ~quieter(X0,X1)) | X0 = X1) [ennf transformation 14] 91. ! [X0,X1] : (~quieter(X1,X0) | ~quieter(X0,X1) | X0 = X1) [flattening 90] 145. ! [X0] : (quieter(X0,paul) | (paul = X0 | ~anywhere(X0))) [ennf transformation 50] 146. ! [X0] : (quieter(X0,paul) | paul = X0 | ~anywhere(X0)) [flattening 145] 149. quieter(paul,john) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 59] 150. quieter(paul,john) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 149] 156. anywhere(X0) [cnf transformation 5] 166. ~quieter(X1,X0) | ~quieter(X0,X1) | X0 = X1 [cnf transformation 91] 220. paul != john [cnf transformation 43] 244. quieter(X0,paul) | paul = X0 | ~anywhere(X0) [cnf transformation 146] 253. quieter(paul,john) [cnf transformation 150] 269. quieter(X0,paul) | paul = X0 [subsumption resolution 244,156] 276. ~quieter(john,paul) | paul = john [resolution 166,253] 279. ~quieter(john,paul) [subsumption resolution 276,220] 284. paul = john [resolution 279,269] 285. $false [subsumption resolution 284,220] % SZS output end Proof for 7199625113371023494985668 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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. Either “no one anywhere enjoys stargazing or does not enjoy stargazing” or “everyone anywhere does not enjoy stargazing or does not enjoy camping and organizing outdoor survival workshops” but not both. Everyone in the room enjoys camping and organizing outdoor survival workshops. Everyone in the room who plays the drums enjoys camping and organizing outdoor survival workshops. Everyone outside the room enjoys stargazing if they enjoys camping and organizing outdoor survival workshops. If someone plays the drums then he/she enjoys stargazing. Everyone in the room who does not enjoy stargazing enjoys camping and organizing outdoor survival workshops. No one anywhere who enjoys camping and organizing outdoor survival workshops plays the drums.

Everyone outside the room does not enjoy camping and organizing outdoor survival workshops.

entailment

(there_is_a_room)& ((~?[X]:(anywhere(X)=>(((does_not_enjoy_stargazing(X))|(enjoys_stargazing(X))))))<~>(![X]:(anywhere(X)=>(((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))|(does_not_enjoy_stargazing(X)))))))& (![X]:(room(X)=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))& (![X]:(room(X)=>(((plays_the_drums(X))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))& (![X]:(~room(X)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))=>(enjoys_stargazing(X))))))& ((![X]:((plays_the_drums(X))=>(enjoys_stargazing(X)))))& (![X]:(room(X)=>(((does_not_enjoy_stargazing(X))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))& (~?[X]:(anywhere(X)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))=>(plays_the_drums(X))))))

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

% SZS status Unsatisfiable for 8726465914985041212427289 % SZS output start Proof for 8726465914985041212427289 5. ! [X0] : anywhere(X0) [input b4] 44. there_is_a_room [input p0] 45. ~? [X0] : (anywhere(X0) => (predb(X0) | ~predb(X0))) <~> ! [X0] : (anywhere(X0) => (~predb(X0) | ~preda(X0))) [input p1] 48. ! [X0] : (~room(X0) => (preda(X0) => predb(X0))) [input p4] 51. ~? [X0] : (anywhere(X0) => (preda(X0) => predc(X0))) [input p7] 52. ~(! [X0] : (~room(X0) => ~preda(X0)) & there_is_a_room) [input hypothesis] 53. ~? [X0] : (anywhere(X0) => (predb(X0) | ~predb(X0))) <~> ! [X1] : (anywhere(X1) => (~predb(X1) | ~preda(X1))) [rectify 45] 54. ~? [X0] : (anywhere(X0) => ~preda(X0)) [pure predicate removal 51] 128. ! [X0] : ((~predb(X0) & predb(X0)) & anywhere(X0)) <~> ! [X1] : ((~predb(X1) | ~preda(X1)) | ~anywhere(X1)) [ennf transformation 53] 129. ! [X0] : (~predb(X0) & predb(X0) & anywhere(X0)) <~> ! [X1] : (~predb(X1) | ~preda(X1) | ~anywhere(X1)) [flattening 128] 131. ! [X0] : ((predb(X0) | ~preda(X0)) | room(X0)) [ennf transformation 48] 132. ! [X0] : (predb(X0) | ~preda(X0) | room(X0)) [flattening 131] 135. ! [X0] : (preda(X0) & anywhere(X0)) [ennf transformation 54] 136. ? [X0] : (preda(X0) & ~room(X0)) | ~there_is_a_room [ennf transformation 52] 137. sP0 <=> ! [X0] : (~predb(X0) & predb(X0) & anywhere(X0)) [predicate definition introduction] 138. sP0 <~> ! [X1] : (~predb(X1) | ~preda(X1) | ~anywhere(X1)) [definition folding 129,137] 140. (sP0 | ? [X0] : (predb(X0) | ~predb(X0) | ~anywhere(X0))) & (! [X0] : (~predb(X0) & predb(X0) & anywhere(X0)) | ~sP0) [nnf transformation 137] 141. (sP0 | ? [X0] : (predb(X0) | ~predb(X0) | ~anywhere(X0))) & (! [X1] : (~predb(X1) & predb(X1) & anywhere(X1)) | ~sP0) [rectify 140] 142. ? [X0] : (predb(X0) | ~predb(X0) | ~anywhere(X0)) => (predb(sK1) | ~predb(sK1) | ~anywhere(sK1)) [choice axiom] 143. (sP0 | (predb(sK1) | ~predb(sK1) | ~anywhere(sK1))) & (! [X1] : (~predb(X1) & predb(X1) & anywhere(X1)) | ~sP0) [skolemisation 141,142] 144. (? [X1] : (predb(X1) & preda(X1) & anywhere(X1)) | ~sP0) & (! [X1] : (~predb(X1) | ~preda(X1) | ~anywhere(X1)) | sP0) [nnf transformation 138] 145. (? [X0] : (predb(X0) & preda(X0) & anywhere(X0)) | ~sP0) & (! [X1] : (~predb(X1) | ~preda(X1) | ~anywhere(X1)) | sP0) [rectify 144] 146. ? [X0] : (predb(X0) & preda(X0) & anywhere(X0)) => (predb(sK2) & preda(sK2) & anywhere(sK2)) [choice axiom] 147. ((predb(sK2) & preda(sK2) & anywhere(sK2)) | ~sP0) & (! [X1] : (~predb(X1) | ~preda(X1) | ~anywhere(X1)) | sP0) [skolemisation 145,146] 148. ? [X0] : (preda(X0) & ~room(X0)) => (preda(sK3) & ~room(sK3)) [choice axiom] 149. (preda(sK3) & ~room(sK3)) | ~there_is_a_room [skolemisation 136,148] 150. anywhere(X0) [cnf transformation 5] 231. there_is_a_room [cnf transformation 44] 234. ~predb(X1) | ~sP0 [cnf transformation 143] 236. ~predb(X1) | ~preda(X1) | ~anywhere(X1) | sP0 [cnf transformation 147] 241. ~preda(X0) | predb(X0) | room(X0) [cnf transformation 132] 244. preda(X0) [cnf transformation 135] 245. ~room(sK3) | ~there_is_a_room [cnf transformation 149] 248. 1 <=> sP0 [avatar definition] 252. 2 <=> ! [X1] : ~predb(X1) [avatar definition] 253. ~predb(X1) <- (2) [avatar component clause 252] 254. ~1 | 2 [avatar split clause 234,252,248] 269. ~predb(X1) | ~preda(X1) | sP0 [subsumption resolution 236,150] 271. 6 <=> ! [X1] : (~predb(X1) | ~preda(X1)) [avatar definition] 272. ~predb(X1) | ~preda(X1) <- (6) [avatar component clause 271] 273. 1 | 6 [avatar split clause 269,271,248] 274. ~room(sK3) [subsumption resolution 245,231] 275. ~predb(X1) <- (6) [subsumption resolution 272,244] 276. 2 | ~6 [avatar split clause 275,271,252] 281. predb(X0) | room(X0) [resolution 241,244] 282. room(X0) <- (2) [subsumption resolution 281,253] 283. $false <- (2) [resolution 282,274] 285. ~2 [avatar contradiction clause 283] 286. $false [avatar sat refutation 254,273,276,285] % SZS output end Proof for 8726465914985041212427289 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Jay, Daniel are the only persons in the room. If "everyone in the room is an enthusiastic bird watcher who travels for rare sightings" then "everyone in the room is not a chess master who participates in national tournaments or is a client of Costco". If "everyone in the room is not a chess master who participates in national tournaments or is a client of Costco" then "if someone does not enjoy landscape photography then he/she is a certified yoga instructor teaching classes weekly". Everyone in the room who is not a chess master who participates in national tournaments collects vintage vinyl records. Everyone in the room enjoys rooftop gardening if they collects vintage vinyl records. Everyone in the room works as a freelance web developer specializing in e-commerce sites if they is a chess master who participates in national tournaments. Everyone outside the room does not work as a freelance web developer specializing in e-commerce sites. Everyone in the room does not have a saltwater aquarium if they collects foreign coins and vice versa. If someone is not a culinary enthusiast who experiments with international cuisines, does not practice pilates or practices pilates then he/she does not enjoy rooftop gardening. If someone does not enjoy landscape photography then he/she is a certified yoga instructor teaching classes weekly. Everyone in the room is not a chess master who participates in national tournaments or is a client of Costco. Everyone in the room enjoys rooftop gardening if they owns an Android phone.

Jay collects vintage vinyl records.

contradiction

room(jay)&room(daniel)&(![X]:(room(X)=>(X='jay'|X='daniel')))& (((![X]:(room(X)=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))=>(![X]:(room(X)=>(((is_a_client_of_Costco(X))|(is_not_a_chess_master_who_participates_in_national_tournaments(X)))))))& ((![X]:(room(X)=>(((is_a_client_of_Costco(X))|(is_not_a_chess_master_who_participates_in_national_tournaments(X))))))=>((![X]:((does_not_enjoy_landscape_photography(X))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X)))))))& (![X]:(room(X)=>(((is_not_a_chess_master_who_participates_in_national_tournaments(X))=>(collects_vintage_vinyl_records(X))))))& (![X]:(room(X)=>(((collects_vintage_vinyl_records(X))=>(enjoys_rooftop_gardening(X))))))& (![X]:(room(X)=>(((is_a_chess_master_who_participates_in_national_tournaments(X))=>(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))& (![X]:(~room(X)=>(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))& (![X]:(room(X)=>(((does_not_have_a_saltwater_aquarium(X))<=>(collects_foreign_coins(X))))))& ((![X]:((((is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(does_not_practice_pilates(X))|(practices_pilates(X))))=>(does_not_enjoy_rooftop_gardening(X)))))& ((![X]:((does_not_enjoy_landscape_photography(X))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X)))))& (![X]:(room(X)=>(((is_a_client_of_Costco(X))|(is_not_a_chess_master_who_participates_in_national_tournaments(X))))))& (![X]:(room(X)=>(((owns_an_Android_phone(X))=>(enjoys_rooftop_gardening(X))))))

room(jay)&room(daniel)&(![X]:(room(X)=>(X='jay'|X='daniel')))& collects_vintage_vinyl_records(jay)

% SZS status Unsatisfiable for 4475124048562009543785126 % SZS output start Proof for 4475124048562009543785126 44. ! [X0] : (room(X0) => (predf(X0) => predn(X0))) & ! [X0] : (room(X0) => (~predo(X0) | predu(X0))) & ! [X0] : (~predq(X0) => predw(X0)) & ! [X0] : ((predv(X0) | ~predv(X0) | ~predx(X0)) => ~predn(X0)) & ! [X0] : (room(X0) => (~predz(X0) <=> predp(X0))) & ! [X0] : (~room(X0) => ~predr(X0)) & ! [X0] : (room(X0) => (predo(X0) => predr(X0))) & ! [X0] : (room(X0) => (predb(X0) => predn(X0))) & ! [X0] : (room(X0) => (~predo(X0) => predb(X0))) & (! [X0] : (room(X0) => (~predo(X0) | predu(X0))) => ! [X0] : (~predq(X0) => predw(X0))) & (! [X0] : (room(X0) => predi(X0)) => ! [X0] : (room(X0) => (~predo(X0) | predu(X0)))) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. predb(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 46. ! [X0] : (room(X0) => (predf(X0) => predn(X0))) & ! [X1] : (room(X1) => (~predo(X1) | predu(X1))) & ! [X2] : (~predq(X2) => predw(X2)) & ! [X3] : ((predv(X3) | ~predv(X3) | ~predx(X3)) => ~predn(X3)) & ! [X4] : (room(X4) => (~predz(X4) <=> predp(X4))) & ! [X5] : (~room(X5) => ~predr(X5)) & ! [X6] : (room(X6) => (predo(X6) => predr(X6))) & ! [X7] : (room(X7) => (predb(X7) => predn(X7))) & ! [X8] : (room(X8) => (~predo(X8) => predb(X8))) & (! [X9] : (room(X9) => (~predo(X9) | predu(X9))) => ! [X10] : (~predq(X10) => predw(X10))) & (! [X11] : (room(X11) => predi(X11)) => ! [X12] : (room(X12) => (~predo(X12) | predu(X12)))) & ! [X13] : (room(X13) => (paul = X13 | mary = X13)) & room(paul) & room(mary) [rectify 44] 47. ! [X1] : (room(X1) => (~predo(X1) | predu(X1))) & ! [X2] : (~predq(X2) => predw(X2)) & ! [X3] : ((predv(X3) | ~predv(X3) | ~predx(X3)) => ~predn(X3)) & ! [X4] : (room(X4) => (~predz(X4) <=> predp(X4))) & ! [X5] : (~room(X5) => ~predr(X5)) & ! [X6] : (room(X6) => (predo(X6) => predr(X6))) & ! [X7] : (room(X7) => (predb(X7) => predn(X7))) & ! [X8] : (room(X8) => (~predo(X8) => predb(X8))) & (! [X9] : (room(X9) => (~predo(X9) | predu(X9))) => ! [X10] : (~predq(X10) => predw(X10))) & (! [X11] : (room(X11) => predi(X11)) => ! [X12] : (room(X12) => (~predo(X12) | predu(X12)))) & ! [X13] : (room(X13) => (paul = X13 | mary = X13)) & room(paul) & room(mary) [pure predicate removal 46] 48. ! [X1] : (room(X1) => (~predo(X1) | predu(X1))) & ! [X2] : (~predq(X2) => predw(X2)) & ! [X3] : ((predv(X3) | ~predv(X3)) => ~predn(X3)) & ! [X4] : (room(X4) => (~predz(X4) <=> predp(X4))) & ! [X5] : (~room(X5) => ~predr(X5)) & ! [X6] : (room(X6) => (predo(X6) => predr(X6))) & ! [X7] : (room(X7) => (predb(X7) => predn(X7))) & ! [X8] : (room(X8) => (~predo(X8) => predb(X8))) & (! [X9] : (room(X9) => (~predo(X9) | predu(X9))) => ! [X10] : (~predq(X10) => predw(X10))) & (! [X11] : (room(X11) => predi(X11)) => ! [X12] : (room(X12) => (~predo(X12) | predu(X12)))) & ! [X13] : (room(X13) => (paul = X13 | mary = X13)) & room(paul) & room(mary) [pure predicate removal 47] 49. ! [X1] : (room(X1) => (~predo(X1) | predu(X1))) & ! [X3] : ((predv(X3) | ~predv(X3)) => ~predn(X3)) & ! [X4] : (room(X4) => (~predz(X4) <=> predp(X4))) & ! [X5] : (~room(X5) => ~predr(X5)) & ! [X6] : (room(X6) => (predo(X6) => predr(X6))) & ! [X7] : (room(X7) => (predb(X7) => predn(X7))) & ! [X8] : (room(X8) => (~predo(X8) => predb(X8))) & (! [X11] : (room(X11) => predi(X11)) => ! [X12] : (room(X12) => (~predo(X12) | predu(X12)))) & ! [X13] : (room(X13) => (paul = X13 | mary = X13)) & room(paul) & room(mary) [pure predicate removal 48] 50. ! [X3] : ((predv(X3) | ~predv(X3)) => ~predn(X3)) & ! [X4] : (room(X4) => (~predz(X4) <=> predp(X4))) & ! [X5] : (~room(X5) => ~predr(X5)) & ! [X6] : (room(X6) => (predo(X6) => predr(X6))) & ! [X7] : (room(X7) => (predb(X7) => predn(X7))) & ! [X8] : (room(X8) => (~predo(X8) => predb(X8))) & ! [X13] : (room(X13) => (paul = X13 | mary = X13)) & room(paul) & room(mary) [pure predicate removal 49] 123. ! [X3] : (~predn(X3) | (~predv(X3) & predv(X3))) & ! [X4] : ((~predz(X4) <=> predp(X4)) | ~room(X4)) & ! [X5] : (~predr(X5) | room(X5)) & ! [X6] : ((predr(X6) | ~predo(X6)) | ~room(X6)) & ! [X7] : ((predn(X7) | ~predb(X7)) | ~room(X7)) & ! [X8] : ((predb(X8) | predo(X8)) | ~room(X8)) & ! [X13] : ((paul = X13 | mary = X13) | ~room(X13)) & room(paul) & room(mary) [ennf transformation 50] 124. ! [X3] : (~predn(X3) | (~predv(X3) & predv(X3))) & ! [X4] : ((~predz(X4) <=> predp(X4)) | ~room(X4)) & ! [X5] : (~predr(X5) | room(X5)) & ! [X6] : (predr(X6) | ~predo(X6) | ~room(X6)) & ! [X7] : (predn(X7) | ~predb(X7) | ~room(X7)) & ! [X8] : (predb(X8) | predo(X8) | ~room(X8)) & ! [X13] : (paul = X13 | mary = X13 | ~room(X13)) & room(paul) & room(mary) [flattening 123] 125. predb(mary) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 45] 126. predb(mary) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 125] 128. ! [X3] : (~predn(X3) | (~predv(X3) & predv(X3))) & ! [X4] : (((~predz(X4) | ~predp(X4)) & (predp(X4) | predz(X4))) | ~room(X4)) & ! [X5] : (~predr(X5) | room(X5)) & ! [X6] : (predr(X6) | ~predo(X6) | ~room(X6)) & ! [X7] : (predn(X7) | ~predb(X7) | ~room(X7)) & ! [X8] : (predb(X8) | predo(X8) | ~room(X8)) & ! [X13] : (paul = X13 | mary = X13 | ~room(X13)) & room(paul) & room(mary) [nnf transformation 124] 129. ! [X0] : (~predn(X0) | (~predv(X0) & predv(X0))) & ! [X1] : (((~predz(X1) | ~predp(X1)) & (predp(X1) | predz(X1))) | ~room(X1)) & ! [X2] : (~predr(X2) | room(X2)) & ! [X3] : (predr(X3) | ~predo(X3) | ~room(X3)) & ! [X4] : (predn(X4) | ~predb(X4) | ~room(X4)) & ! [X5] : (predb(X5) | predo(X5) | ~room(X5)) & ! [X6] : (paul = X6 | mary = X6 | ~room(X6)) & room(paul) & room(mary) [rectify 128] 210. room(mary) [cnf transformation 129] 214. predn(X4) | ~predb(X4) | ~room(X4) [cnf transformation 129] 219. ~predn(X0) | predv(X0) [cnf transformation 129] 220. ~predv(X0) | ~predn(X0) [cnf transformation 129] 224. predb(mary) [cnf transformation 126] 225. ~predn(X0) [subsumption resolution 219,220] 226. ~predb(X4) | ~room(X4) [subsumption resolution 214,225] 228. ~room(mary) [resolution 226,224] 229. $false [subsumption resolution 228,210] % SZS output end Proof for 4475124048562009543785126 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.025 s % ------------------------------ % ------------------------------

Jacinta, Heidi are the only persons in the room. If “no one in the room does not create augmented reality experiences for mobile applications or writes in-depth travel guides for off-the-beaten-path destinations” then “everyone in the room is not a wine connoisseur with a private cellar of vintage wines or does not travel domestically frequently”. If “Jacinta writes in-depth travel guides for off-the-beaten-path destinations” then “if someone writes poetry then he/she does not practice pilates and vice versa”. Jacinta does not enjoy fishing. Heidi either is a wine connoisseur with a private cellar of vintage wines or does not own a microscope but not both. Everyone anywhere has a curated collection of mid-century modern furniture only if they enjoys fishing. It is true that “everyone in the room enjoys fishing only if they creates augmented reality experiences for mobile applications”. Heidi who drives a hybrid car writes poetry. Everyone in the room who does not write in-depth travel guides for off-the-beaten-path destinations composes and performs experimental electronic music. Heidi who enjoys landscape photography can play the piano. Heidi travels domestically frequently. Jacinta uses contact lenses. Jacinta is a skilled home brewer experimenting with craft beer recipes. Everyone in the room writes in-depth travel guides for off-the-beaten-path destinations only if they uses contact lenses. Jacinta neither practices pilates nor does not own an extensive assortment of vintage comic book memorabilia. Jacinta writes in-depth travel guides for off-the-beaten-path destinations.

Jacinta writes poetry.

entailment

room(jacinta)&room(heidi)&(![X]:(room(X)=>(X='jacinta'|X='heidi')))& ((~?[X]:(room(X)=>(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))|(does_not_create_augmented_reality_experiences_for_mobile_applications(X))))))=>(![X]:(room(X)=>(((does_not_travel_domestically_frequently(X))|(is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X)))))))& ((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(jacinta))=>((![X]:((writes_poetry(X))<=>(does_not_practice_pilates(X))))))& (does_not_enjoy_fishing(jacinta))& (((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(heidi))<~>(does_not_own_a_microscope(heidi))))& (![X]:(anywhere(X)=>(((enjoys_fishing(X))<=(has_a_curated_collection_of_mid-century_modern_furniture(X))))))& (![X]:(room(X)=>(((creates_augmented_reality_experiences_for_mobile_applications(X))<=(enjoys_fishing(X))))))& ((drives_a_hybrid_car(heidi))&(writes_poetry(heidi)))& (![X]:(room(X)=>(((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))=>(composes_and_performs_experimental_electronic_music(X))))))& ((enjoys_landscape_photography(heidi))&(can_play_the_piano(heidi)))& (travels_domestically_frequently(heidi))& (uses_contact_lenses(jacinta))& (is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(jacinta))& (![X]:(room(X)=>(((uses_contact_lenses(X))<=(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))& (![X]:(room(X)=>(((does_not_own_a_smart_tv(X))=>(creates_augmented_reality_experiences_for_mobile_applications(X))))))& (trains_for_and_competes_in_international_triathlons(heidi))& (~((practices_pilates(jacinta))|(does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(jacinta))))& (![X]:(room(X)=>(((enjoys_fishing(X))=>(has_a_curated_collection_of_mid-century_modern_furniture(X))))))& (![X]:(room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(is_not_a_professional_photographer_specializing_in_portrait_photography(X))))))& (![X]:(room(X)=>(((does_not_compose_and_performs_experimental_electronic_music(X))|(enjoys_landscape_photography(X))))))& (writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(jacinta))& (is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(jacinta))& (![X]:(~room(X)=>(((enjoys_fishing(X))=>(collects_rare_minerals(X))))))& (~![X]:(room(X)=>(((collects_rare_minerals(X))=>(does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))))))

room(jacinta)&room(heidi)&(![X]:(room(X)=>(X='jacinta'|X='heidi')))& writes_poetry(jacinta)

% SZS status Unsatisfiable for 3628928702723488575589850 % SZS output start Proof for 3628928702723488575589850 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 46. predb(mary) => ! [X0] : (predg(X0) <=> ~predr(X0)) [input p2] 60. ~(~predy(mary) | predr(mary)) [input p16] 64. predb(mary) [input p20] 68. ~(predg(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 74. ~predr(mary) [pure predicate removal 60] 156. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 157. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 156] 160. ! [X0] : (predg(X0) <=> ~predr(X0)) | ~predb(mary) [ennf transformation 46] 165. ~predr(mary) [ennf transformation 74] 169. ~predg(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 68] 170. ~predg(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 169] 175. ! [X0] : ((predg(X0) | predr(X0)) & (~predr(X0) | ~predg(X0))) | ~predb(mary) [nnf transformation 160] 179. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 180. ~predg(mary) | (paul != sK2 & mary != sK2 & room(sK2)) | ~room(paul) | ~room(mary) [skolemisation 170,179] 262. room(mary) [cnf transformation 157] 263. room(paul) [cnf transformation 157] 264. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 157] 267. predg(X0) | predr(X0) | ~predb(mary) [cnf transformation 175] 275. ~predr(mary) [cnf transformation 165] 277. predb(mary) [cnf transformation 64] 280. ~predg(mary) | room(sK2) | ~room(paul) | ~room(mary) [cnf transformation 180] 281. ~predg(mary) | mary != sK2 | ~room(paul) | ~room(mary) [cnf transformation 180] 282. ~predg(mary) | paul != sK2 | ~room(paul) | ~room(mary) [cnf transformation 180] 300. 5 <=> predb(mary) [avatar definition] 304. 6 <=> ! [X0] : (predg(X0) | predr(X0)) [avatar definition] 305. predr(X0) | predg(X0) <- (6) [avatar component clause 304] 306. ~5 | 6 [avatar split clause 267,304,300] 322. 5 [avatar split clause 277,300] 323. ~predg(mary) | paul != sK2 | ~room(mary) [subsumption resolution 282,263] 324. ~predg(mary) | paul != sK2 [subsumption resolution 323,262] 326. 10 <=> paul = sK2 [avatar definition] 328. paul != sK2 <- (~10) [avatar component clause 326] 330. 11 <=> predg(mary) [avatar definition] 333. ~10 | ~11 [avatar split clause 324,330,326] 334. ~predg(mary) | mary != sK2 | ~room(mary) [subsumption resolution 281,263] 335. ~predg(mary) | mary != sK2 [subsumption resolution 334,262] 337. 12 <=> mary = sK2 [avatar definition] 339. mary != sK2 <- (~12) [avatar component clause 337] 340. ~12 | ~11 [avatar split clause 335,330,337] 341. ~predg(mary) | room(sK2) | ~room(mary) [subsumption resolution 280,263] 342. ~predg(mary) | room(sK2) [subsumption resolution 341,262] 344. 13 <=> room(sK2) [avatar definition] 346. room(sK2) <- (13) [avatar component clause 344] 347. 13 | ~11 [avatar split clause 342,330,344] 348. predg(mary) <- (6) [resolution 305,275] 351. 11 | ~6 [avatar split clause 348,304,330] 356. mary = sK2 | paul = sK2 <- (13) [resolution 264,346] 366. paul = sK2 <- (~12, 13) [subsumption resolution 356,339] 367. $false <- (~10, ~12, 13) [subsumption resolution 366,328] 368. 10 | 12 | ~13 [avatar contradiction clause 367] 369. $false [avatar sat refutation 306,322,333,340,347,351,368] % SZS output end Proof for 3628928702723488575589850 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Nakia, David, Christopher are the only persons in the room. If 'at least one person outside the room volunteers for local environmental conservation projects' then 'everyone anywhere who own a television practices zumba'. Nakia collects antique jewelry. Everyone in the room who own a television owns an Android phone, designs and sews custom cosplay costumes for conventions or has a specialized collection of handmade artisan pottery. Everyone in the room does not enjoy stargazing or owns an Android phone, designs and sews custom cosplay costumes for conventions or has a specialized collection of handmade artisan pottery. Everyone in the room who does not enjoy stargazing creates large-scale murals for public art installations. Nakia volunteers for local environmental conservation projects. Everyone in the room creates large-scale murals for public art installations if they has a specialized collection of handmade artisan pottery. If someone own a television then he/she does enjoy trail running. Everyone in the room who has completed a triathlon practices graffiti art. Everyone in the room practices graffiti art only if they regularly goes on multi-day backpacking trips in national parks.

Everyone in the room does not create large-scale murals for public art installations or creates large-scale murals for public art installations.

entailment

room(nakia)&room(david)&room(christopher)&(![X]:(room(X)=>(X='nakia'|X='david'|X='christopher')))& ((((?[X]:(~room(X)&volunteers_for_local_environmental_conservation_projects(X)))))=>(![X]:(anywhere(X)=>(((own_a_television(X))=>(practices_zumba(X)))))))& (collects_antique_jewelry(nakia))& (![X]:(room(X)=>(((own_a_television(X))=>(((owns_an_Android_phone(X))|(designs_and_sews_custom_cosplay_costumes_for_conventions(X))|(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))))& (![X]:(room(X)=>(((((owns_an_Android_phone(X))|(designs_and_sews_custom_cosplay_costumes_for_conventions(X))|(has_a_specialized_collection_of_handmade_artisan_pottery(X))))|(does_not_enjoy_stargazing(X))))))& (![X]:(room(X)=>(((does_not_enjoy_stargazing(X))=>(creates_large-scale_murals_for_public_art_installations(X))))))& (volunteers_for_local_environmental_conservation_projects(nakia))& (![X]:(room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))=>(creates_large-scale_murals_for_public_art_installations(X))))))& ((![X]:((own_a_television(X))=>(does_enjoy_trail_running(X)))))& (![X]:(room(X)=>(((has_completed_a_triathlon(X))=>(practices_graffiti_art(X))))))& (![X]:(room(X)=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))<=(practices_graffiti_art(X))))))

room(nakia)&room(david)&room(christopher)&(![X]:(room(X)=>(X='nakia'|X='david'|X='christopher')))& ![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))|(does_not_create_large-scale_murals_for_public_art_installations(X)))))

% SZS status Unsatisfiable for 8923566977513810543176212 % SZS output start Proof for 8923566977513810543176212 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 55. ~(! [X0] : (room(X0) => (~preda(X0) | preda(X0))) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 57. ~(! [X0] : (room(X0) => (~preda(X0) | preda(X0))) & ! [X1] : (room(X1) => (fred = X1 | paul = X1 | mary = X1)) & room(fred) & room(paul) & room(mary)) [rectify 55] 140. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 141. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 140] 142. ? [X0] : ((preda(X0) & ~preda(X0)) & room(X0)) | ? [X1] : ((fred != X1 & paul != X1 & mary != X1) & room(X1)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 57] 143. ? [X0] : (preda(X0) & ~preda(X0) & room(X0)) | ? [X1] : (fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 142] 144. ? [X1] : (fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP0 [predicate definition introduction] 145. ? [X0] : (preda(X0) & ~preda(X0) & room(X0)) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [definition folding 143,144] 147. ? [X1] : (fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~sP0 [nnf transformation 144] 148. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~sP0 [rectify 147] 149. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) [choice axiom] 150. (fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) | ~sP0 [skolemisation 148,149] 151. ? [X0] : (preda(X0) & ~preda(X0) & room(X0)) => (preda(sK2) & ~preda(sK2) & room(sK2)) [choice axiom] 152. (preda(sK2) & ~preda(sK2) & room(sK2)) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 145,151] 233. room(mary) [cnf transformation 141] 234. room(paul) [cnf transformation 141] 235. room(fred) [cnf transformation 141] 236. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 141] 237. room(sK1) | ~sP0 [cnf transformation 150] 238. mary != sK1 | ~sP0 [cnf transformation 150] 239. paul != sK1 | ~sP0 [cnf transformation 150] 240. fred != sK1 | ~sP0 [cnf transformation 150] 242. ~preda(sK2) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 152] 243. preda(sK2) | sP0 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 152] 245. 1 <=> sP0 [avatar definition] 249. 2 <=> fred = sK1 [avatar definition] 251. fred != sK1 <- (~2) [avatar component clause 249] 252. ~1 | ~2 [avatar split clause 240,249,245] 254. 3 <=> paul = sK1 [avatar definition] 256. paul != sK1 <- (~3) [avatar component clause 254] 257. ~1 | ~3 [avatar split clause 239,254,245] 259. 4 <=> mary = sK1 [avatar definition] 261. mary != sK1 <- (~4) [avatar component clause 259] 262. ~1 | ~4 [avatar split clause 238,259,245] 264. 5 <=> room(sK1) [avatar definition] 266. room(sK1) <- (5) [avatar component clause 264] 267. ~1 | 5 [avatar split clause 237,264,245] 268. preda(sK2) | sP0 | ~room(paul) | ~room(mary) [subsumption resolution 243,235] 269. preda(sK2) | sP0 | ~room(mary) [subsumption resolution 268,234] 270. preda(sK2) | sP0 [subsumption resolution 269,233] 272. 6 <=> preda(sK2) [avatar definition] 275. 1 | 6 [avatar split clause 270,272,245] 276. ~preda(sK2) | sP0 | ~room(paul) | ~room(mary) [subsumption resolution 242,235] 277. ~preda(sK2) | sP0 | ~room(mary) [subsumption resolution 276,234] 278. ~preda(sK2) | sP0 [subsumption resolution 277,233] 279. 1 | ~6 [avatar split clause 278,272,245] 327. paul = sK1 | mary = sK1 | fred = sK1 <- (5) [resolution 236,266] 328. mary = sK1 | fred = sK1 <- (~3, 5) [subsumption resolution 327,256] 329. fred = sK1 <- (~3, ~4, 5) [subsumption resolution 328,261] 330. $false <- (~2, ~3, ~4, 5) [subsumption resolution 329,251] 331. 2 | 3 | 4 | ~5 [avatar contradiction clause 330] 332. $false [avatar sat refutation 252,257,262,267,275,279,331] % SZS output end Proof for 8923566977513810543176212 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Ronnie, Melissa, Harlan are the only persons in the room. Either 'Ronnie neither is not a Linux enthusiast nor does not enjoy snowboarding' or 'not everyone in the room either is not a Linux enthusiast or does not collect vintage stamps but not both' but not both. Everyone in the room does not collect vintage stamps or does not enjoy snowboarding or both. Only one person anywhere does not practice calligraphy or does not enjoy skydiving or both. Ronnie does not have completed a triathlon or does not enjoy snowboarding or both. Everyone in the room does not enjoy coding in Python. Only one person in the room does not have a specialized collection of handmade artisan pottery or is not a Linux enthusiast or both. Everyone in the room neither does not develop open-source software projects in their free time nor is not a dedicated advocate for digital privacy and encryption. Everyone in the room does not collect vintage stamps. Everyone in the room cannot play the flute and does not have a piercing. Everyone in the room does not have a piercing. Everyone in the room does not have completed a triathlon. Ronnie does not enjoy mountain biking. Melissa either cannot play the flute or does not enjoy mountain biking but not both. Everyone in the room does not make intricate hand-cut paper art for exhibitions. Ronnie does not enjoy spelunking. Everyone anywhere does not have a piercing.

Everyone anywhere collects vintage stamps.

contradiction

room(ronnie)&room(melissa)&room(harlan)&(![X]:(room(X)=>(X='ronnie'|X='melissa'|X='harlan')))& ((~((is_not_a_Linux_enthusiast(ronnie))|(does_not_enjoy_snowboarding(ronnie))))<~>(~![X]:(room(X)=>(((is_not_a_Linux_enthusiast(X))<~>(does_not_collect_vintage_stamps(X)))))))& (![X]:(room(X)=>(((does_not_collect_vintage_stamps(X))|(does_not_enjoy_snowboarding(X))))))& (((?[X]:(anywhere(X)&((does_not_practice_calligraphy(X))|(does_not_enjoy_skydiving(X)))))&(![X,Y]:((anywhere(X)&anywhere(Y)&(((does_not_practice_calligraphy(X))|(does_not_enjoy_skydiving(X))))&(((does_not_practice_calligraphy(Y))|(does_not_enjoy_skydiving(Y)))))=>(X=Y)))))& (((does_not_have_completed_a_triathlon(ronnie))|(does_not_enjoy_snowboarding(ronnie))))& (![X]:(room(X)=>(does_not_enjoy_coding_in_Python(X))))& (((?[X]:(room(X)&((does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))|(is_not_a_Linux_enthusiast(X)))))&(![X,Y]:((room(X)&room(Y)&(((does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))|(is_not_a_Linux_enthusiast(X))))&(((does_not_have_a_specialized_collection_of_handmade_artisan_pottery(Y))|(is_not_a_Linux_enthusiast(Y)))))=>(X=Y)))))& (![X]:(room(X)=>(~((does_not_develop_open-source_software_projects_in_their_free_time(X))|(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))& (![X]:(room(X)=>(does_not_collect_vintage_stamps(X))))& (![X]:(room(X)=>(((cannot_play_the_flute(X))&(does_not_have_a_piercing(X))))))& (![X]:(room(X)=>(does_not_have_a_piercing(X))))& (![X]:(room(X)=>(does_not_have_completed_a_triathlon(X))))& (does_not_enjoy_mountain_biking(ronnie))& (((cannot_play_the_flute(melissa))<~>(does_not_enjoy_mountain_biking(melissa))))& (![X]:(room(X)=>(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))))& (does_not_enjoy_spelunking(ronnie))& (![X]:(anywhere(X)=>(does_not_have_a_piercing(X))))& (((does_not_practice_calligraphy(ronnie))<~>(does_not_have_completed_a_triathlon(ronnie))))& (((does_not_enjoy_coding_in_Python(melissa))<~>(does_not_enjoy_snowboarding(melissa))))

room(ronnie)&room(melissa)&room(harlan)&(![X]:(room(X)=>(X='ronnie'|X='melissa'|X='harlan')))& ![X]:(anywhere(X)=>(collects_vintage_stamps(X)))

% SZS status Unsatisfiable for 52737763832691032287248 % SZS output start Proof for 52737763832691032287248 5. ! [X0] : anywhere(X0) [input b4] 50. ! [X0,X1] : (((~predj(X1) | ~predr(X1)) & (~predj(X0) | ~predr(X0)) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : ((~predj(X0) | ~predr(X0)) & room(X0)) [input p6] 52. ! [X0] : (room(X0) => ~predb(X0)) [input p8] 63. ! [X0] : (anywhere(X0) => predb(X0)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 65. ! [X0,X1] : (((~predj(X1) | ~predr(X1)) & (~predj(X0) | ~predr(X0)) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : ((~predj(X2) | ~predr(X2)) & room(X2)) [rectify 50] 66. ! [X0] : (anywhere(X0) => predb(X0)) & ! [X1] : (room(X1) => (fred = X1 | paul = X1 | mary = X1)) & room(fred) & room(paul) & room(mary) [rectify 63] 153. ! [X0,X1] : (X0 = X1 | ((predj(X1) & predr(X1)) | (predj(X0) & predr(X0)) | ~room(X1) | ~room(X0))) & ? [X2] : ((~predj(X2) | ~predr(X2)) & room(X2)) [ennf transformation 65] 154. ! [X0,X1] : (X0 = X1 | (predj(X1) & predr(X1)) | (predj(X0) & predr(X0)) | ~room(X1) | ~room(X0)) & ? [X2] : ((~predj(X2) | ~predr(X2)) & room(X2)) [flattening 153] 155. ! [X0] : (~predb(X0) | ~room(X0)) [ennf transformation 52] 158. ! [X0] : (predb(X0) | ~anywhere(X0)) & ! [X1] : ((fred = X1 | paul = X1 | mary = X1) | ~room(X1)) & room(fred) & room(paul) & room(mary) [ennf transformation 66] 159. ! [X0] : (predb(X0) | ~anywhere(X0)) & ! [X1] : (fred = X1 | paul = X1 | mary = X1 | ~room(X1)) & room(fred) & room(paul) & room(mary) [flattening 158] 168. ? [X2] : ((~predj(X2) | ~predr(X2)) & room(X2)) => ((~predj(sK2) | ~predr(sK2)) & room(sK2)) [choice axiom] 169. ! [X0,X1] : (X0 = X1 | (predj(X1) & predr(X1)) | (predj(X0) & predr(X0)) | ~room(X1) | ~room(X0)) & ((~predj(sK2) | ~predr(sK2)) & room(sK2)) [skolemisation 154,168] 173. anywhere(X0) [cnf transformation 5] 275. room(sK2) [cnf transformation 169] 281. ~predb(X0) | ~room(X0) [cnf transformation 155] 295. predb(X0) | ~anywhere(X0) [cnf transformation 159] 385. predb(X0) [subsumption resolution 295,173] 391. ~room(X0) [resolution 281,385] 396. $false [resolution 391,275] % SZS output end Proof for 52737763832691032287248 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Mildred, Anthony are the only persons in the room. If 'everyone in the room is a skilled home brewer experimenting with craft beer recipes or cannot play the harmonica' then 'everyone in the room who is a skilled home brewer experimenting with craft beer recipes can play the harmonica'. If 'someone in the room can play the harmonica' then 'everyone outside the room who writes poetry and practices kickboxing can play the harmonica'.

Everyone in the room does not practice digital art.

neutral

room(mildred)&room(anthony)&(![X]:(room(X)=>(X='mildred'|X='anthony')))& ((![X]:(room(X)=>(((cannot_play_the_harmonica(X))|(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))=>(![X]:(room(X)=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))=>(can_play_the_harmonica(X)))))))& ((?[X]:(room(X)&(can_play_the_harmonica(X))))=>(![X]:(~room(X)=>(((((writes_poetry(X))&(practices_kickboxing(X))))=>(can_play_the_harmonica(X)))))))& ((![X]:(~room(X)=>(((does_not_enjoy_cross-country_skiing(X))|(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))<~>(![X]:(room(X)=>(((does_not_practice_zumba(X))|(can_play_the_harmonica(X)))))))& ((((?[X]:(room(X)&~((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))|(cannot_play_the_harmonica(X)))))))=>(practices_zumba(mildred)))& ((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(mildred))=>(![X]:(room(X)=>(((owns_a_smartwatch(X))=>(can_play_the_harmonica(X)))))))& (writes_poetry(mildred))& (![X]:(room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))<=(hosts_regular_workshops_on_creative_writing(X))))))& ((![X]:((hosts_regular_workshops_on_creative_writing(X))=>(writes_poetry(X)))))& (![X]:(room(X)=>(((owns_a_smartwatch(X))=>(can_play_the_harmonica(X))))))& (~![X]:(room(X)=>(((writes_poetry(X))=>(does_enjoy_mountain_biking(X))))))& (![X]:(room(X)=>(((does_enjoy_mountain_biking(X))=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))& (hosts_regular_workshops_on_creative_writing(mildred))& ((![X]:((does_not_write_poetry(X))=>(uses_an_ios_phone(X)))))& (plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(mildred))& (![X]:(room(X)=>(((does_not_enjoy_mountain_biking(X))=>(has_a_tattoo(X))))))& (~![X]:(room(X)=>(((has_a_tattoo(X))=>(trains_for_and_competes_in_international_triathlons(X))))))& (is_a_Linux_enthusiast(mildred))& (owns_a_smartwatch(mildred))& (((enjoys_cross-country_skiing(mildred))<~>(practices_digital_art(mildred))))& (has_a_tattoo(mildred))& (![X]:(~room(X)=>(((hosts_regular_workshops_on_creative_writing(X))=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))& (![X]:(room(X)=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))& (![X]:(room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))=>(competes_in_national_level_swimming_championships(X))))))& (![X]:(room(X)=>(((does_not_host_regular_workshops_on_creative_writing(X))=>(collects_first_edition_books(X))))))& (collects_first_edition_books(mildred))& (does_enjoy_mountain_biking(mildred))& (![X]:(room(X)=>(((trains_for_and_competes_in_international_triathlons(X))=>(does_enjoy_mountain_biking(X))))))

room(mildred)&room(anthony)&(![X]:(room(X)=>(X='mildred'|X='anthony')))& ![X]:(room(X)=>(does_not_practice_digital_art(X)))

Callie, Victoriaetta, Valerie, Leo, Victoria are the only persons in the room. If “everyone in the room maintains a large, organic vegetable garden year-round or cannot play the harmonica” then “everyone in the room does not own a significant collection of rare gemstones and minerals”. Either “Callie collects rare minerals” or “someone in the room does not write poetry” but not both. Either “no one in the room maintains a large, organic vegetable garden year-round or does not own a significant collection of rare gemstones and minerals” or “Callie enjoys kayaking” but not both. Either “everyone anywhere either collects rare minerals or does not enjoy kayaking but not both” or “everyone in the room knows morse code or does not create bespoke furniture pieces from reclaimed wood” but not both. If “Victoriaetta enjoys kayaking” then “Victoriaetta does not maintain a large, organic vegetable garden year-round”. If “Victoriaetta does not maintain a large, organic vegetable garden year-round” then “Callie neither maintains a large, organic vegetable garden year-round nor is dedicated to sustainable living and zero-waste practices”. If “it is true that “not everyone in the room is an avid mountain climber who has scaled several peaks or does not enjoy camping and organizing outdoor survival workshops”” then “Valerie cannot play the harmonica”. If “Callie cannot play the harmonica” then “Valerie does not write poetry”. If “Valerie does not write poetry” then “everyone in the room knows morse code if they does not know morse code”. Either “not everyone in the room cannot play the harmonica or is not dedicated to sustainable living and zero-waste practices” or “Valerie neither is not dedicated to sustainable living and zero-waste practices nor makes intricate hand-cut paper art for exhibitions” but not both. “Everyone in the room practices pilates or does not create bespoke furniture pieces from reclaimed wood” only if “Valerie collects rare minerals”. If “Victoriaetta enjoys camping and organizing outdoor survival workshops” then “Victoriaetta practices pilates”. If “Victoriaetta practices pilates” then “Callie does not practice pilates”. If “everyone in the room is not dedicated to sustainable living and zero-waste practices or does not practice pilates” then “everyone in the room is not dedicated to sustainable living and zero-waste practices only if they practices pilates”.

Everyone in the room does not own a telescope.

neutral

room(callie)&room(victoriaetta)&room(valerie)&room(leo)&room(victoria)&(![X]:(room(X)=>(X='callie'|X='victoriaetta'|X='valerie'|X='leo'|X='victoria')))& ((![X]:(room(X)=>(((cannot_play_the_harmonica(X))|(maintains_a_large,_organic_vegetable_garden_year-round(X))))))=>(![X]:(room(X)=>(does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X)))))& ((collects_rare_minerals(callie))<~>(?[X]:(room(X)&(does_not_write_poetry(X)))))& ((~?[X]:(room(X)=>(((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))|(maintains_a_large,_organic_vegetable_garden_year-round(X))))))<~>(enjoys_kayaking(callie)))& ((![X]:(anywhere(X)=>(((collects_rare_minerals(X))<~>(does_not_enjoy_kayaking(X))))))<~>(![X]:(room(X)=>(((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))|(knows_morse_code(X)))))))& (((enjoys_kayaking(victoriaetta))=>(does_not_maintain_a_large,_organic_vegetable_garden_year-round(victoriaetta)))& ((does_not_maintain_a_large,_organic_vegetable_garden_year-round(victoriaetta))=>(~((maintains_a_large,_organic_vegetable_garden_year-round(callie))|(is_dedicated_to_sustainable_living_and_zero-waste_practices(callie))))))& ((~![X]:(room(X)=>(((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))|(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))=>(cannot_play_the_harmonica(valerie)))& (((cannot_play_the_harmonica(callie))=>(does_not_write_poetry(valerie)))& ((does_not_write_poetry(valerie))=>(![X]:(room(X)=>(((does_not_know_morse_code(X))=>(knows_morse_code(X))))))))& ((~![X]:(room(X)=>(((is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(cannot_play_the_harmonica(X))))))<~>(~((is_not_dedicated_to_sustainable_living_and_zero-waste_practices(valerie))|(makes_intricate_hand-cut_paper_art_for_exhibitions(valerie)))))& ((![X]:(room(X)=>(((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))|(practices_pilates(X))))))=>(collects_rare_minerals(valerie)))& (((enjoys_camping_and_organizing_outdoor_survival_workshops(victoriaetta))=>(practices_pilates(victoriaetta)))& ((practices_pilates(victoriaetta))=>(does_not_practice_pilates(callie))))& ((![X]:(room(X)=>(((does_not_practice_pilates(X))|(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))=>(![X]:(room(X)=>(((practices_pilates(X))<=(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X)))))))& (is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(victoriaetta))& (((can_play_the_harmonica(victoriaetta))&(is_allergic_to_anything(victoriaetta))))& (is_not_dedicated_to_sustainable_living_and_zero-waste_practices(valerie))& (does_not_write_poetry(valerie))& (does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(victoriaetta))& (enjoys_camping_and_organizing_outdoor_survival_workshops(victoriaetta))& (![X]:(room(X)=>(((does_not_practice_pilates(X))=>(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))))))& (cannot_play_the_harmonica(valerie))& (![X]:(room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))=>(~((enjoys_kayaking(X))|(owns_a_telescope(X))))))))& (?[X]:(room(X)&(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))& (does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(callie))& (is_dedicated_to_sustainable_living_and_zero-waste_practices(callie))& (![X]:(~room(X)=>(((does_not_enjoy_kayaking(X))=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))& (knows_morse_code(callie))& (?[X]:(room(X)&(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))& (does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(victoriaetta))

room(callie)&room(victoriaetta)&room(valerie)&room(leo)&room(victoria)&(![X]:(room(X)=>(X='callie'|X='victoriaetta'|X='valerie'|X='leo'|X='victoria')))& ![X]:(room(X)=>(does_not_own_a_telescope(X)))

Georgia is the only person in the room. If "everyone in the room does not enjoy salsa dancing or frequently participates in hackathons and coding competitions" then "someone in the room enjoys salsa dancing". "Someone in the room frequently participates in hackathons and coding competitions" if "everyone in the room is not a coffee connoisseur or is a dedicated volunteer for local community service projects". If "everyone in the room does not enjoy coding in Python or frequently participates in hackathons and coding competitions" then "only one person in the room creates large-scale murals for public art installations". If "everyone outside the room does not play the drums or collects classic novels" then "everyone in the room who does not play the drums enjoys coding in Python". If someone enjoys salsa dancing then he/she neither frequently participates in hackathons and coding competitions nor enjoys snowboarding. More than one person anywhere is a coffee connoisseur. Everyone in the room who collects limited-edition art prints from contemporary artists collects rare minerals. If someone enjoys virtual reality gaming then he/she is a client of LVMH. If someone is a coffee connoisseur then he/she either is a client of LVMH or enjoys virtual reality gaming but not both. If someone either frequently participates in hackathons and coding competitions or writes a travel blog but not both then he/she participates in long-distance cycling events across the country.

Georgia enjoys virtual reality gaming.

contradiction

room(georgia)&(![X]:(room(X)=>(X='georgia')))& ((![X]:(room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))|(does_not_enjoy_salsa_dancing(X))))))=>(?[X]:(room(X)&(enjoys_salsa_dancing(X)))))& ((![X]:(room(X)=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))|(is_not_a_coffee_connoisseur(X))))))=>(?[X]:(room(X)&(frequently_participates_in_hackathons_and_coding_competitions(X)))))& ((![X]:(room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))|(does_not_enjoy_coding_in_Python(X))))))=>(((?[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))))))& ((![X]:(~room(X)=>(((collects_classic_novels(X))|(does_not_play_the_drums(X))))))=>(![X]:(room(X)=>(((does_not_play_the_drums(X))=>(enjoys_coding_in_Python(X)))))))& ((![X]:((enjoys_salsa_dancing(X))=>(~((frequently_participates_in_hackathons_and_coding_competitions(X))|(enjoys_snowboarding(X)))))))& ((?[X,Y]:(anywhere(X)&anywhere(Y)&(is_a_coffee_connoisseur(X)&is_a_coffee_connoisseur(Y))&(X!=Y))))& (![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))=>(collects_rare_minerals(X))))))& ((![X]:((enjoys_virtual_reality_gaming(X))=>(is_a_client_of_LVMH(X)))))& ((![X]:((is_a_coffee_connoisseur(X))=>(((is_a_client_of_LVMH(X))<~>(enjoys_virtual_reality_gaming(X)))))))& ((![X]:((((frequently_participates_in_hackathons_and_coding_competitions(X))<~>(writes_a_travel_blog(X))))=>(participates_in_long-distance_cycling_events_across_the_country(X)))))& (![X]:(room(X)=>(((is_a_coffee_connoisseur(X))<=(plays_the_drums(X))))))

room(georgia)&(![X]:(room(X)=>(X='georgia')))& enjoys_virtual_reality_gaming(georgia)

% SZS status Unsatisfiable for 185472995996798565692781 % SZS output start Proof for 185472995996798565692781 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 45. ! [X0] : (room(X0) => (~predc(X0) | predi(X0))) => ? [X0] : (predc(X0) & room(X0)) [input p1] 46. ! [X0] : (room(X0) => (~predl(X0) | predh(X0))) => ? [X0] : (predi(X0) & room(X0)) [input p2] 49. ! [X0] : (predc(X0) => ~(predg(X0) | predi(X0))) [input p5] 52. ! [X0] : (predf(X0) => prede(X0)) [input p8] 53. ! [X0] : (predl(X0) => (prede(X0) <~> predf(X0))) [input p9] 56. predf(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 57. ! [X0] : (room(X0) => (~predc(X0) | predi(X0))) => ? [X1] : (predc(X1) & room(X1)) [rectify 45] 58. ! [X0] : (room(X0) => (~predl(X0) | predh(X0))) => ? [X1] : (predi(X1) & room(X1)) [rectify 46] 63. ! [X0] : (predc(X0) => ~predi(X0)) [pure predicate removal 49] 68. ! [X0] : (room(X0) => ~predl(X0)) => ? [X1] : (predi(X1) & room(X1)) [pure predicate removal 58] 142. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 143. ? [X1] : (predc(X1) & room(X1)) | ? [X0] : ((predc(X0) & ~predi(X0)) & room(X0)) [ennf transformation 57] 144. ? [X1] : (predc(X1) & room(X1)) | ? [X0] : (predc(X0) & ~predi(X0) & room(X0)) [flattening 143] 145. ? [X1] : (predi(X1) & room(X1)) | ? [X0] : (predl(X0) & room(X0)) [ennf transformation 68] 148. ! [X0] : (~predi(X0) | ~predc(X0)) [ennf transformation 63] 149. ! [X0] : (prede(X0) | ~predf(X0)) [ennf transformation 52] 150. ! [X0] : ((prede(X0) <~> predf(X0)) | ~predl(X0)) [ennf transformation 53] 151. predf(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 56] 153. ? [X0] : (predc(X0) & room(X0)) | ? [X1] : (predc(X1) & ~predi(X1) & room(X1)) [rectify 144] 154. ? [X0] : (predc(X0) & room(X0)) => (predc(sK0) & room(sK0)) [choice axiom] 155. ? [X1] : (predc(X1) & ~predi(X1) & room(X1)) => (predc(sK1) & ~predi(sK1) & room(sK1)) [choice axiom] 156. (predc(sK0) & room(sK0)) | (predc(sK1) & ~predi(sK1) & room(sK1)) [skolemisation 153,155,154] 157. ? [X0] : (predi(X0) & room(X0)) | ? [X1] : (predl(X1) & room(X1)) [rectify 145] 158. ? [X0] : (predi(X0) & room(X0)) => (predi(sK2) & room(sK2)) [choice axiom] 159. ? [X1] : (predl(X1) & room(X1)) => (predl(sK3) & room(sK3)) [choice axiom] 160. (predi(sK2) & room(sK2)) | (predl(sK3) & room(sK3)) [skolemisation 157,159,158] 167. ! [X0] : (((~predf(X0) | ~prede(X0)) & (predf(X0) | prede(X0))) | ~predl(X0)) [nnf transformation 150] 249. ~room(X0) | mary = X0 [cnf transformation 142] 250. room(sK0) | room(sK1) [cnf transformation 156] 251. room(sK0) | ~predi(sK1) [cnf transformation 156] 253. predc(sK0) | room(sK1) [cnf transformation 156] 254. predc(sK0) | ~predi(sK1) [cnf transformation 156] 256. room(sK2) | room(sK3) [cnf transformation 160] 257. room(sK2) | predl(sK3) [cnf transformation 160] 258. predi(sK2) | room(sK3) [cnf transformation 160] 259. predi(sK2) | predl(sK3) [cnf transformation 160] 266. ~predc(X0) | ~predi(X0) [cnf transformation 148] 270. ~predf(X0) | prede(X0) [cnf transformation 149] 272. ~predf(X0) | ~prede(X0) | ~predl(X0) [cnf transformation 167] 275. predf(mary) [cnf transformation 151] 281. 2 <=> predc(sK0) [avatar definition] 283. predc(sK0) <- (2) [avatar component clause 281] 286. 3 <=> predi(sK1) [avatar definition] 288. ~predi(sK1) <- (~3) [avatar component clause 286] 289. ~3 | 2 [avatar split clause 254,281,286] 291. 4 <=> room(sK1) [avatar definition] 293. room(sK1) <- (4) [avatar component clause 291] 294. 4 | 2 [avatar split clause 253,281,291] 296. 5 <=> room(sK0) [avatar definition] 298. room(sK0) <- (5) [avatar component clause 296] 300. ~3 | 5 [avatar split clause 251,296,286] 301. 4 | 5 [avatar split clause 250,296,291] 303. 6 <=> predl(sK3) [avatar definition] 305. predl(sK3) <- (6) [avatar component clause 303] 307. 7 <=> predi(sK2) [avatar definition] 309. predi(sK2) <- (7) [avatar component clause 307] 310. 6 | 7 [avatar split clause 259,307,303] 312. 8 <=> room(sK3) [avatar definition] 314. room(sK3) <- (8) [avatar component clause 312] 315. 8 | 7 [avatar split clause 258,307,312] 317. 9 <=> room(sK2) [avatar definition] 319. room(sK2) <- (9) [avatar component clause 317] 320. 6 | 9 [avatar split clause 257,317,303] 321. 8 | 9 [avatar split clause 256,317,312] 347. ~predf(X0) | ~predl(X0) [subsumption resolution 272,270] 349. ~predi(sK0) <- (2) [resolution 266,283] 351. ~predl(mary) [resolution 347,275] 356. mary = sK0 <- (5) [resolution 249,298] 357. mary = sK3 <- (8) [resolution 249,314] 359. ~predi(mary) <- (2, 5) [backward demodulation 349,356] 363. predl(mary) <- (6, 8) [backward demodulation 305,357] 365. $false <- (6, 8) [subsumption resolution 363,351] 366. ~6 | ~8 [avatar contradiction clause 365] 370. mary = sK2 <- (9) [resolution 319,249] 371. predi(mary) <- (7, 9) [backward demodulation 309,370] 373. $false <- (2, 5, 7, 9) [subsumption resolution 371,359] 374. ~2 | ~5 | ~7 | ~9 [avatar contradiction clause 373] 379. mary = sK1 <- (4) [resolution 293,249] 381. ~predi(mary) <- (~3, 4) [backward demodulation 288,379] 385. $false <- (~3, 4, 7, 9) [subsumption resolution 381,371] 386. 3 | ~4 | ~7 | ~9 [avatar contradiction clause 385] 387. $false [avatar sat refutation 289,294,300,301,310,315,320,321,366,374,386] % SZS output end Proof for 185472995996798565692781 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Eugene, David are the only persons in the room. It is not the case that “Eugene knows morse code”. David has a tattoo. David neither enjoys writing detailed reviews of new and classic board games nor does not participate in citizen science projects related to wildlife monitoring. David who does not practice and performs acrobatic dance routines is not a dedicated volunteer for local community service projects. It is not the case that “David knows morse code”. David is an enthusiastic bird watcher who travels for rare sightings.

David either does not practice digital art or does not frequently participates in hackathons and coding competitions but not both.

neutral

room(eugene)&room(david)&(![X]:(room(X)=>(X='eugene'|X='david')))& (~(knows_morse_code(eugene)))& (has_a_tattoo(david))& (~((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(david))|(does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(david))))& ((does_not_practice_and_performs_acrobatic_dance_routines(david))&(is_not_a_dedicated_volunteer_for_local_community_service_projects(david)))& (~(knows_morse_code(david)))& (is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(david))& (is_a_craft_beer_aficionado(eugene))& (enjoys_watercolor_painting(eugene))& (~((?[X,Y]:(room(X)&room(Y)&(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))|(can_play_the_harmonica(X))|(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X)))&((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(Y))|(can_play_the_harmonica(Y))|(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(Y))))&(X!=Y)))))& (travels_domestically_frequently(david))& ((![X]:((((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))|(has_a_tattoo(X))|(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))=>(competes_in_national_level_swimming_championships(X)))))& (((?[X]:(room(X)&owns_an_Android_phone(X)))&(![X,Y]:((room(X)&room(Y)&(owns_an_Android_phone(X))&(owns_an_Android_phone(Y)))=>(X=Y)))))& (is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(eugene))& (~((?[X,Y]:(room(X)&room(Y)&(is_not_a_cybersecurity_expert(X)&is_not_a_cybersecurity_expert(Y))&(X!=Y)))))& (does_not_collect_comic_books(david))& (~(is_a_cybersecurity_expert(david)))& (enjoys_writing_detailed_reviews_of_new_and_classic_board_games(eugene))& (((?[X]:(room(X)&collects_comic_books(X)))))& (is_a_cybersecurity_expert(eugene))& ((?[X,Y]:(room(X)&room(Y)&(enjoys_stargazing(X)&enjoys_stargazing(Y))&(X!=Y))))& (does_not_frequently_participates_in_hackathons_and_coding_competitions(eugene))& (practices_digital_art(eugene))

room(eugene)&room(david)&(![X]:(room(X)=>(X='eugene'|X='david')))& ((does_not_practice_digital_art(david))<~>(does_not_frequently_participates_in_hackathons_and_coding_competitions(david)))

Sylvia, Luis, Gail, Marguerite are the only persons in the room. If “Luis enjoys deep-sea diving and exploring underwater caves or regularly goes on multi-day backpacking trips in national parks or both” then “if someone regularly goes on multi-day backpacking trips in national parks then he/she does not regularly goes on multi-day backpacking trips in national parks”. Marguerite regularly goes on multi-day backpacking trips in national parks. Gail enjoys deep-sea diving and exploring underwater caves. Gail regularly goes on multi-day backpacking trips in national parks. Sylvia who has completed a triathlon regularly goes on multi-day backpacking trips in national parks. Gail has completed a triathlon. If someone regularly goes on multi-day backpacking trips in national parks then he/she has completed a triathlon and enjoys deep-sea diving and exploring underwater caves. Sylvia has completed a triathlon.

Marguerite enjoys deep-sea diving and exploring underwater caves.

entailment

room(sylvia)&room(luis)&room(gail)&room(marguerite)&(![X]:(room(X)=>(X='sylvia'|X='luis'|X='gail'|X='marguerite')))& ((((enjoys_deep-sea_diving_and_exploring_underwater_caves(luis))|(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(luis))))=>((![X]:((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))=>(does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))& (regularly_goes_on_multi-day_backpacking_trips_in_national_parks(marguerite))& (enjoys_deep-sea_diving_and_exploring_underwater_caves(gail))& (regularly_goes_on_multi-day_backpacking_trips_in_national_parks(gail))& ((has_completed_a_triathlon(sylvia))&(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(sylvia)))& (has_completed_a_triathlon(gail))& ((![X]:((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))=>(((has_completed_a_triathlon(X))&(enjoys_deep-sea_diving_and_exploring_underwater_caves(X)))))))& (has_completed_a_triathlon(sylvia))

room(sylvia)&room(luis)&room(gail)&room(marguerite)&(![X]:(room(X)=>(X='sylvia'|X='luis'|X='gail'|X='marguerite')))& enjoys_deep-sea_diving_and_exploring_underwater_caves(marguerite)

% SZS status Unsatisfiable for 8617718724045715164740819 % SZS output start Proof for 8617718724045715164740819 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 46. predc(alice) [input p2] 51. ! [X0] : (predc(X0) => (preda(X0) & predb(X0))) [input p7] 53. ~(preda(alice) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 55. ! [X0] : (predc(X0) => preda(X0)) [pure predicate removal 51] 130. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 131. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 130] 133. ! [X0] : (preda(X0) | ~predc(X0)) [ennf transformation 55] 134. ~preda(alice) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 53] 135. ~preda(alice) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 134] 137. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK0 & fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) [choice axiom] 138. ~preda(alice) | (alice != sK0 & fred != sK0 & paul != sK0 & mary != sK0 & room(sK0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 135,137] 219. room(mary) [cnf transformation 131] 220. room(paul) [cnf transformation 131] 221. room(fred) [cnf transformation 131] 222. room(alice) [cnf transformation 131] 223. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 131] 226. predc(alice) [cnf transformation 46] 230. ~predc(X0) | preda(X0) [cnf transformation 133] 231. ~preda(alice) | room(sK0) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 138] 232. ~preda(alice) | mary != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 138] 233. ~preda(alice) | paul != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 138] 234. ~preda(alice) | fred != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 138] 235. ~preda(alice) | alice != sK0 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 138] 251. ~preda(alice) | alice != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 235,222] 252. ~preda(alice) | alice != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 251,221] 253. ~preda(alice) | alice != sK0 | ~room(mary) [subsumption resolution 252,220] 254. ~preda(alice) | alice != sK0 [subsumption resolution 253,219] 256. 4 <=> alice = sK0 [avatar definition] 258. alice != sK0 <- (~4) [avatar component clause 256] 260. 5 <=> preda(alice) [avatar definition] 263. ~4 | ~5 [avatar split clause 254,260,256] 264. ~preda(alice) | fred != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 234,222] 265. ~preda(alice) | fred != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 264,221] 266. ~preda(alice) | fred != sK0 | ~room(mary) [subsumption resolution 265,220] 267. ~preda(alice) | fred != sK0 [subsumption resolution 266,219] 269. 6 <=> fred = sK0 [avatar definition] 271. fred != sK0 <- (~6) [avatar component clause 269] 272. ~6 | ~5 [avatar split clause 267,260,269] 273. ~preda(alice) | paul != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 233,222] 274. ~preda(alice) | paul != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 273,221] 275. ~preda(alice) | paul != sK0 | ~room(mary) [subsumption resolution 274,220] 276. ~preda(alice) | paul != sK0 [subsumption resolution 275,219] 278. 7 <=> paul = sK0 [avatar definition] 280. paul != sK0 <- (~7) [avatar component clause 278] 281. ~7 | ~5 [avatar split clause 276,260,278] 282. ~preda(alice) | mary != sK0 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 232,222] 283. ~preda(alice) | mary != sK0 | ~room(paul) | ~room(mary) [subsumption resolution 282,221] 284. ~preda(alice) | mary != sK0 | ~room(mary) [subsumption resolution 283,220] 285. ~preda(alice) | mary != sK0 [subsumption resolution 284,219] 287. 8 <=> mary = sK0 [avatar definition] 289. mary != sK0 <- (~8) [avatar component clause 287] 290. ~8 | ~5 [avatar split clause 285,260,287] 291. ~preda(alice) | room(sK0) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 231,222] 292. ~preda(alice) | room(sK0) | ~room(paul) | ~room(mary) [subsumption resolution 291,221] 293. ~preda(alice) | room(sK0) | ~room(mary) [subsumption resolution 292,220] 294. ~preda(alice) | room(sK0) [subsumption resolution 293,219] 296. 9 <=> room(sK0) [avatar definition] 298. room(sK0) <- (9) [avatar component clause 296] 299. 9 | ~5 [avatar split clause 294,260,296] 300. preda(alice) [resolution 230,226] 305. 5 [avatar split clause 300,260] 352. fred = sK0 | paul = sK0 | mary = sK0 | alice = sK0 <- (9) [resolution 223,298] 353. paul = sK0 | mary = sK0 | alice = sK0 <- (~6, 9) [subsumption resolution 352,271] 354. mary = sK0 | alice = sK0 <- (~6, ~7, 9) [subsumption resolution 353,280] 355. alice = sK0 <- (~6, ~7, ~8, 9) [subsumption resolution 354,289] 356. $false <- (~4, ~6, ~7, ~8, 9) [subsumption resolution 355,258] 357. 4 | 6 | 7 | 8 | ~9 [avatar contradiction clause 356] 358. $false [avatar sat refutation 263,272,281,290,299,305,357] % SZS output end Proof for 8617718724045715164740819 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

There is a room. Everyone in the room does not enjoy origami. Everyone in the room neither does not practice yoga nor is not a dedicated advocate for digital privacy and encryption. Everyone in the room is not passionate about collecting and restoring classic cars or does not volunteer for local environmental conservation projects or both. If someone either is not an avid collector of autographed memorabilia from famous musicians or does not create bespoke furniture pieces from reclaimed wood but not both then he/she neither does not volunteer for local environmental conservation projects nor is not a dedicated advocate for digital privacy and encryption. Everyone in the room does not practice yoga, is not an avid collector of autographed memorabilia from famous musicians and does not read mystery novels. Everyone outside the room does not participate in long-distance cycling events across the country. If someone does not collect classic novels, does not create bespoke furniture pieces from reclaimed wood and does not practice pilates then he/she is not a dedicated advocate for digital privacy and encryption, does not volunteer for local environmental conservation projects or does not write and illustrates their own graphic novels. If someone does not have a tattoo then he/she is not an avid collector of autographed memorabilia from famous musicians or does not practice yoga or both. Everyone in the room neither does not read mystery novels nor is not passionate about collecting and restoring classic cars. Everyone in the room is not passionate about collecting and restoring classic cars. Herman dreamt that everyone in the room does not own an extensive assortment of vintage comic book memorabilia. Everyone anywhere does not enjoy bird watching, does not create bespoke furniture pieces from reclaimed wood and does not collect classic novels. Everyone in the room does not work on fridays. Everyone in the room either does not have a saltwater aquarium or is not an avid mountain climber who has scaled several peaks but not both. Everyone in the room does not write and illustrates their own graphic novels.

Everyone in the room does not practice pilates.

entailment

(there_is_a_room)& (![X]:(room(X)=>(does_not_enjoy_origami(X))))& (![X]:(room(X)=>(~((does_not_practice_yoga(X))|(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))& (![X]:(room(X)=>(((is_not_passionate_about_collecting_and_restoring_classic_cars(X))|(does_not_volunteer_for_local_environmental_conservation_projects(X))))))& ((![X]:((((is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))<~>(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))=>(~((does_not_volunteer_for_local_environmental_conservation_projects(X))|(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X)))))))& (![X]:(room(X)=>(((does_not_practice_yoga(X))&(is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))&(does_not_read_mystery_novels(X))))))& (![X]:(~room(X)=>(does_not_participate_in_long-distance_cycling_events_across_the_country(X))))& ((![X]:((((does_not_collect_classic_novels(X))&(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))&(does_not_practice_pilates(X))))=>(((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(does_not_volunteer_for_local_environmental_conservation_projects(X))|(does_not_write_and_illustrates_their_own_graphic_novels(X)))))))& ((![X]:((does_not_have_a_tattoo(X))=>(((is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))|(does_not_practice_yoga(X)))))))& (![X]:(room(X)=>(~((does_not_read_mystery_novels(X))|(is_not_passionate_about_collecting_and_restoring_classic_cars(X))))))& (![X]:(room(X)=>(is_not_passionate_about_collecting_and_restoring_classic_cars(X))))& ((herman_dream=>(![X]:(room(X)=>(does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))))& (![X]:(anywhere(X)=>(((does_not_enjoy_bird_watching(X))&(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))&(does_not_collect_classic_novels(X))))))& (![X]:(room(X)=>(does_not_work_on_fridays(X))))& (![X]:(room(X)=>(((does_not_have_a_saltwater_aquarium(X))<~>(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))& (![X]:(room(X)=>(does_not_write_and_illustrates_their_own_graphic_novels(X))))

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

% SZS status Unsatisfiable for 442401953259071539651073 % SZS output start Proof for 442401953259071539651073 44. there_is_a_room [input p0] 46. ! [X0] : (room(X0) => ~(~predt(X0) | ~predr(X0))) [input p2] 49. ! [X0] : (room(X0) => (~predd(X0) & ~preds(X0) & ~predr(X0))) [input p5] 60. ~(! [X0] : (room(X0) => ~predm(X0)) & there_is_a_room) [input hypothesis] 68. ! [X0] : (room(X0) => ~~predr(X0)) [pure predicate removal 46] 70. ~(! [X0] : ~room(X0) & there_is_a_room) [pure predicate removal 60] 144. ! [X0] : (predr(X0) | ~room(X0)) [ennf transformation 68] 148. ! [X0] : ((~predd(X0) & ~preds(X0) & ~predr(X0)) | ~room(X0)) [ennf transformation 49] 153. ? [X0] : room(X0) | ~there_is_a_room [ennf transformation 70] 157. ? [X0] : room(X0) => room(sK0) [choice axiom] 158. room(sK0) | ~there_is_a_room [skolemisation 153,157] 240. there_is_a_room [cnf transformation 44] 241. predr(X0) | ~room(X0) [cnf transformation 144] 245. ~predr(X0) | ~room(X0) [cnf transformation 148] 254. room(sK0) | ~there_is_a_room [cnf transformation 158] 255. ~room(X0) [subsumption resolution 245,241] 257. ~there_is_a_room [subsumption resolution 254,255] 258. $false [subsumption resolution 257,240] % SZS output end Proof for 442401953259071539651073 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Brendan is the only person in the room. Everyone in the room is older than Kenneth if they is wise. If someone is older than Jacob then he/she is a creative person and vice versa. No one anywhere who is quiet is not calm. Someone anywhere is quieter than Kenneth. Brendan is older than Jacob. Brendan is older than Jacob, is quieter than Kenneth and is older than Kenneth. Everyone outside the room is a creative brave person if they is quieter than Jacob. Brendan is older than Kenneth. If someone is not a brave old person then he/she is richer than Kenneth, is happy or is a quiet tall person. Brendan is richer than Jacob. Jacob is quieter than Brendan. If someone is a funny patient person then he/she is a tall patient person. Brendan is not a old person. All humble person is tall. Brendan is quieter than Kenneth. Brendan is wise. Brendan is richer than Kenneth. Someone who is quiet is richer than someone who is quieter than Jacob. Someone who is not generous is quieter than someone who is richer than Kenneth. Someone who is a curious generous patient creative brave person is older than someone who is quieter than Kenneth, is not a kind person and is older than Kenneth. Everyone in the room who is not kind or is a tall person or both is brave. Everyone in the room is brave only if they is older than Kenneth. Everyone in the room is a humble person if they is quieter than Kenneth.

Brendan is brave.

entailment

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

room(brendan)&(![X]:(room(X)=>(X='brendan')))& brave(brendan)

% SZS status Unsatisfiable for 5842702869462610336964512 % SZS output start Proof for 5842702869462610336964512 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 46. ! [X0] : (older(paul,X0) <=> (person(X0) & creative(X0))) [input p2] 49. older(paul,mary) [input p5] 50. older(fred,mary) & quieter(fred,mary) & older(paul,mary) [input p6] 58. ! [X0] : (humble(X0) => tall(X0)) [input p14] 65. ! [X0] : (room(X0) => (((person(X0) & tall(X0)) | ~kind(X0)) => brave(X0))) [input p21] 67. ! [X0] : (room(X0) => (quieter(fred,X0) => (person(X0) & humble(X0)))) [input p23] 68. ~(brave(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 148. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 155. ! [X0] : (tall(X0) | ~humble(X0)) [ennf transformation 58] 157. ! [X0] : ((brave(X0) | ((~person(X0) | ~tall(X0)) & kind(X0))) | ~room(X0)) [ennf transformation 65] 158. ! [X0] : (brave(X0) | ((~person(X0) | ~tall(X0)) & kind(X0)) | ~room(X0)) [flattening 157] 161. ! [X0] : (((person(X0) & humble(X0)) | ~quieter(fred,X0)) | ~room(X0)) [ennf transformation 67] 162. ! [X0] : ((person(X0) & humble(X0)) | ~quieter(fred,X0) | ~room(X0)) [flattening 161] 163. ~brave(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 68] 165. ! [X0] : ((older(paul,X0) | (~person(X0) | ~creative(X0))) & ((person(X0) & creative(X0)) | ~older(paul,X0))) [nnf transformation 46] 166. ! [X0] : ((older(paul,X0) | ~person(X0) | ~creative(X0)) & ((person(X0) & creative(X0)) | ~older(paul,X0))) [flattening 165] 175. ? [X0] : (mary != X0 & room(X0)) => (mary != sK7 & room(sK7)) [choice axiom] 176. ~brave(mary) | (mary != sK7 & room(sK7)) | ~room(mary) [skolemisation 163,175] 257. room(mary) [cnf transformation 148] 258. ~room(X0) | mary = X0 [cnf transformation 148] 261. ~older(paul,X0) | person(X0) [cnf transformation 166] 265. older(paul,mary) [cnf transformation 49] 267. quieter(fred,mary) [cnf transformation 50] 276. ~humble(X0) | tall(X0) [cnf transformation 155] 295. ~tall(X0) | ~person(X0) | brave(X0) | ~room(X0) [cnf transformation 158] 297. ~quieter(fred,X0) | humble(X0) | ~room(X0) [cnf transformation 162] 299. ~brave(mary) | room(sK7) | ~room(mary) [cnf transformation 176] 300. ~brave(mary) | mary != sK7 | ~room(mary) [cnf transformation 176] 306. 2 <=> person(mary) [avatar definition] 307. person(mary) <- (2) [avatar component clause 306] 319. ~brave(mary) | mary != sK7 [subsumption resolution 300,257] 321. 5 <=> mary = sK7 [avatar definition] 323. mary != sK7 <- (~5) [avatar component clause 321] 325. 6 <=> brave(mary) [avatar definition] 328. ~5 | ~6 [avatar split clause 319,325,321] 329. ~brave(mary) | room(sK7) [subsumption resolution 299,257] 331. 7 <=> room(sK7) [avatar definition] 333. room(sK7) <- (7) [avatar component clause 331] 334. 7 | ~6 [avatar split clause 329,325,331] 337. person(mary) [resolution 261,265] 340. 2 [avatar split clause 337,306] 376. humble(mary) | ~room(mary) [resolution 297,267] 387. humble(mary) [subsumption resolution 376,257] 400. tall(mary) [resolution 387,276] 401. ~person(mary) | brave(mary) | ~room(mary) [resolution 400,295] 402. brave(mary) | ~room(mary) <- (2) [subsumption resolution 401,307] 406. brave(mary) <- (2) [subsumption resolution 402,257] 407. 6 | ~2 [avatar split clause 406,306,325] 414. mary = sK7 <- (7) [resolution 333,258] 424. $false <- (~5, 7) [subsumption resolution 414,323] 425. 5 | ~7 [avatar contradiction clause 424] 426. $false [avatar sat refutation 328,334,340,407,425] % SZS output end Proof for 5842702869462610336964512 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Willie, Sherry are the only persons in the room. Someone in the room does not have a tattoo if someone in the room does not practice pilates. If someone in the room does not collect historical artifacts related to ancient civilizations then someone in the room does not work on fridays. If someone in the room does not work on fridays then someone outside the room does not have a tattoo. Someone in the room either does not practice pilates or does not have a tattoo but not both if someone in the room is not a craft beer aficionado. Someone in the room does not collect historical artifacts related to ancient civilizations if someone in the room does not work on fridays. If someone in the room does not collect foreign coins then someone in the room either is not a craft beer aficionado or is not a member of a local theater group specializing in improv but not both. If someone in the room either is not a craft beer aficionado or is not a member of a local theater group specializing in improv but not both then someone outside the room is not a client of Costco. If it is true that someone in the room does not make intricate hand-cut paper art for exhibitions then someone in the room does not host themed dinner parties featuring gourmet home-cooked meals. If someone in the room does not host themed dinner parties featuring gourmet home-cooked meals then someone in the room is not a culinary enthusiast who experiments with international cuisines. It is true that someone outside the room either does not own a significant collection of rare gemstones and minerals or is not a culinary enthusiast who experiments with international cuisines but not both if someone anywhere does not collect vintage vinyl records. Someone anywhere does not have a tattoo. Someone in the room either is not an enthusiastic bird watcher who travels for rare sightings or does not have a piercing but not both.

More than one person in the room makes intricate hand-cut paper art for exhibitions.

neutral

room(willie)&room(sherry)&(![X]:(room(X)=>(X='willie'|X='sherry')))& ((?[X]:(room(X)&(does_not_practice_pilates(X))))=>(?[X]:(room(X)&(does_not_have_a_tattoo(X)))))& (((?[X]:(room(X)&(does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))))=>(?[X]:(room(X)&(does_not_work_on_fridays(X)))))& ((?[X]:(room(X)&(does_not_work_on_fridays(X))))=>(?[X]:(~room(X)&(does_not_have_a_tattoo(X))))))& ((?[X]:(room(X)&(is_not_a_craft_beer_aficionado(X))))=>(?[X]:(room(X)&(((does_not_practice_pilates(X))<~>(does_not_have_a_tattoo(X)))))))& ((?[X]:(room(X)&(does_not_work_on_fridays(X))))=>(?[X]:(room(X)&(does_not_collect_historical_artifacts_related_to_ancient_civilizations(X)))))& (((?[X]:(room(X)&(does_not_collect_foreign_coins(X))))=>(?[X]:(room(X)&(((is_not_a_craft_beer_aficionado(X))<~>(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X)))))))& ((?[X]:(room(X)&(((is_not_a_craft_beer_aficionado(X))<~>(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))))))=>(?[X]:(~room(X)&(is_not_a_client_of_Costco(X))))))& (((?[X]:(room(X)&(does_not_make_intricate_hand-cut_paper_art_for_exhibitions(X))))=>(?[X]:(room(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))))=>(?[X]:(room(X)&(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))& ((?[X]:(anywhere(X)&(does_not_collect_vintage_vinyl_records(X))))=>(?[X]:(~room(X)&(((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))<~>(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X)))))))& (?[X]:(anywhere(X)&(does_not_have_a_tattoo(X))))& (?[X]:(room(X)&(((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))<~>(does_not_have_a_piercing(X))))))& (?[X]:(~room(X)&(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))& (?[X]:(room(X)&(is_not_a_client_of_Costco(X))))& (((?[X]:(anywhere(X)&((does_not_make_homemade_pastries(X))<~>(does_not_have_a_tattoo(X)))))&(![X,Y]:((anywhere(X)&anywhere(Y)&(((does_not_make_homemade_pastries(X))<~>(does_not_have_a_tattoo(X))))&(((does_not_make_homemade_pastries(Y))<~>(does_not_have_a_tattoo(Y)))))=>(X=Y)))))& (?[X]:(room(X)&(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))))& (((?[X]:(room(X)&does_not_practice_pilates(X)))&(![X,Y]:((room(X)&room(Y)&(does_not_practice_pilates(X))&(does_not_practice_pilates(Y)))=>(X=Y)))))& (?[X]:(room(X)&(does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))))& (?[X]:(room(X)&(does_not_practice_pilates(X))))& (?[X]:(room(X)&(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))& (((?[X]:(room(X)&does_not_have_a_tattoo(X)))&(![X,Y]:((room(X)&room(Y)&(does_not_have_a_tattoo(X))&(does_not_have_a_tattoo(Y)))=>(X=Y)))))& (?[X]:(~room(X)&(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))& (?[X]:(room(X)&(does_not_know_morse_code(X))))& ((willie_dream=>((willie_dream=>(?[X]:(room(X)&(does_not_collect_foreign_coins(X))))))))& (?[X]:(room(X)&(does_not_collect_foreign_coins(X))))& (?[X]:(room(X)&(does_not_collect_vintage_vinyl_records(X))))& (((?[X]:(room(X)&is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X)))&(![X,Y]:((room(X)&room(Y)&(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))&(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(Y)))=>(X=Y)))))& (?[X]:(room(X)&(does_not_work_on_fridays(X))))& (((?[X]:(room(X)&does_not_make_homemade_pastries(X)))&(![X,Y]:((room(X)&room(Y)&(does_not_make_homemade_pastries(X))&(does_not_make_homemade_pastries(Y)))=>(X=Y)))))

room(willie)&room(sherry)&(![X]:(room(X)=>(X='willie'|X='sherry')))& (?[X,Y]:(room(X)&room(Y)&(makes_intricate_hand-cut_paper_art_for_exhibitions(X)&makes_intricate_hand-cut_paper_art_for_exhibitions(Y))&(X!=Y)))

There is a room. If “everyone in the room does not enjoy virtual reality gaming or does not own a 3D printer” then “if someone owns a high-end gaming PC with custom-built components then he/she enjoys camping and organizing outdoor survival workshops, maintains a personal blog focused on cybersecurity tips or owns a high-end gaming PC with custom-built components”. “Everyone in the room who does not enjoy camping and organizing outdoor survival workshops and owns a high-end gaming PC with custom-built components enjoys virtual reality gaming and does enjoy trail running” if “everyone outside the room does not enjoy camping and organizing outdoor survival workshops and does not play eSports competitively”. Everyone outside the room enjoys virtual reality gaming and does enjoy trail running if and only if they owns a significant collection of rare gemstones and minerals, is a client of LVMH or hosts regular workshops on creative writing. If someone is not a client of LVMH then he/she does enjoy trail running and vice versa.

Everyone in the room does not enjoy virtual reality gaming or can play the guitar.

neutral

(there_is_a_room)& ((![X]:(room(X)=>(((does_not_own_a_3D_printer(X))|(does_not_enjoy_virtual_reality_gaming(X))))))=>((![X]:((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))|(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))|(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))))& ((![X]:(~room(X)=>(((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))&(does_not_play_eSports_competitively(X))))))=>(![X]:(room(X)=>(((((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))&(owns_a_high-end_gaming_PC_with_custom-built_components(X))))=>(((enjoys_virtual_reality_gaming(X))&(does_enjoy_trail_running(X)))))))))& (![X]:(~room(X)=>(((((enjoys_virtual_reality_gaming(X))&(does_enjoy_trail_running(X))))<=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))|(is_a_client_of_LVMH(X))|(hosts_regular_workshops_on_creative_writing(X))))))))& ((![X]:((is_not_a_client_of_LVMH(X))<=>(does_enjoy_trail_running(X)))))& (![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))=>(enjoys_salsa_dancing(X))))))& (![X]:(room(X)=>(((enjoys_salsa_dancing(X))=>(does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))))))& (![X]:(room(X)=>(((does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))& (![X]:(room(X)=>(creates_large-scale_murals_for_public_art_installations(X))))& (![X]:(~room(X)=>(((owns_a_3D_printer(X))=>(((does_not_enjoy_salsa_dancing(X))&(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))))& (![X]:(room(X)=>(((((does_not_enjoy_salsa_dancing(X))&(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))=>(does_not_collect_comic_books(X))))))& (~?[X]:(anywhere(X)=>(((does_not_collect_comic_books(X))=>(((collects_comic_books(X))|(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))|(owns_a_3D_printer(X))))))))& (![X]:(room(X)=>(does_enjoy_trail_running(X))))& ((![X]:((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))=>(((does_not_play_eSports_competitively(X))&(is_not_a_client_of_LVMH(X)))))))& (![X]:(anywhere(X)=>(((does_not_play_eSports_competitively(X))|(does_not_own_a_3D_printer(X))))))& (![X]:(room(X)=>(((((is_a_client_of_LVMH(X))|(hosts_regular_workshops_on_creative_writing(X))|(writes_a_travel_blog(X))))=>(((collects_comic_books(X))|(does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))|(does_not_create_large-scale_murals_for_public_art_installations(X))))))))& (![X]:(room(X)=>(((owns_a_3D_printer(X))<=>(does_not_enjoy_virtual_reality_gaming(X))))))& (![X]:(room(X)=>(((does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))|(streams_on_Twitch(X))|(does_not_enjoy_salsa_dancing(X))))))& (![X]:(room(X)=>(((~((writes_a_travel_blog(X))|(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))<~>(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))))))))& (![X]:(anywhere(X)=>(((((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))<~>(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))))<=>(~((is_a_client_of_LVMH(X))|(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))))))))& (![X]:(~room(X)=>(can_play_the_guitar(X))))& (![X]:(room(X)=>(((plays_eSports_competitively(X))=>(~((does_not_enjoy_salsa_dancing(X))|(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))))& (![X]:(~room(X)=>(((((writes_a_travel_blog(X))&(owns_a_high-end_gaming_PC_with_custom-built_components(X))))<=(plays_eSports_competitively(X))))))

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

There is a room. If "everyone in the room owns an Android phone or does not use an ios phone" then "no one in the room who owns an Android phone uses an ios phone". "Everyone in the room is not a dedicated advocate for digital privacy and encryption or owns a telescope" only if "everyone in the room is not a Linux enthusiast or is not a dedicated advocate for digital privacy and encryption". "Everyone in the room who enjoys deep-sea diving and exploring underwater caves bakes bread at home" unless "everyone outside the room is not a Linux enthusiast or is a dedicated advocate for digital privacy and encryption". If "everyone outside the room bakes bread at home or does not collect foreign coins" then "everyone in the room who bakes bread at home is a wine connoisseur with a private cellar of vintage wines". "Everyone in the room who is a Linux enthusiast enjoys virtual reality gaming" if "everyone in the room is a Linux enthusiast or does not maintain a large, organic vegetable garden year-round". If "everyone in the room is not a wine connoisseur with a private cellar of vintage wines or practices and performs acrobatic dance routines" then "Ruth dreamt that "everyone in the room who is not a wine connoisseur with a private cellar of vintage wines is an expert in identifying and foraging wild edible plants"". No one in the room who practices and performs acrobatic dance routines and is a wine connoisseur with a private cellar of vintage wines is a Linux enthusiast.

Everyone in the room is a Linux enthusiast.

contradiction

(there_is_a_room)& ((![X]:(room(X)=>(((does_not_use_an_ios_phone(X))|(owns_an_Android_phone(X))))))=>(~?[X]:(room(X)=>(((owns_an_Android_phone(X))=>(uses_an_ios_phone(X)))))))& ((![X]:(room(X)=>(((owns_a_telescope(X))|(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))=>(![X]:(room(X)=>(((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(is_not_a_Linux_enthusiast(X)))))))& (~(![X]:(~room(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(is_not_a_Linux_enthusiast(X))))))=>(![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))=>(bakes_bread_at_home(X)))))))& ((![X]:(~room(X)=>(((does_not_collect_foreign_coins(X))|(bakes_bread_at_home(X))))))=>(![X]:(room(X)=>(((bakes_bread_at_home(X))=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X)))))))& ((![X]:(room(X)=>(((does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))|(is_a_Linux_enthusiast(X))))))=>(![X]:(room(X)=>(((is_a_Linux_enthusiast(X))=>(enjoys_virtual_reality_gaming(X)))))))& ((![X]:(room(X)=>(((practices_and_performs_acrobatic_dance_routines(X))|(is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))=>((ruth_dream=>(![X]:(room(X)=>(((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X)))))))))& ((![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))|(does_not_enjoy_stand-up_paddleboarding(X))))))=>(~![X]:(room(X)=>(((does_not_enjoy_stand-up_paddleboarding(X))=>(builds_model_airplanes(X)))))))& ((~![X]:(anywhere(X)=>(((owns_a_telescope(X))|(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))=>(![X]:(room(X)=>(((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))=>(hosts_regular_workshops_on_creative_writing(X)))))))& (~(![X]:(room(X)=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))|(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))))))=>(![X]:(room(X)=>(((builds_model_airplanes(X))=>(practices_urban_gardening(X)))))))& ((![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))|(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))=>(~?[X]:(anywhere(X)=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))=>(is_a_craft_beer_aficionado(X)))))))& ((![X]:(room(X)=>(((is_a_Linux_enthusiast(X))|(does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))))))=>(![X]:(room(X)=>(((enjoys_stand-up_paddleboarding(X))=>(((practices_and_performs_acrobatic_dance_routines(X))&(collects_rare_and_antique_scientific_instruments(X)))))))))& (~![X]:(room(X)=>(((((practices_and_performs_acrobatic_dance_routines(X))&(collects_rare_and_antique_scientific_instruments(X))))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))& (![X]:(room(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))=>(has_completed_a_triathlon(X))))))& (![X]:(room(X)=>(((has_completed_a_triathlon(X))<=>(((enjoys_macrame(X))&(owns_an_Android_phone(X))&(enjoys_stand-up_paddleboarding(X))))))))& (![X]:(room(X)=>(((((uses_an_ios_phone(X))|(is_passionate_about_collecting_and_restoring_classic_cars(X))))<=(((enjoys_macrame(X))&(owns_an_Android_phone(X))&(enjoys_stand-up_paddleboarding(X))))))))& (![X]:(room(X)=>(((enjoys_stand-up_paddleboarding(X))=>(((practices_and_performs_acrobatic_dance_routines(X))&(collects_rare_and_antique_scientific_instruments(X))))))))& (![X]:(room(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))<=(enjoys_virtual_reality_gaming(X))))))& (((?[X]:(room(X)&maintains_a_large,_organic_vegetable_garden_year-round(X)))&(![X,Y]:((room(X)&room(Y)&(maintains_a_large,_organic_vegetable_garden_year-round(X))&(maintains_a_large,_organic_vegetable_garden_year-round(Y)))=>(X=Y)))))& (~?[X]:(room(X)=>(((((practices_and_performs_acrobatic_dance_routines(X))&(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))=>(is_a_Linux_enthusiast(X))))))& (![X]:(room(X)=>(((is_a_Linux_enthusiast(X))=>(enjoys_stand-up_paddleboarding(X))))))& (![X]:(~room(X)=>(((((is_a_Linux_enthusiast(X))<~>(is_a_craft_beer_aficionado(X))))=>(practices_urban_gardening(X))))))& (((?[X]:(anywhere(X)&is_a_craft_beer_aficionado(X)))))

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

% SZS status Unsatisfiable for 6629969312166324028318613 % SZS output start Proof for 6629969312166324028318613 63. ~? [X0] : (room(X0) => ((predc(X0) & predl(X0)) => predk(X0))) [input p19] 67. ! [X0] : (room(X0) => predk(X0)) & there_is_a_room [input hypothesis] 96. ~? [X0] : (room(X0) => (predc(X0) => predk(X0))) [pure predicate removal 63] 102. ~? [X0] : (room(X0) => predk(X0)) [pure predicate removal 96] 104. ! [X0] : (room(X0) => predk(X0)) [pure predicate removal 67] 190. ! [X0] : (~predk(X0) & room(X0)) [ennf transformation 102] 193. ! [X0] : (predk(X0) | ~room(X0)) [ennf transformation 104] 331. room(X0) [cnf transformation 190] 332. ~predk(X0) [cnf transformation 190] 335. predk(X0) | ~room(X0) [cnf transformation 193] 364. 7 <=> ! [X0] : room(X0) [avatar definition] 365. room(X0) <- (7) [avatar component clause 364] 436. 7 [avatar split clause 331,364] 437. ~room(X0) [subsumption resolution 335,332] 442. $false <- (7) [subsumption resolution 365,437] 443. ~7 [avatar contradiction clause 442] 444. $false [avatar sat refutation 436,443] % SZS output end Proof for 6629969312166324028318613 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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. No one in the room who is a drone photographer regularly contributes to tech forums and online communities. Everyone in the room streams on Twitch, is a client of Meta or is a drone photographer only if they enjoys rooftop gardening. Everyone in the room who enjoys rooftop gardening does not have a curated collection of mid-century modern furniture. Everyone in the room neither frequently participates in hackathons and coding competitions nor collects rare and antique scientific instruments if they frequently participates in hackathons and coding competitions. Everyone in the room who neither frequently participates in hackathons and coding competitions nor collects rare and antique scientific instruments has a curated collection of mid-century modern furniture.

Everyone in the room collects rare and antique scientific instruments.

entailment

(there_is_a_room)& (![X]:(room(X)=>(((((enjoys_rooftop_gardening(X))<~>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))<=>(frequently_participates_in_hackathons_and_coding_competitions(X))))))& (![X]:(room(X)=>(((collects_luxury_watches(X))=>(is_a_drone_photographer(X))))))& (![X]:(room(X)=>(((is_a_drone_photographer(X))=>(plays_the_violin(X))))))& (![X]:(room(X)=>(((plays_the_violin(X))=>(is_a_drone_photographer(X))))))& (~?[X]:(room(X)=>(((is_a_drone_photographer(X))=>(regularly_contributes_to_tech_forums_and_online_communities(X))))))& ((josephric_dream=>(?[X]:(room(X)&(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))& (![X]:(room(X)=>(((enjoys_rooftop_gardening(X))<=(((streams_on_Twitch(X))|(is_a_client_of_Meta(X))|(is_a_drone_photographer(X))))))))& (![X]:(room(X)=>(((enjoys_rooftop_gardening(X))=>(does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))))))& (![X]:(room(X)=>(((does_not_enjoy_rooftop_gardening(X))=>(((is_a_drone_photographer(X))&(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))))& (![X]:(room(X)=>(((((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))|(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(is_a_chess_master_who_participates_in_national_tournaments(X))))<=(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))& (![X]:(room(X)=>(((((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))|(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(is_a_chess_master_who_participates_in_national_tournaments(X))))=>(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))& (![X]:(room(X)=>(((((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))&(does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))))=>(((collects_luxury_watches(X))|(streams_on_Twitch(X))|(enjoys_rooftop_gardening(X))))))))& (~?[X]:(room(X)=>(((((collects_luxury_watches(X))|(streams_on_Twitch(X))|(enjoys_rooftop_gardening(X))))=>(can_play_the_harmonica(X))))))& (![X]:(room(X)=>(((((plays_the_violin(X))<~>(has_a_curated_collection_of_mid-century_modern_furniture(X))))<=(frequently_participates_in_hackathons_and_coding_competitions(X))))))& (![X]:(room(X)=>(((((plays_the_violin(X))<~>(has_a_curated_collection_of_mid-century_modern_furniture(X))))=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))& (![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(frequently_participates_in_hackathons_and_coding_competitions(X))))))& (![X]:(room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))=>(~((frequently_participates_in_hackathons_and_coding_competitions(X))|(collects_rare_and_antique_scientific_instruments(X))))))))& (![X]:(room(X)=>(((~((frequently_participates_in_hackathons_and_coding_competitions(X))|(collects_rare_and_antique_scientific_instruments(X))))=>(has_a_curated_collection_of_mid-century_modern_furniture(X))))))& (![X]:(room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))=>(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))& (~?[X]:(room(X)=>(((collects_comic_books(X))<=(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))& (![X]:(room(X)=>(((does_enjoy_trail_running(X))<=(collects_comic_books(X))))))& (![X]:(~room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))<=(does_enjoy_trail_running(X))))))& (![X]:(room(X)=>(((does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))<=(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))

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

% SZS status Unsatisfiable for 453809816997286531296425 % SZS output start Proof for 453809816997286531296425 44. there_is_a_room [input p0] 49. ~? [X0] : (room(X0) => (predo(X0) => predd(X0))) [input p5] 51. ! [X0] : (room(X0) => ((predo(X0) | predr(X0) | predm(X0)) => predp(X0))) [input p7] 52. ! [X0] : (room(X0) => (predp(X0) => ~predl(X0))) [input p8] 61. ! [X0] : (room(X0) => (predn(X0) => ~(predk(X0) | predn(X0)))) [input p17] 62. ! [X0] : (room(X0) => (~(predk(X0) | predn(X0)) => predl(X0))) [input p18] 68. ~(! [X0] : (room(X0) => predk(X0)) & there_is_a_room) [input hypothesis] 81. ! [X0] : (room(X0) => ((predo(X0) | predm(X0)) => predp(X0))) [pure predicate removal 51] 86. ~? [X0] : (room(X0) => ~predo(X0)) [pure predicate removal 49] 166. ! [X0] : (predo(X0) & room(X0)) [ennf transformation 86] 167. ! [X0] : ((predp(X0) | (~predo(X0) & ~predm(X0))) | ~room(X0)) [ennf transformation 81] 168. ! [X0] : (predp(X0) | (~predo(X0) & ~predm(X0)) | ~room(X0)) [flattening 167] 169. ! [X0] : ((~predl(X0) | ~predp(X0)) | ~room(X0)) [ennf transformation 52] 170. ! [X0] : (~predl(X0) | ~predp(X0) | ~room(X0)) [flattening 169] 176. ! [X0] : (((~predk(X0) & ~predn(X0)) | ~predn(X0)) | ~room(X0)) [ennf transformation 61] 177. ! [X0] : ((~predk(X0) & ~predn(X0)) | ~predn(X0) | ~room(X0)) [flattening 176] 178. ! [X0] : ((predl(X0) | (predk(X0) | predn(X0))) | ~room(X0)) [ennf transformation 62] 179. ! [X0] : (predl(X0) | predk(X0) | predn(X0) | ~room(X0)) [flattening 178] 181. ? [X0] : (~predk(X0) & room(X0)) | ~there_is_a_room [ennf transformation 68] 185. ? [X0] : (~predk(X0) & room(X0)) => (~predk(sK0) & room(sK0)) [choice axiom] 186. (~predk(sK0) & room(sK0)) | ~there_is_a_room [skolemisation 181,185] 267. there_is_a_room [cnf transformation 44] 275. room(X0) [cnf transformation 166] 276. predo(X0) [cnf transformation 166] 278. predp(X0) | ~predo(X0) | ~room(X0) [cnf transformation 168] 279. ~predl(X0) | ~predp(X0) | ~room(X0) [cnf transformation 170] 285. ~predn(X0) | ~predn(X0) | ~room(X0) [cnf transformation 177] 287. predl(X0) | predk(X0) | predn(X0) | ~room(X0) [cnf transformation 179] 290. ~predk(sK0) | ~there_is_a_room [cnf transformation 186] 291. ~predn(X0) | ~room(X0) [duplicate literal removal 285] 292. predp(X0) | ~room(X0) [subsumption resolution 278,276] 293. predp(X0) [subsumption resolution 292,275] 294. ~predl(X0) | ~room(X0) [subsumption resolution 279,293] 295. ~predl(X0) [subsumption resolution 294,275] 299. ~predn(X0) [subsumption resolution 291,275] 300. predk(X0) | predn(X0) | ~room(X0) [subsumption resolution 287,295] 301. predk(X0) | ~room(X0) [subsumption resolution 300,299] 302. predk(X0) [subsumption resolution 301,275] 303. ~there_is_a_room [subsumption resolution 290,302] 304. $false [subsumption resolution 303,267] % SZS output end Proof for 453809816997286531296425 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.036 s % ------------------------------ % ------------------------------

There is a room. “Everyone anywhere makes homemade pastries or does not enjoy windsurfing” if “everyone in the room owns a high-end gaming PC with custom-built components or is not an avid hiker” and vice versa. “Someone in the room collects action figures” if “everyone in the room is a tea enthusiast or does not know morse code” and vice versa. Either “everyone in the room is not a tea enthusiast or enjoys windsurfing” or “no one in the room does not own a high-end gaming PC with custom-built components or is not an avid hiker” but not both. Only one person in the room makes homemade pastries. Someone outside the room enjoys windsurfing. Everyone in the room is a tea enthusiast if they is allergic to anything and vice versa. Everyone in the room knows morse code if they neither hosts a YouTube channel dedicated to art tutorials nor does not maintain a large, organic vegetable garden year-round. Everyone in the room neither is not allergic to anything nor is not a tea enthusiast if they knows morse code. Everyone in the room does not maintain a large, organic vegetable garden year-round if they neither is not allergic to anything nor is not a tea enthusiast. If someone maintains a large, organic vegetable garden year-round then he/she makes homemade pastries and vice versa. At least one person in the room does not know morse code.

Everyone in the room is not a tea enthusiast or is an avid hiker.

neutral

(there_is_a_room)& ((![X]:(room(X)=>(((is_not_an_avid_hiker(X))|(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))<=>(![X]:(anywhere(X)=>(((does_not_enjoy_windsurfing(X))|(makes_homemade_pastries(X)))))))& ((![X]:(room(X)=>(((does_not_know_morse_code(X))|(is_a_tea_enthusiast(X))))))<=>(?[X]:(room(X)&(collects_action_figures(X)))))& ((![X]:(room(X)=>(((enjoys_windsurfing(X))|(is_not_a_tea_enthusiast(X))))))<~>(~?[X]:(room(X)=>(((is_not_an_avid_hiker(X))|(does_not_own_a_high-end_gaming_PC_with_custom-built_components(X)))))))& (((?[X]:(room(X)&makes_homemade_pastries(X)))&(![X,Y]:((room(X)&room(Y)&(makes_homemade_pastries(X))&(makes_homemade_pastries(Y)))=>(X=Y)))))& (?[X]:(~room(X)&(enjoys_windsurfing(X))))& (![X]:(room(X)=>(((is_a_tea_enthusiast(X))<=>(is_allergic_to_anything(X))))))& (![X]:(room(X)=>(((~((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))|(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))))=>(knows_morse_code(X))))))& (![X]:(room(X)=>(((knows_morse_code(X))=>(~((is_not_allergic_to_anything(X))|(is_not_a_tea_enthusiast(X))))))))& (![X]:(room(X)=>(((~((is_not_allergic_to_anything(X))|(is_not_a_tea_enthusiast(X))))=>(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))))))& ((![X]:((maintains_a_large,_organic_vegetable_garden_year-round(X))<=>(makes_homemade_pastries(X)))))& (((?[X]:(room(X)&does_not_know_morse_code(X)))))

(there_is_a_room)& ![X]:(room(X)=>(((is_an_avid_hiker(X))|(is_not_a_tea_enthusiast(X)))))

There is a room. If “no one outside the room does not collect modern art or does not regularly contributes to tech forums and online communities” then “everyone outside the room who does not collect modern art does enjoy mountain biking, enjoys salsa dancing and is a night owl”. If “everyone in the room does not enjoy deep-sea diving and exploring underwater caves or collects modern art” then “everyone in the room does not enjoy deep-sea diving and exploring underwater caves if they is an enthusiastic bird watcher who travels for rare sightings”. “Everyone anywhere who is a culinary enthusiast who experiments with international cuisines knows morse code” if “someone in the room creates large-scale murals for public art installations”. “Everyone in the room is a client of LVMH or is not a culinary enthusiast who experiments with international cuisines” if “no one in the room creates YouTube content or does not know morse code” and vice versa. If “everyone anywhere does not collect modern art or does not work on fridays” then “everyone in the room is not a culinary enthusiast who experiments with international cuisines or does not collect modern art”. “Everyone anywhere is not a culinary enthusiast who experiments with international cuisines if they is not an avid collector of autographed memorabilia from famous musicians” if “everyone in the room does not create YouTube content or is an active member of a local robotics club”. Everyone in the room is a culinary enthusiast who experiments with international cuisines. Everyone in the room who is not an enthusiastic bird watcher who travels for rare sightings is an active member of a local robotics club. Everyone outside the room can play the harmonica and is an active member of a local robotics club. Everyone in the room enjoys deep-sea diving and exploring underwater caves if they is a night owl. Everyone in the room who does enjoy mountain biking regularly contributes to tech forums and online communities. Someone in the room knows morse code. Everyone in the room does not enjoy deep-sea diving and exploring underwater caves if they is an enthusiastic bird watcher who travels for rare sightings. At least one person anywhere is not a culinary enthusiast who experiments with international cuisines. At least one person in the room does not know morse code. Everyone in the room is not an active member of a local robotics club or knows morse code.

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

contradiction

(there_is_a_room)& ((~?[X]:(~room(X)=>(((does_not_regularly_contributes_to_tech_forums_and_online_communities(X))|(does_not_collect_modern_art(X))))))=>(![X]:(~room(X)=>(((does_not_collect_modern_art(X))=>(((does_enjoy_mountain_biking(X))&(enjoys_salsa_dancing(X))&(is_a_night_owl(X)))))))))& ((![X]:(room(X)=>(((collects_modern_art(X))|(does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))))))=>(![X]:(room(X)=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X)))))))& ((?[X]:(room(X)&(creates_large-scale_murals_for_public_art_installations(X))))=>(![X]:(anywhere(X)=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))=>(knows_morse_code(X)))))))& ((~?[X]:(room(X)=>(((does_not_know_morse_code(X))|(creates_YouTube_content(X))))))<=>(![X]:(room(X)=>(((is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(is_a_client_of_LVMH(X)))))))& ((![X]:(anywhere(X)=>(((does_not_work_on_fridays(X))|(does_not_collect_modern_art(X))))))=>(![X]:(room(X)=>(((does_not_collect_modern_art(X))|(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X)))))))& ((![X]:(room(X)=>(((is_an_active_member_of_a_local_robotics_club(X))|(does_not_create_YouTube_content(X))))))=>(![X]:(anywhere(X)=>(((is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))=>(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X)))))))& (![X]:(room(X)=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))& (![X]:(room(X)=>(((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(is_an_active_member_of_a_local_robotics_club(X))))))& (![X]:(~room(X)=>(((can_play_the_harmonica(X))&(is_an_active_member_of_a_local_robotics_club(X))))))& (![X]:(room(X)=>(((is_a_night_owl(X))=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))& (![X]:(room(X)=>(((does_enjoy_mountain_biking(X))=>(regularly_contributes_to_tech_forums_and_online_communities(X))))))& (?[X]:(room(X)&(knows_morse_code(X))))& (![X]:(room(X)=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))))))& (((?[X]:(anywhere(X)&is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X)))))& (((?[X]:(room(X)&does_not_know_morse_code(X)))))& (![X]:(room(X)=>(((knows_morse_code(X))|(is_not_an_active_member_of_a_local_robotics_club(X))))))

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

% SZS status Unsatisfiable for 8491710031632728566311018 % SZS output start Proof for 8491710031632728566311018 53. ! [X0] : (~room(X0) => (predc(X0) & predg(X0))) [input p9] 59. ? [X0] : (~prede(X0) & room(X0)) [input p15] 60. ! [X0] : (room(X0) => (~predc(X0) | prede(X0))) [input p16] 61. ! [X0] : (room(X0) => predc(X0)) & there_is_a_room [input hypothesis] 68. ! [X0] : (~room(X0) => predc(X0)) [pure predicate removal 53] 77. ! [X0] : (room(X0) => predc(X0)) [pure predicate removal 61] 160. ! [X0] : (predc(X0) | room(X0)) [ennf transformation 68] 167. ! [X0] : ((~predc(X0) | prede(X0)) | ~room(X0)) [ennf transformation 60] 168. ! [X0] : (~predc(X0) | prede(X0) | ~room(X0)) [flattening 167] 169. ! [X0] : (predc(X0) | ~room(X0)) [ennf transformation 77] 194. ? [X0] : (~prede(X0) & room(X0)) => (~prede(sK8) & room(sK8)) [choice axiom] 195. ~prede(sK8) & room(sK8) [skolemisation 59,194] 292. predc(X0) | room(X0) [cnf transformation 160] 299. room(sK8) [cnf transformation 195] 300. ~prede(sK8) [cnf transformation 195] 301. ~predc(X0) | prede(X0) | ~room(X0) [cnf transformation 168] 302. predc(X0) | ~room(X0) [cnf transformation 169] 398. predc(X0) [subsumption resolution 302,292] 406. ~room(X1) | prede(X1) [resolution 301,398] 408. prede(sK8) [resolution 406,299] 410. $false [subsumption resolution 408,300] % SZS output end Proof for 8491710031632728566311018 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Richard, Robert, Bernard, Ernie are the only persons in the room. Richard does not have a saltwater aquarium. Everyone in the room does not have a saltwater aquarium or has a saltwater aquarium or both if they either does not enjoy wildlife photography or does not collect vintage vinyl records but not both and vice versa. Everyone in the room does not collect vintage vinyl records or does not practice zumba or both. Everyone anywhere collects vintage stamps. Everyone in the room enjoys wildlife photography or does not collect vintage vinyl records or both. Everyone anywhere does not collect vintage vinyl records or does not enjoy wildlife photography. Everyone in the room does not collect vintage vinyl records only if they does not have a saltwater aquarium or does not collect vintage stamps or both. Everyone in the room does not collect vintage vinyl records, enjoys wildlife photography and does not have a saltwater aquarium if they does not have a saltwater aquarium or does not collect vintage stamps or both. Everyone outside the room does not collect vintage vinyl records, enjoys wildlife photography and does not have a saltwater aquarium if they does not collect vintage vinyl records and vice versa. Everyone in the room does not have a saltwater aquarium if they does not collect vintage vinyl records. Everyone in the room does not enjoy wildlife photography or does not have a saltwater aquarium or both.

It is not the case that “Robert enjoys wildlife photography”.

contradiction

room(richard)&room(robert)&room(bernard)&room(ernie)&(![X]:(room(X)=>(X='richard'|X='robert'|X='bernard'|X='ernie')))& (does_not_have_a_saltwater_aquarium(richard))& (![X]:(room(X)=>(((((does_not_have_a_saltwater_aquarium(X))|(has_a_saltwater_aquarium(X))))<=>(((does_not_enjoy_wildlife_photography(X))<~>(does_not_collect_vintage_vinyl_records(X))))))))& (![X]:(room(X)=>(((does_not_collect_vintage_vinyl_records(X))|(does_not_practice_zumba(X))))))& (![X]:(anywhere(X)=>(collects_vintage_stamps(X))))& (![X]:(room(X)=>(((enjoys_wildlife_photography(X))|(does_not_collect_vintage_vinyl_records(X))))))& (![X]:(anywhere(X)=>(((does_not_enjoy_wildlife_photography(X))|(does_not_collect_vintage_vinyl_records(X))))))& (![X]:(room(X)=>(((((does_not_have_a_saltwater_aquarium(X))|(does_not_collect_vintage_stamps(X))))<=(does_not_collect_vintage_vinyl_records(X))))))& (![X]:(room(X)=>(((((does_not_have_a_saltwater_aquarium(X))|(does_not_collect_vintage_stamps(X))))=>(((does_not_collect_vintage_vinyl_records(X))&(enjoys_wildlife_photography(X))&(does_not_have_a_saltwater_aquarium(X))))))))& (![X]:(~room(X)=>(((((does_not_collect_vintage_vinyl_records(X))&(enjoys_wildlife_photography(X))&(does_not_have_a_saltwater_aquarium(X))))<=>(does_not_collect_vintage_vinyl_records(X))))))& (![X]:(room(X)=>(((does_not_collect_vintage_vinyl_records(X))=>(does_not_have_a_saltwater_aquarium(X))))))& (![X]:(room(X)=>(((does_not_enjoy_wildlife_photography(X))|(does_not_have_a_saltwater_aquarium(X))))))

room(richard)&room(robert)&room(bernard)&room(ernie)&(![X]:(room(X)=>(X='richard'|X='robert'|X='bernard'|X='ernie')))& ~(enjoys_wildlife_photography(robert))

% SZS status Unsatisfiable for 324876265877968020331217 % SZS output start Proof for 324876265877968020331217 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 46. ! [X0] : (room(X0) => ((predb(X0) | ~predb(X0)) <=> (~predd(X0) <~> ~predc(X0)))) [input p2] 49. ! [X0] : (room(X0) => (~predc(X0) | predd(X0))) [input p5] 56. ~predd(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 129. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 130. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 129] 131. ! [X0] : (((predb(X0) | ~predb(X0)) <=> (~predd(X0) <~> ~predc(X0))) | ~room(X0)) [ennf transformation 46] 133. ! [X0] : ((~predc(X0) | predd(X0)) | ~room(X0)) [ennf transformation 49] 134. ! [X0] : (~predc(X0) | predd(X0) | ~room(X0)) [flattening 133] 146. ~predd(paul) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 56] 147. ~predd(paul) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 146] 149. ! [X0] : ((((predb(X0) | ~predb(X0)) | ((~predd(X0) | predc(X0)) & (~predc(X0) | predd(X0)))) & (((predc(X0) | predd(X0)) & (~predc(X0) | ~predd(X0))) | (~predb(X0) & predb(X0)))) | ~room(X0)) [nnf transformation 131] 150. ! [X0] : (((predb(X0) | ~predb(X0) | ((~predd(X0) | predc(X0)) & (~predc(X0) | predd(X0)))) & (((predc(X0) | predd(X0)) & (~predc(X0) | ~predd(X0))) | (~predb(X0) & predb(X0)))) | ~room(X0)) [flattening 149] 235. room(paul) [cnf transformation 130] 242. predc(X0) | predd(X0) | predb(X0) | ~room(X0) [cnf transformation 150] 243. predc(X0) | predd(X0) | ~predb(X0) | ~room(X0) [cnf transformation 150] 247. ~predc(X0) | predd(X0) | ~room(X0) [cnf transformation 134] 267. ~predd(paul) [cnf transformation 147] 268. predc(X0) | predd(X0) | ~room(X0) [subsumption resolution 242,243] 271. ~room(X0) | predd(X0) [subsumption resolution 247,268] 278. predd(paul) [resolution 271,235] 281. $false [subsumption resolution 278,267] % SZS output end Proof for 324876265877968020331217 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.038 s % ------------------------------ % ------------------------------

Juan, Maurice are the only persons in the room. Everyone in the room makes homemade pastries if they collect rare sneakers. At least one person in the room collects first edition books. Not everyone in the room is an active member of a local robotics club. Everyone in the room does not collect rare sneakers if they mentors a youth basketball team on weekends. Everyone in the room does not collect rare sneakers if they does not practice archery and vice versa. Everyone in the room does not practice archery if they uses contact lenses, enjoys virtual reality gaming and is an enthusiastic bird watcher who travels for rare sightings and vice versa. Everyone in the room uses contact lenses, enjoys virtual reality gaming and is an enthusiastic bird watcher who travels for rare sightings if they does not collect first edition books and vice versa. Not everyone in the room drives a hybrid car. Everyone in the room who collect rare sneakers or uses contact lenses or both does not volunteer for local environmental conservation projects. Not everyone in the room is an avid mountain climber who has scaled several peaks if they mentors a youth basketball team on weekends and vice versa. Everyone in the room does not enjoy deep-sea diving and exploring underwater caves if they hosts regular game nights featuring complex strategy games. Everyone in the room does not enjoy bird watching if they does not enjoy deep-sea diving and exploring underwater caves. Someone in the room has a tattoo. Everyone outside the room reads mystery novels. Everyone in the room is not an avid mountain climber who has scaled several peaks. Everyone in the room collects first edition books if they does not host regular game nights featuring complex strategy games. Everyone in the room enjoys bird watching if they has a tattoo. Everyone outside the room creates bespoke furniture pieces from reclaimed wood if they does not collect first edition books. If someone is right-handed then he/she does not collect first edition books and vice versa.

Everyone in the room does not volunteer for local environmental conservation projects.

entailment

room(juan)&room(maurice)&(![X]:(room(X)=>(X='juan'|X='maurice')))& (![X]:(room(X)=>(((collect_rare_sneakers(X))=>(makes_homemade_pastries(X))))))& (((?[X]:(room(X)&collects_first_edition_books(X)))))& (~![X]:(room(X)=>(is_an_active_member_of_a_local_robotics_club(X))))& (![X]:(room(X)=>(((mentors_a_youth_basketball_team_on_weekends(X))=>(does_not_collect_rare_sneakers(X))))))& (![X]:(room(X)=>(((does_not_collect_rare_sneakers(X))<=>(does_not_practice_archery(X))))))& (![X]:(room(X)=>(((does_not_practice_archery(X))<=>(((uses_contact_lenses(X))&(enjoys_virtual_reality_gaming(X))&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))))& (![X]:(room(X)=>(((((uses_contact_lenses(X))&(enjoys_virtual_reality_gaming(X))&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))<=>(does_not_collect_first_edition_books(X))))))& (~![X]:(room(X)=>(drives_a_hybrid_car(X))))& (![X]:(room(X)=>(((((collect_rare_sneakers(X))|(uses_contact_lenses(X))))=>(does_not_volunteer_for_local_environmental_conservation_projects(X))))))& (~![X]:(room(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))<=>(mentors_a_youth_basketball_team_on_weekends(X))))))& (![X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))))))& (![X]:(room(X)=>(((does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))=>(does_not_enjoy_bird_watching(X))))))& (?[X]:(room(X)&(has_a_tattoo(X))))& (![X]:(~room(X)=>(reads_mystery_novels(X))))& (![X]:(room(X)=>(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))& (![X]:(room(X)=>(((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))=>(collects_first_edition_books(X))))))& (![X]:(room(X)=>(((has_a_tattoo(X))=>(enjoys_bird_watching(X))))))& (![X]:(~room(X)=>(((does_not_collect_first_edition_books(X))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))& ((![X]:((is_right-handed(X))<=>(does_not_collect_first_edition_books(X)))))& (![X]:(anywhere(X)=>(((is_not_a_chess_master_who_participates_in_national_tournaments(X))=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))& (![X]:(room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))=>(collect_rare_sneakers(X))))))

room(juan)&room(maurice)&(![X]:(room(X)=>(X='juan'|X='maurice')))& ![X]:(room(X)=>(does_not_volunteer_for_local_environmental_conservation_projects(X)))

% SZS status Unsatisfiable for 5892902853075826871645158 % SZS output start Proof for 5892902853075826871645158 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 48. ! [X0] : (room(X0) => (predq(X0) => ~preds(X0))) [input p4] 49. ! [X0] : (room(X0) => (~preds(X0) <=> ~predm(X0))) [input p5] 50. ! [X0] : (room(X0) => (~predm(X0) <=> (predn(X0) & preda(X0) & predc(X0)))) [input p6] 53. ! [X0] : (room(X0) => ((predc(X0) | preds(X0)) => ~predh(X0))) [input p9] 54. ~! [X0] : (room(X0) => (predo(X0) <=> predq(X0))) [input p10] 59. ! [X0] : (room(X0) => ~predo(X0)) [input p15] 66. ~(! [X0] : (room(X0) => ~predh(X0)) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 67. ~(! [X0] : (room(X0) => ~predh(X0)) & ! [X1] : (room(X1) => (paul = X1 | mary = X1)) & room(paul) & room(mary)) [rectify 66] 145. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 146. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 145] 148. ! [X0] : ((~preds(X0) | ~predq(X0)) | ~room(X0)) [ennf transformation 48] 149. ! [X0] : (~preds(X0) | ~predq(X0) | ~room(X0)) [flattening 148] 150. ! [X0] : ((~preds(X0) <=> ~predm(X0)) | ~room(X0)) [ennf transformation 49] 151. ! [X0] : ((~predm(X0) <=> (predn(X0) & preda(X0) & predc(X0))) | ~room(X0)) [ennf transformation 50] 154. ! [X0] : ((~predh(X0) | (~predc(X0) & ~preds(X0))) | ~room(X0)) [ennf transformation 53] 155. ! [X0] : (~predh(X0) | (~predc(X0) & ~preds(X0)) | ~room(X0)) [flattening 154] 156. ? [X0] : ((predo(X0) <~> predq(X0)) & room(X0)) [ennf transformation 54] 161. ! [X0] : (~predo(X0) | ~room(X0)) [ennf transformation 59] 170. ? [X0] : (predh(X0) & room(X0)) | ? [X1] : ((paul != X1 & mary != X1) & room(X1)) | ~room(paul) | ~room(mary) [ennf transformation 67] 171. ? [X0] : (predh(X0) & room(X0)) | ? [X1] : (paul != X1 & mary != X1 & room(X1)) | ~room(paul) | ~room(mary) [flattening 170] 177. ! [X0] : (((~preds(X0) | predm(X0)) & (~predm(X0) | preds(X0))) | ~room(X0)) [nnf transformation 150] 178. ! [X0] : (((~predm(X0) | (~predn(X0) | ~preda(X0) | ~predc(X0))) & ((predn(X0) & preda(X0) & predc(X0)) | predm(X0))) | ~room(X0)) [nnf transformation 151] 179. ! [X0] : (((~predm(X0) | ~predn(X0) | ~preda(X0) | ~predc(X0)) & ((predn(X0) & preda(X0) & predc(X0)) | predm(X0))) | ~room(X0)) [flattening 178] 184. ? [X0] : (((~predq(X0) | ~predo(X0)) & (predq(X0) | predo(X0))) & room(X0)) [nnf transformation 156] 185. ? [X0] : ((~predq(X0) | ~predo(X0)) & (predq(X0) | predo(X0)) & room(X0)) [flattening 184] 186. ? [X0] : ((~predq(X0) | ~predo(X0)) & (predq(X0) | predo(X0)) & room(X0)) => ((~predq(sK3) | ~predo(sK3)) & (predq(sK3) | predo(sK3)) & room(sK3)) [choice axiom] 187. (~predq(sK3) | ~predo(sK3)) & (predq(sK3) | predo(sK3)) & room(sK3) [skolemisation 185,186] 190. ? [X0] : (predh(X0) & room(X0)) => (predh(sK5) & room(sK5)) [choice axiom] 191. ? [X1] : (paul != X1 & mary != X1 & room(X1)) => (paul != sK6 & mary != sK6 & room(sK6)) [choice axiom] 192. (predh(sK5) & room(sK5)) | (paul != sK6 & mary != sK6 & room(sK6)) | ~room(paul) | ~room(mary) [skolemisation 171,191,190] 273. room(mary) [cnf transformation 146] 274. room(paul) [cnf transformation 146] 275. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 146] 279. ~predq(X0) | ~preds(X0) | ~room(X0) [cnf transformation 149] 280. ~predm(X0) | preds(X0) | ~room(X0) [cnf transformation 177] 282. ~room(X0) | predm(X0) | predc(X0) [cnf transformation 179] 291. ~predh(X0) | ~preds(X0) | ~room(X0) [cnf transformation 155] 292. ~predh(X0) | ~predc(X0) | ~room(X0) [cnf transformation 155] 293. room(sK3) [cnf transformation 187] 294. predq(sK3) | predo(sK3) [cnf transformation 187] 300. ~predo(X0) | ~room(X0) [cnf transformation 161] 305. room(sK5) | room(sK6) | ~room(paul) | ~room(mary) [cnf transformation 192] 306. room(sK5) | mary != sK6 | ~room(paul) | ~room(mary) [cnf transformation 192] 307. room(sK5) | paul != sK6 | ~room(paul) | ~room(mary) [cnf transformation 192] 308. predh(sK5) | room(sK6) | ~room(paul) | ~room(mary) [cnf transformation 192] 309. predh(sK5) | mary != sK6 | ~room(paul) | ~room(mary) [cnf transformation 192] 310. predh(sK5) | paul != sK6 | ~room(paul) | ~room(mary) [cnf transformation 192] 312. 1 <=> predo(sK3) [avatar definition] 313. predo(sK3) <- (1) [avatar component clause 312] 316. 2 <=> predq(sK3) [avatar definition] 317. predq(sK3) <- (2) [avatar component clause 316] 320. 1 | 2 [avatar split clause 294,316,312] 321. predh(sK5) | paul != sK6 | ~room(mary) [subsumption resolution 310,274] 322. predh(sK5) | paul != sK6 [subsumption resolution 321,273] 324. 3 <=> paul = sK6 [avatar definition] 326. paul != sK6 <- (~3) [avatar component clause 324] 328. 4 <=> predh(sK5) [avatar definition] 330. predh(sK5) <- (4) [avatar component clause 328] 331. ~3 | 4 [avatar split clause 322,328,324] 332. predh(sK5) | mary != sK6 | ~room(mary) [subsumption resolution 309,274] 333. predh(sK5) | mary != sK6 [subsumption resolution 332,273] 335. 5 <=> mary = sK6 [avatar definition] 338. ~5 | 4 [avatar split clause 333,328,335] 339. predh(sK5) | room(sK6) | ~room(mary) [subsumption resolution 308,274] 340. predh(sK5) | room(sK6) [subsumption resolution 339,273] 342. 6 <=> room(sK6) [avatar definition] 344. room(sK6) <- (6) [avatar component clause 342] 345. 6 | 4 [avatar split clause 340,328,342] 346. room(sK5) | paul != sK6 | ~room(mary) [subsumption resolution 307,274] 347. room(sK5) | paul != sK6 [subsumption resolution 346,273] 349. 7 <=> room(sK5) [avatar definition] 351. room(sK5) <- (7) [avatar component clause 349] 352. ~3 | 7 [avatar split clause 347,349,324] 353. room(sK5) | mary != sK6 | ~room(mary) [subsumption resolution 306,274] 354. room(sK5) | mary != sK6 [subsumption resolution 353,273] 355. ~5 | 7 [avatar split clause 354,349,335] 356. room(sK5) | room(sK6) | ~room(mary) [subsumption resolution 305,274] 357. room(sK5) | room(sK6) [subsumption resolution 356,273] 358. 6 | 7 [avatar split clause 357,349,342] 359. ~preds(sK3) | ~room(sK3) <- (2) [resolution 279,317] 360. ~preds(sK3) <- (2) [subsumption resolution 359,293] 361. predm(mary) | predc(mary) [resolution 282,273] 370. 8 <=> predc(mary) [avatar definition] 372. predc(mary) <- (8) [avatar component clause 370] 374. 9 <=> predm(mary) [avatar definition] 376. predm(mary) <- (9) [avatar component clause 374] 377. 8 | 9 [avatar split clause 361,374,370] 383. 11 <=> predm(paul) [avatar definition] 385. predm(paul) <- (11) [avatar component clause 383] 419. 19 <=> predm(sK3) [avatar definition] 420. ~predm(sK3) <- (~19) [avatar component clause 419] 421. predm(sK3) <- (19) [avatar component clause 419] 489. preds(mary) | ~room(mary) <- (9) [resolution 376,280] 490. preds(mary) <- (9) [subsumption resolution 489,273] 507. preds(paul) | ~room(paul) <- (11) [resolution 385,280] 508. preds(paul) <- (11) [subsumption resolution 507,274] 600. predm(sK5) | predc(sK5) <- (7) [resolution 351,282] 616. 49 <=> predc(sK5) [avatar definition] 617. ~predc(sK5) <- (~49) [avatar component clause 616] 621. 50 <=> predm(sK5) [avatar definition] 623. predm(sK5) <- (50) [avatar component clause 621] 626. 49 | 50 | ~7 [avatar split clause 600,349,621,616] 633. ~preds(sK5) | ~room(sK5) <- (4) [resolution 291,330] 636. ~predc(sK5) | ~room(sK5) <- (4) [resolution 292,330] 651. preds(sK3) | ~room(sK3) <- (19) [resolution 421,280] 652. ~room(sK3) <- (2, 19) [subsumption resolution 651,360] 653. $false <- (2, 19) [subsumption resolution 652,293] 654. ~2 | ~19 [avatar contradiction clause 653] 656. ~room(sK3) <- (1) [resolution 313,300] 657. $false <- (1) [subsumption resolution 656,293] 658. ~1 [avatar contradiction clause 657] 659. ~preds(sK3) | ~room(sK3) <- (2) [resolution 317,279] 660. ~preds(sK3) <- (2) [subsumption resolution 659,293] 667. mary = sK3 | paul = sK3 [resolution 275,293] 669. mary = sK6 | paul = sK6 <- (6) [resolution 275,344] 698. 57 <=> paul = sK3 [avatar definition] 700. paul = sK3 <- (57) [avatar component clause 698] 702. 58 <=> mary = sK3 [avatar definition] 704. mary = sK3 <- (58) [avatar component clause 702] 705. 57 | 58 [avatar split clause 667,702,698] 718. mary = sK6 <- (~3, 6) [subsumption resolution 669,326] 719. 5 | 3 | ~6 [avatar split clause 718,342,324,335] 720. ~7 | ~49 | ~4 [avatar split clause 636,328,616,349] 722. 61 <=> preds(sK5) [avatar definition] 724. ~preds(sK5) <- (~61) [avatar component clause 722] 725. ~7 | ~61 | ~4 [avatar split clause 633,328,722,349] 741. ~preds(paul) <- (2, 57) [backward demodulation 660,700] 745. $false <- (2, 11, 57) [subsumption resolution 741,508] 746. ~2 | ~11 | ~57 [avatar contradiction clause 745] 795. mary = sK5 | paul = sK5 <- (7) [resolution 351,275] 804. 62 <=> paul = sK5 [avatar definition] 806. paul = sK5 <- (62) [avatar component clause 804] 808. 63 <=> mary = sK5 [avatar definition] 810. mary = sK5 <- (63) [avatar component clause 808] 811. 62 | 63 | ~7 [avatar split clause 795,349,808,804] 822. ~predc(mary) <- (~49, 63) [backward demodulation 617,810] 823. ~preds(mary) <- (~61, 63) [backward demodulation 724,810] 828. $false <- (8, ~49, 63) [subsumption resolution 822,372] 829. ~8 | 49 | ~63 [avatar contradiction clause 828] 830. $false <- (9, ~61, 63) [subsumption resolution 823,490] 831. ~9 | 61 | ~63 [avatar contradiction clause 830] 851. predm(paul) <- (50, 62) [backward demodulation 623,806] 852. ~preds(paul) <- (~61, 62) [backward demodulation 724,806] 854. 11 | ~50 | ~62 [avatar split clause 851,804,621,383] 859. ~predm(mary) <- (~19, 58) [backward demodulation 420,704] 864. ~9 | 19 | ~58 [avatar split clause 859,702,419,374] 909. preds(paul) | ~room(paul) <- (11) [resolution 385,280] 910. ~room(paul) <- (11, ~61, 62) [subsumption resolution 909,852] 911. $false <- (11, ~61, 62) [subsumption resolution 910,274] 912. ~11 | 61 | ~62 [avatar contradiction clause 911] 913. $false [avatar sat refutation 320,331,338,345,352,355,358,377,626,654,658,705,719,720,725,746,811,829,831,854,864,912] % SZS output end Proof for 5892902853075826871645158 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5500 % Time elapsed: 0.042 s % ------------------------------ % ------------------------------

Ella, Alysia, Brenda, Nikole are the only persons in the room. If “everyone in the room has completed a triathlon or is not an avid hiker” then “everyone in the room owns a microscope if they has completed a triathlon” otherwise “Ella is a certified yoga instructor teaching classes weekly”. Either “Ella collects antique jewelry” or “everyone in the room does enjoy trail running or is not an avid hiker” but not both. Ella has completed a triathlon and does not collect antique jewelry. Only one person in the room is not an avid hiker. Ella enjoys kayaking. Ella either is a certified yoga instructor teaching classes weekly or creates augmented reality experiences for mobile applications but not both. Everyone in the room does not enjoy kayaking and enjoys kayaking if they is a skilled home brewer experimenting with craft beer recipes and practices zumba. Ella practices zumba or does not create augmented reality experiences for mobile applications or both. Everyone in the room who creates large-scale murals for public art installations enjoys deep-sea diving and exploring underwater caves. Someone in the room creates bespoke furniture pieces from reclaimed wood. Not everyone in the room is an avid hiker if they collects antique jewelry. Everyone anywhere is not allergic to anything if they is a skilled home brewer experimenting with craft beer recipes and vice versa. Everyone in the room who is a skilled home brewer experimenting with craft beer recipes either mentors a youth basketball team on weekends or collects antique jewelry but not both. Everyone in the room who either mentors a youth basketball team on weekends or collects antique jewelry but not both does not practice calligraphy. Everyone in the room is a certified yoga instructor teaching classes weekly if they enjoys kayaking and vice versa.

Ella does enjoy trail running.

entailment

room(ella)&room(alysia)&room(brenda)&room(nikole)&(![X]:(room(X)=>(X='ella'|X='alysia'|X='brenda'|X='nikole')))& (((![X]:(room(X)=>(((is_not_an_avid_hiker(X))|(has_completed_a_triathlon(X))))))=>(![X]:(room(X)=>(((has_completed_a_triathlon(X))=>(owns_a_microscope(X)))))))&((~(![X]:(room(X)=>(((is_not_an_avid_hiker(X))|(has_completed_a_triathlon(X)))))))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(ella))))& ((collects_antique_jewelry(ella))<~>(![X]:(room(X)=>(((is_not_an_avid_hiker(X))|(does_enjoy_trail_running(X)))))))& (((has_completed_a_triathlon(ella))&(does_not_collect_antique_jewelry(ella))))& (((?[X]:(room(X)&is_not_an_avid_hiker(X)))&(![X,Y]:((room(X)&room(Y)&(is_not_an_avid_hiker(X))&(is_not_an_avid_hiker(Y)))=>(X=Y)))))& (enjoys_kayaking(ella))& (((is_a_certified_yoga_instructor_teaching_classes_weekly(ella))<~>(creates_augmented_reality_experiences_for_mobile_applications(ella))))& (![X]:(room(X)=>(((((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))&(practices_zumba(X))))=>(((does_not_enjoy_kayaking(X))&(enjoys_kayaking(X))))))))& (((practices_zumba(ella))|(does_not_create_augmented_reality_experiences_for_mobile_applications(ella))))& (![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))& (?[X]:(room(X)&(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))& (~![X]:(room(X)=>(((collects_antique_jewelry(X))=>(is_an_avid_hiker(X))))))& (![X]:(anywhere(X)=>(((is_not_allergic_to_anything(X))<=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))& (![X]:(room(X)=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))=>(((mentors_a_youth_basketball_team_on_weekends(X))<~>(collects_antique_jewelry(X))))))))& (![X]:(room(X)=>(((((mentors_a_youth_basketball_team_on_weekends(X))<~>(collects_antique_jewelry(X))))=>(does_not_practice_calligraphy(X))))))& (![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))<=>(enjoys_kayaking(X))))))

room(ella)&room(alysia)&room(brenda)&room(nikole)&(![X]:(room(X)=>(X='ella'|X='alysia'|X='brenda'|X='nikole')))& does_enjoy_trail_running(ella)

% SZS status Unsatisfiable for 6039065728921108387709393 % SZS output start Proof for 6039065728921108387709393 44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 46. predx(mary) <~> ! [X0] : (room(X0) => (predf(X0) | ~predc(X0))) [input p2] 47. ~predx(mary) & predi(mary) [input p3] 48. ! [X0,X1] : ((~predc(X1) & ~predc(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (~predc(X0) & room(X0)) [input p4] 55. ~! [X0] : (room(X0) => (predx(X0) => predc(X0))) [input p11] 60. ~(predf(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 62. ! [X0,X1] : ((~predc(X1) & ~predc(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (~predc(X2) & room(X2)) [rectify 48] 67. ~predx(mary) [pure predicate removal 47] 140. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 141. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 140] 142. predx(mary) <~> ! [X0] : ((predf(X0) | ~predc(X0)) | ~room(X0)) [ennf transformation 46] 143. predx(mary) <~> ! [X0] : (predf(X0) | ~predc(X0) | ~room(X0)) [flattening 142] 144. ! [X0,X1] : (X0 = X1 | (predc(X1) | predc(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (~predc(X2) & room(X2)) [ennf transformation 62] 145. ! [X0,X1] : (X0 = X1 | predc(X1) | predc(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (~predc(X2) & room(X2)) [flattening 144] 148. ? [X0] : ((~predc(X0) & predx(X0)) & room(X0)) [ennf transformation 55] 149. ? [X0] : (~predc(X0) & predx(X0) & room(X0)) [flattening 148] 154. ~predf(mary) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 60] 155. ~predf(mary) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 154] 157. (? [X0] : (~predf(X0) & predc(X0) & room(X0)) | ~predx(mary)) & (! [X0] : (predf(X0) | ~predc(X0) | ~room(X0)) | predx(mary)) [nnf transformation 143] 158. (? [X0] : (~predf(X0) & predc(X0) & room(X0)) | ~predx(mary)) & (! [X1] : (predf(X1) | ~predc(X1) | ~room(X1)) | predx(mary)) [rectify 157] 159. ? [X0] : (~predf(X0) & predc(X0) & room(X0)) => (~predf(sK0) & predc(sK0) & room(sK0)) [choice axiom] 160. ((~predf(sK0) & predc(sK0) & room(sK0)) | ~predx(mary)) & (! [X1] : (predf(X1) | ~predc(X1) | ~room(X1)) | predx(mary)) [skolemisation 158,159] 161. ? [X2] : (~predc(X2) & room(X2)) => (~predc(sK1) & room(sK1)) [choice axiom] 162. ! [X0,X1] : (X0 = X1 | predc(X1) | predc(X0) | ~room(X1) | ~room(X0)) & (~predc(sK1) & room(sK1)) [skolemisation 145,161] 166. ? [X0] : (~predc(X0) & predx(X0) & room(X0)) => (~predc(sK3) & predx(sK3) & room(sK3)) [choice axiom] 167. ~predc(sK3) & predx(sK3) & room(sK3) [skolemisation 149,166] 171. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK4 & fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) [choice axiom] 172. ~predf(mary) | (alice != sK4 & fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 155,171] 254. room(mary) [cnf transformation 141] 255. room(paul) [cnf transformation 141] 256. room(fred) [cnf transformation 141] 257. room(alice) [cnf transformation 141] 258. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 141] 259. predf(X1) | ~predc(X1) | ~room(X1) | predx(mary) [cnf transformation 160] 263. ~predx(mary) [cnf transformation 67] 266. ~room(X1) | predc(X1) | predc(X0) | X0 = X1 | ~room(X0) [cnf transformation 162] 274. room(sK3) [cnf transformation 167] 275. predx(sK3) [cnf transformation 167] 276. ~predc(sK3) [cnf transformation 167] 283. ~predf(mary) | room(sK4) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 172] 284. ~predf(mary) | mary != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 172] 285. ~predf(mary) | paul != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 172] 286. ~predf(mary) | fred != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 172] 287. ~predf(mary) | alice != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 172] 289. 1 <=> predx(mary) [avatar definition] 291. ~predx(mary) <- (~1) [avatar component clause 289] 308. 5 <=> ! [X1] : (predf(X1) | ~room(X1) | ~predc(X1)) [avatar definition] 309. ~predc(X1) | ~room(X1) | predf(X1) <- (5) [avatar component clause 308] 310. 1 | 5 [avatar split clause 259,308,289] 311. ~1 [avatar split clause 263,289] 330. ~predf(mary) | alice != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 287,257] 331. ~predf(mary) | alice != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 330,256] 332. ~predf(mary) | alice != sK4 | ~room(mary) [subsumption resolution 331,255] 333. ~predf(mary) | alice != sK4 [subsumption resolution 332,254] 335. 9 <=> alice = sK4 [avatar definition] 337. alice != sK4 <- (~9) [avatar component clause 335] 339. 10 <=> predf(mary) [avatar definition] 342. ~9 | ~10 [avatar split clause 333,339,335] 343. ~predf(mary) | fred != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 286,257] 344. ~predf(mary) | fred != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 343,256] 345. ~predf(mary) | fred != sK4 | ~room(mary) [subsumption resolution 344,255] 346. ~predf(mary) | fred != sK4 [subsumption resolution 345,254] 348. 11 <=> fred = sK4 [avatar definition] 350. fred != sK4 <- (~11) [avatar component clause 348] 351. ~11 | ~10 [avatar split clause 346,339,348] 352. ~predf(mary) | paul != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 285,257] 353. ~predf(mary) | paul != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 352,256] 354. ~predf(mary) | paul != sK4 | ~room(mary) [subsumption resolution 353,255] 355. ~predf(mary) | paul != sK4 [subsumption resolution 354,254] 357. 12 <=> paul = sK4 [avatar definition] 359. paul != sK4 <- (~12) [avatar component clause 357] 360. ~12 | ~10 [avatar split clause 355,339,357] 361. ~predf(mary) | mary != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 284,257] 362. ~predf(mary) | mary != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 361,256] 363. ~predf(mary) | mary != sK4 | ~room(mary) [subsumption resolution 362,255] 364. ~predf(mary) | mary != sK4 [subsumption resolution 363,254] 366. 13 <=> mary = sK4 [avatar definition] 368. mary != sK4 <- (~13) [avatar component clause 366] 369. ~13 | ~10 [avatar split clause 364,339,366] 370. ~predf(mary) | room(sK4) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 283,257] 371. ~predf(mary) | room(sK4) | ~room(paul) | ~room(mary) [subsumption resolution 370,256] 372. ~predf(mary) | room(sK4) | ~room(mary) [subsumption resolution 371,255] 373. ~predf(mary) | room(sK4) [subsumption resolution 372,254] 375. 14 <=> room(sK4) [avatar definition] 377. room(sK4) <- (14) [avatar component clause 375] 378. 14 | ~10 [avatar split clause 373,339,375] 424. predc(mary) | predc(X0) | mary = X0 | ~room(X0) [resolution 266,254] 432. 15 <=> ! [X0] : (predc(X0) | ~room(X0) | mary = X0) [avatar definition] 433. ~room(X0) | predc(X0) | mary = X0 <- (15) [avatar component clause 432] 435. 16 <=> predc(mary) [avatar definition] 437. predc(mary) <- (16) [avatar component clause 435] 438. 15 | 16 [avatar split clause 424,435,432] 479. predc(sK3) | mary = sK3 <- (15) [resolution 433,274] 496. mary = sK3 <- (15) [subsumption resolution 479,276] 499. predx(mary) <- (15) [backward demodulation 275,496] 501. $false <- (~1, 15) [subsumption resolution 499,291] 502. 1 | ~15 [avatar contradiction clause 501] 506. ~room(mary) | predf(mary) <- (5, 16) [resolution 437,309] 507. predf(mary) <- (5, 16) [subsumption resolution 506,254] 510. 10 | ~5 | ~16 [avatar split clause 507,435,308,339] 527. fred = sK4 | paul = sK4 | mary = sK4 | alice = sK4 <- (14) [resolution 258,377] 575. paul = sK4 | mary = sK4 | alice = sK4 <- (~11, 14) [subsumption resolution 527,350] 576. mary = sK4 | alice = sK4 <- (~11, ~12, 14) [subsumption resolution 575,359] 577. alice = sK4 <- (~11, ~12, ~13, 14) [subsumption resolution 576,368] 578. $false <- (~9, ~11, ~12, ~13, 14) [subsumption resolution 577,337] 579. 9 | 11 | 12 | 13 | ~14 [avatar contradiction clause 578] 580. $false [avatar sat refutation 310,311,342,351,360,369,378,438,502,510,579] % SZS output end Proof for 6039065728921108387709393 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.039 s % ------------------------------ % ------------------------------

There is a room. “Everyone in the room does not collect vintage stamps or travels domestically frequently” if “everyone in the room does not enjoy macrame or makes intricate hand-cut paper art for exhibitions” and vice versa. If “everyone in the room is not allergic to anything or collects action figures” then “everyone in the room who is not allergic to anything creates large-scale murals for public art installations” otherwise “not everyone outside the room who enjoys macrame does not own a telescope”. If “no one in the room does not practice zumba or creates augmented reality experiences for mobile applications” then “everyone in the room does not practice zumba if they travels domestically frequently and vice versa”. If “everyone in the room does not collect action figures or does not enjoy windsurfing” then “everyone in the room collects action figures, mentors a youth basketball team on weekends and has a specialized collection of handmade artisan pottery if they does not collect action figures” otherwise “if someone creates YouTube content then he/she does not own a smart tv and vice versa”. Everyone anywhere is allergic to anything, does not enjoy coding in Python and does not travel domestically frequently. Everyone outside the room who does not own a smart tv, creates YouTube content or travels domestically frequently mentors a youth basketball team on weekends or enjoys snowboarding or both. Everyone in the room practices zumba, travels domestically frequently and is a tea enthusiast if they makes intricate hand-cut paper art for exhibitions. Everyone in the room makes intricate hand-cut paper art for exhibitions if they owns a telescope. Everyone in the room enjoys kayaking if they makes intricate hand-cut paper art for exhibitions. No one in the room who does not create augmented reality experiences for mobile applications is a tea enthusiast. Everyone anywhere enjoys windsurfing.

Everyone outside the room mentors a youth basketball team on weekends.

entailment

(there_is_a_room)& ((![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))|(does_not_enjoy_macrame(X))))))<=>(![X]:(room(X)=>(((travels_domestically_frequently(X))|(does_not_collect_vintage_stamps(X)))))))& (((![X]:(room(X)=>(((collects_action_figures(X))|(is_not_allergic_to_anything(X))))))=>(![X]:(room(X)=>(((is_not_allergic_to_anything(X))=>(creates_large-scale_murals_for_public_art_installations(X)))))))&((~(![X]:(room(X)=>(((collects_action_figures(X))|(is_not_allergic_to_anything(X)))))))=>(~![X]:(~room(X)=>(((enjoys_macrame(X))=>(does_not_own_a_telescope(X))))))))& ((~?[X]:(room(X)=>(((creates_augmented_reality_experiences_for_mobile_applications(X))|(does_not_practice_zumba(X))))))=>(![X]:(room(X)=>(((does_not_practice_zumba(X))<=>(travels_domestically_frequently(X)))))))& (((![X]:(room(X)=>(((does_not_enjoy_windsurfing(X))|(does_not_collect_action_figures(X))))))=>(![X]:(room(X)=>(((does_not_collect_action_figures(X))=>(((collects_action_figures(X))&(mentors_a_youth_basketball_team_on_weekends(X))&(has_a_specialized_collection_of_handmade_artisan_pottery(X)))))))))&((~(![X]:(room(X)=>(((does_not_enjoy_windsurfing(X))|(does_not_collect_action_figures(X)))))))=>((![X]:((creates_YouTube_content(X))<=>(does_not_own_a_smart_tv(X)))))))& (![X]:(anywhere(X)=>(((is_allergic_to_anything(X))&(does_not_enjoy_coding_in_Python(X))&(does_not_travel_domestically_frequently(X))))))& (![X]:(~room(X)=>(((((does_not_own_a_smart_tv(X))|(creates_YouTube_content(X))|(travels_domestically_frequently(X))))=>(((mentors_a_youth_basketball_team_on_weekends(X))|(enjoys_snowboarding(X))))))))& (![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))=>(((practices_zumba(X))&(travels_domestically_frequently(X))&(is_a_tea_enthusiast(X))))))))& (![X]:(room(X)=>(((owns_a_telescope(X))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))& (![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))=>(enjoys_kayaking(X))))))& (~?[X]:(room(X)=>(((does_not_create_augmented_reality_experiences_for_mobile_applications(X))=>(is_a_tea_enthusiast(X))))))& (![X]:(anywhere(X)=>(enjoys_windsurfing(X))))& (![X]:(room(X)=>(collects_vintage_stamps(X))))& (![X]:(room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))|(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))))))& ((![X]:((enjoys_kayaking(X))<=>(practices_kickboxing(X)))))& (![X]:(room(X)=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))=>(enjoys_kayaking(X))))))& (![X]:(room(X)=>(((enjoys_kayaking(X))=>(((enjoys_windsurfing(X))&(owns_a_telescope(X))&(is_not_a_tea_enthusiast(X))))))))& ((![X]:((creates_YouTube_content(X))<=>(does_not_own_a_smart_tv(X)))))& (![X]:(room(X)=>(((practices_kickboxing(X))=>(practices_zumba(X))))))& (![X]:(room(X)=>(((practices_zumba(X))=>(does_enjoy_trail_running(X))))))& (![X]:(room(X)=>(((does_enjoy_trail_running(X))=>(is_a_scotch_connoisseur(X))))))& (![X]:(room(X)=>(((is_a_scotch_connoisseur(X))=>(collects_vintage_stamps(X))))))& (![X]:(room(X)=>(((does_not_own_a_smart_tv(X))=>(writes_poetry(X))))))& (~?[X]:(room(X)=>(((creates_augmented_reality_experiences_for_mobile_applications(X))|(does_not_practice_zumba(X))))))& (![X]:(room(X)=>(((is_a_tea_enthusiast(X))=>(does_not_enjoy_windsurfing(X))))))

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

% SZS status Unsatisfiable for 362657103821676729219012 % SZS output start Proof for 362657103821676729219012 44. there_is_a_room [input p0] 54. ~? [X0] : (room(X0) => (~predb(X0) => predw(X0))) [input p10] 69. ~(! [X0] : (~room(X0) => predc(X0)) & there_is_a_room) [input hypothesis] 167. ! [X0] : ((~predw(X0) & ~predb(X0)) & room(X0)) [ennf transformation 54] 168. ! [X0] : (~predw(X0) & ~predb(X0) & room(X0)) [flattening 167] 185. ? [X0] : (~predc(X0) & ~room(X0)) | ~there_is_a_room [ennf transformation 69] 205. ? [X0] : (~predc(X0) & ~room(X0)) => (~predc(sK5) & ~room(sK5)) [choice axiom] 206. (~predc(sK5) & ~room(sK5)) | ~there_is_a_room [skolemisation 185,205] 288. there_is_a_room [cnf transformation 44] 315. room(X0) [cnf transformation 168] 335. ~room(sK5) | ~there_is_a_room [cnf transformation 206] 462. ~there_is_a_room [subsumption resolution 335,315] 463. $false [subsumption resolution 462,288] % SZS output end Proof for 362657103821676729219012 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Arlene, Robert, Bill are the only persons in the room. Either “everyone in the room is not a Linux enthusiast or collects vintage stamps” or “everyone in the room collects vintage stamps” but not both. Robert who owns a 3D printer can play the flute. Everyone anywhere neither plays the violin nor has a curated collection of mid-century modern furniture if they owns a 3D printer. Everyone in the room mentors a youth basketball team on weekends if they neither plays the violin nor has a curated collection of mid-century modern furniture. Only one person in the room mentors a youth basketball team on weekends.

Arlene mentors a youth basketball team on weekends.

contradiction

room(arlene)&room(robert)&room(bill)&(![X]:(room(X)=>(X='arlene'|X='robert'|X='bill')))& ((![X]:(room(X)=>(((collects_vintage_stamps(X))|(is_not_a_Linux_enthusiast(X))))))<~>(![X]:(room(X)=>(collects_vintage_stamps(X)))))& ((![X]:(room(X)=>(((does_not_have_a_piercing(X))|(plays_the_violin(X))))))=>((owns_a_3D_printer(robert))&(can_play_the_flute(robert))))& (~(does_not_have_a_tattoo(bill)))& (![X]:(room(X)=>(((does_not_have_a_piercing(X))=>(is_a_Linux_enthusiast(X))))))& ((owns_a_3D_printer(robert))&(can_play_the_flute(robert)))& (![X]:(room(X)=>(((does_not_have_a_piercing(X))=>(((plays_the_violin(X))<~>(can_play_the_flute(X))))))))& (can_play_the_flute(bill))& (![X]:(room(X)=>(((has_a_tattoo(X))<=(is_a_Linux_enthusiast(X))))))& (~(has_a_piercing(arlene)))& (does_not_have_a_piercing(arlene))& (![X]:(anywhere(X)=>(((owns_a_3D_printer(X))=>(~((plays_the_violin(X))|(has_a_curated_collection_of_mid-century_modern_furniture(X))))))))& (![X]:(room(X)=>(((~((plays_the_violin(X))|(has_a_curated_collection_of_mid-century_modern_furniture(X))))=>(mentors_a_youth_basketball_team_on_weekends(X))))))& (![X]:(room(X)=>(((((mentors_a_youth_basketball_team_on_weekends(X))&(enjoys_coding_in_Python(X))&(practices_urban_gardening(X))))=>(((plays_the_violin(X))&(has_a_pet_dog(X))))))))& (![X]:(room(X)=>(does_not_practice_urban_gardening(X))))& (![X]:(anywhere(X)=>(((has_a_tattoo(X))<=>(can_play_the_flute(X))))))& (![X]:(~room(X)=>(((drives_a_hybrid_car(X))=>(has_a_curated_collection_of_mid-century_modern_furniture(X))))))& (((?[X]:(room(X)&mentors_a_youth_basketball_team_on_weekends(X)))&(![X,Y]:((room(X)&room(Y)&(mentors_a_youth_basketball_team_on_weekends(X))&(mentors_a_youth_basketball_team_on_weekends(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((can_play_the_flute(X))=>(((has_a_pet_dog(X))|(collects_vintage_stamps(X))))))))& (![X]:(~room(X)=>(((((has_a_pet_dog(X))|(collects_vintage_stamps(X))))<=>(does_not_enjoy_coding_in_Python(X))))))& ((drives_a_hybrid_car(robert))&(((does_not_collect_classic_novels(robert))|(has_a_curated_collection_of_mid-century_modern_furniture(robert))|(collects_classic_novels(robert)))))& (creates_large-scale_murals_for_public_art_installations(arlene))

room(arlene)&room(robert)&room(bill)&(![X]:(room(X)=>(X='arlene'|X='robert'|X='bill')))& mentors_a_youth_basketball_team_on_weekends(arlene)

% SZS status Unsatisfiable for 6805549778555425748240412 % SZS output start Proof for 6805549778555425748240412 5. ! [X0] : anywhere(X0) [input b4] 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 49. predi(paul) & predm(paul) [input p5] 55. ! [X0] : (anywhere(X0) => (predm(X0) => ~(predk(X0) | predf(X0)))) [input p11] 56. ! [X0] : (room(X0) => (~(predk(X0) | predf(X0)) => predb(X0))) [input p12] 61. ! [X0,X1] : ((predb(X1) & predb(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predb(X0) & room(X0)) [input p17] 66. predb(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 68. ! [X0,X1] : ((predb(X1) & predb(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predb(X2) & room(X2)) [rectify 61] 143. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 144. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 143] 155. ! [X0] : (((~predk(X0) & ~predf(X0)) | ~predm(X0)) | ~anywhere(X0)) [ennf transformation 55] 156. ! [X0] : ((~predk(X0) & ~predf(X0)) | ~predm(X0) | ~anywhere(X0)) [flattening 155] 157. ! [X0] : ((predb(X0) | (predk(X0) | predf(X0))) | ~room(X0)) [ennf transformation 56] 158. ! [X0] : (predb(X0) | predk(X0) | predf(X0) | ~room(X0)) [flattening 157] 162. ! [X0,X1] : (X0 = X1 | (~predb(X1) | ~predb(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (predb(X2) & room(X2)) [ennf transformation 68] 163. ! [X0,X1] : (X0 = X1 | ~predb(X1) | ~predb(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (predb(X2) & room(X2)) [flattening 162] 167. predb(mary) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 66] 168. predb(mary) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 167] 179. ? [X2] : (predb(X2) & room(X2)) => (predb(sK3) & room(sK3)) [choice axiom] 180. ! [X0,X1] : (X0 = X1 | ~predb(X1) | ~predb(X0) | ~room(X1) | ~room(X0)) & (predb(sK3) & room(sK3)) [skolemisation 163,179] 183. anywhere(X0) [cnf transformation 5] 228. mary != paul [cnf transformation 43] 264. room(mary) [cnf transformation 144] 265. room(paul) [cnf transformation 144] 283. predm(paul) [cnf transformation 49] 291. ~predf(X0) | ~predm(X0) | ~anywhere(X0) [cnf transformation 156] 292. ~predk(X0) | ~predm(X0) | ~anywhere(X0) [cnf transformation 156] 293. ~room(X0) | predk(X0) | predf(X0) | predb(X0) [cnf transformation 158] 299. ~predb(X1) | X0 = X1 | ~predb(X0) | ~room(X1) | ~room(X0) [cnf transformation 180] 310. predb(mary) [cnf transformation 168] 364. 12 <=> predm(paul) [avatar definition] 366. predm(paul) <- (12) [avatar component clause 364] 371. 12 [avatar split clause 283,364] 372. ~predk(X0) | ~predm(X0) [subsumption resolution 292,183] 373. ~predm(X0) | ~predf(X0) [subsumption resolution 291,183] 376. ~predf(paul) <- (12) [resolution 373,366] 493. predk(paul) | predf(paul) | predb(paul) [resolution 293,265] 498. predk(paul) | predb(paul) <- (12) [subsumption resolution 493,376] 500. 27 <=> predb(paul) [avatar definition] 502. predb(paul) <- (27) [avatar component clause 500] 504. 28 <=> predk(paul) [avatar definition] 506. predk(paul) <- (28) [avatar component clause 504] 507. 27 | 28 | ~12 [avatar split clause 498,364,504,500] 717. mary = X0 | ~predb(X0) | ~room(mary) | ~room(X0) [resolution 299,310] 719. ~predb(X0) | mary = X0 | ~room(X0) [subsumption resolution 717,264] 736. mary = paul | ~room(paul) <- (27) [resolution 719,502] 737. ~room(paul) <- (27) [subsumption resolution 736,228] 738. $false <- (27) [subsumption resolution 737,265] 739. ~27 [avatar contradiction clause 738] 794. ~predm(paul) <- (28) [resolution 506,372] 795. $false <- (12, 28) [subsumption resolution 794,366] 796. ~12 | ~28 [avatar contradiction clause 795] 797. $false [avatar sat refutation 371,507,739,796] % SZS output end Proof for 6805549778555425748240412 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5373 % Time elapsed: 0.038 s % ------------------------------ % ------------------------------

Leona, Lester, Vera, Irene, Thomas are the only persons in the room. Thomas practices graffiti art, owns a smartwatch and is tall. Stars are visible during the daytime only on Sundays. Leona dreamt that "Thomas is poorer than Charles". Everyone in the room who is calm is not funny. Thomas makes homemade pastries. "A door randomly teleports those who pass through it." or "A bridge sings when it is crossed." but not both. Everyone in the room is generous if they does not enjoy salsa dancing. No brave person is curious. If someone is a sibling of Shane then he/she does not hate Charles and vice versa. Shane and Leona hate each other. Everyone in the room is old only if they owns a smartwatch. "A bridge does not sing when it is crossed." or "Stars are not visible during the daytime only on Sundays." but not both. Leona creates large-scale murals for public art installations. If someone travels domestically frequently then he/she is a patient person and vice versa. Shane is richer than Lester. If someone is old then he/she owns a smartwatch and vice versa. It is not the case that "someone in the room does not enjoy landscape photography". Vera is a wise tourist. All old persons are happy. Everyone anywhere is louder than Shane if they is a sibling of Charles. Irene enjoys landscape photography. Everyone in the room is a curious strong european if they enjoys watercolor painting. Someone who enjoys salsa dancing like someone who is a sibling of Shane. Irene is the oldest in the room. Irene is not passionate about collecting and restoring classic cars.

Irene is old.

entailment

room(leona)&room(lester)&room(vera)&room(irene)&room(thomas)&(![X]:(room(X)=>(X='leona'|X='lester'|X='vera'|X='irene'|X='thomas')))& (((practices_graffiti_art(thomas))&(owns_a_smartwatch(thomas))&(tall(thomas))))& (Stars_are_visible_during_the_daytime_only_on_Sundays.)& ((leona_dream=>(poorer(charles,thomas))))& (![X]:(room(X)=>(((calm(X))=>(~funny(X))))))& (makes_homemade_pastries(thomas))& (((A_door_randomly_teleports_those_who_pass_through_it.)<~>(A_bridge_sings_when_it_is_crossed.)))& (![X]:(room(X)=>(((does_not_enjoy_salsa_dancing(X))=>(generous(X))))))& (~?[X]:(brave(X)=>curious(X)))& ((![X]:((sibling(shane,X))<=>(~hate(charles,X)))))& ((hate(shane,leona) & hate(leona,shane)))& (![X]:(room(X)=>(((owns_a_smartwatch(X))<=(old(X))))))& (((A_bridge_does_not_sing_when_it_is_crossed.)<~>(Stars_are_not_visible_during_the_daytime_only_on_Sundays.)))& (creates_large-scale_murals_for_public_art_installations(leona))& ((![X]:((travels_domestically_frequently(X))<=>(patient(X)&person(X)))))& (richer(lester,shane))& ((![X]:((old(X))<=>(owns_a_smartwatch(X)))))& (~(?[X]:(room(X)&(does_not_enjoy_landscape_photography(X)))))& (wise(vera)&tourist(vera))& (![X]:(old(X)=>happy(X)))& (![X]:(anywhere(X)=>(((sibling(charles,X))=>(louder(shane,X))))))& (enjoys_landscape_photography(irene))& (![X]:(room(X)=>(((enjoys_watercolor_painting(X))=>(curious(X)&strong(X)&european(X))))))& (?[X,Y]:((enjoys_salsa_dancing(X))&(sibling(shane,Y))&(like(X,Y))))& (![X]:((room(X)&(X!=irene))=>older(X,irene)))& (is_not_passionate_about_collecting_and_restoring_classic_cars(irene))

room(leona)&room(lester)&room(vera)&room(irene)&room(thomas)&(![X]:(room(X)=>(X='leona'|X='lester'|X='vera'|X='irene'|X='thomas')))& old(irene)

% SZS status Unsatisfiable for 1556241329607557889716719 % SZS output start Proof for 1556241329607557889716719 21. ! [X0,X1] : (X0 != X1 => ((old(X0) & older(X0,X1)) => old(X1))) [input b20] 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] 45. tall(john) & predw(john) & predf(john) [input p1] 60. ! [X0] : (old(X0) <=> predw(X0)) [input p16] 68. ! [X0] : ((alice != X0 & room(X0)) => older(X0,alice)) [input p24] 70. ~(old(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] 90. predw(john) & predf(john) [pure predicate removal 45] 91. predw(john) [pure predicate removal 90] 123. ! [X0,X1] : ((old(X1) | (~old(X0) | ~older(X0,X1))) | X0 = X1) [ennf transformation 21] 124. ! [X0,X1] : (old(X1) | ~old(X0) | ~older(X0,X1) | X0 = X1) [flattening 123] 163. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 164. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 163] 169. ! [X0] : (older(X0,alice) | (alice = X0 | ~room(X0))) [ennf transformation 68] 170. ! [X0] : (older(X0,alice) | alice = X0 | ~room(X0)) [flattening 169] 171. ~old(alice) | ? [X0] : ((john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 70] 172. ~old(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 171] 177. ! [X0] : ((old(X0) | ~predw(X0)) & (predw(X0) | ~old(X0))) [nnf transformation 60] 180. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK2 & alice != sK2 & fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 181. ~old(alice) | (john != sK2 & alice != sK2 & fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 172,180] 201. ~older(X0,X1) | ~old(X0) | old(X1) | X0 = X1 [cnf transformation 124] 250. alice != john [cnf transformation 43] 265. room(mary) [cnf transformation 164] 266. room(paul) [cnf transformation 164] 267. room(fred) [cnf transformation 164] 268. room(alice) [cnf transformation 164] 269. room(john) [cnf transformation 164] 270. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 164] 271. predw(john) [cnf transformation 91] 284. ~predw(X0) | old(X0) [cnf transformation 177] 288. older(X0,alice) | alice = X0 | ~room(X0) [cnf transformation 170] 289. ~old(alice) | room(sK2) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181] 290. ~old(alice) | mary != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181] 291. ~old(alice) | paul != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181] 292. ~old(alice) | fred != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181] 293. ~old(alice) | alice != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181] 294. ~old(alice) | john != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181] 308. ~old(alice) | john != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 294,269] 309. ~old(alice) | john != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 308,268] 310. ~old(alice) | john != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 309,267] 311. ~old(alice) | john != sK2 | ~room(mary) [subsumption resolution 310,266] 312. ~old(alice) | john != sK2 [subsumption resolution 311,265] 314. 3 <=> john = sK2 [avatar definition] 316. john != sK2 <- (~3) [avatar component clause 314] 318. 4 <=> old(alice) [avatar definition] 320. ~old(alice) <- (~4) [avatar component clause 318] 321. ~3 | ~4 [avatar split clause 312,318,314] 322. ~old(alice) | alice != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 293,269] 323. ~old(alice) | alice != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 322,268] 324. ~old(alice) | alice != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 323,267] 325. ~old(alice) | alice != sK2 | ~room(mary) [subsumption resolution 324,266] 326. ~old(alice) | alice != sK2 [subsumption resolution 325,265] 328. 5 <=> alice = sK2 [avatar definition] 330. alice != sK2 <- (~5) [avatar component clause 328] 331. ~5 | ~4 [avatar split clause 326,318,328] 332. ~old(alice) | fred != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 292,269] 333. ~old(alice) | fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 332,268] 334. ~old(alice) | fred != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 333,267] 335. ~old(alice) | fred != sK2 | ~room(mary) [subsumption resolution 334,266] 336. ~old(alice) | fred != sK2 [subsumption resolution 335,265] 338. 6 <=> fred = sK2 [avatar definition] 340. fred != sK2 <- (~6) [avatar component clause 338] 341. ~6 | ~4 [avatar split clause 336,318,338] 342. ~old(alice) | paul != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 291,269] 343. ~old(alice) | paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 342,268] 344. ~old(alice) | paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 343,267] 345. ~old(alice) | paul != sK2 | ~room(mary) [subsumption resolution 344,266] 346. ~old(alice) | paul != sK2 [subsumption resolution 345,265] 348. 7 <=> paul = sK2 [avatar definition] 350. paul != sK2 <- (~7) [avatar component clause 348] 351. ~7 | ~4 [avatar split clause 346,318,348] 352. ~old(alice) | mary != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 290,269] 353. ~old(alice) | mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 352,268] 354. ~old(alice) | mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 353,267] 355. ~old(alice) | mary != sK2 | ~room(mary) [subsumption resolution 354,266] 356. ~old(alice) | mary != sK2 [subsumption resolution 355,265] 358. 8 <=> mary = sK2 [avatar definition] 360. mary != sK2 <- (~8) [avatar component clause 358] 361. ~8 | ~4 [avatar split clause 356,318,358] 362. ~old(alice) | room(sK2) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 289,269] 363. ~old(alice) | room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 362,268] 364. ~old(alice) | room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 363,267] 365. ~old(alice) | room(sK2) | ~room(mary) [subsumption resolution 364,266] 366. ~old(alice) | room(sK2) [subsumption resolution 365,265] 368. 9 <=> room(sK2) [avatar definition] 370. room(sK2) <- (9) [avatar component clause 368] 371. 9 | ~4 [avatar split clause 366,318,368] 372. old(john) [resolution 284,271] 460. ~old(X0) | old(alice) | alice = X0 | alice = X0 | ~room(X0) [resolution 201,288] 461. ~old(X0) | old(alice) | alice = X0 | ~room(X0) [duplicate literal removal 460] 462. ~room(X0) | alice = X0 | ~old(X0) <- (~4) [subsumption resolution 461,320] 475. alice = john | ~old(john) <- (~4) [resolution 462,269] 479. ~old(john) <- (~4) [subsumption resolution 475,250] 480. $false <- (~4) [subsumption resolution 479,372] 481. 4 [avatar contradiction clause 480] 538. alice = sK2 | fred = sK2 | paul = sK2 | mary = sK2 | john = sK2 <- (9) [resolution 270,370] 539. fred = sK2 | paul = sK2 | mary = sK2 | john = sK2 <- (~5, 9) [subsumption resolution 538,330] 540. paul = sK2 | mary = sK2 | john = sK2 <- (~5, ~6, 9) [subsumption resolution 539,340] 541. mary = sK2 | john = sK2 <- (~5, ~6, ~7, 9) [subsumption resolution 540,350] 542. john = sK2 <- (~5, ~6, ~7, ~8, 9) [subsumption resolution 541,360] 543. $false <- (~3, ~5, ~6, ~7, ~8, 9) [subsumption resolution 542,316] 544. 3 | 5 | 6 | 7 | 8 | ~9 [avatar contradiction clause 543] 545. $false [avatar sat refutation 321,331,341,351,361,371,481,544] % SZS output end Proof for 1556241329607557889716719 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Douglas, Cynthia, Carol are the only persons in the room. “Douglas is a certified yoga instructor teaching classes weekly” if “Douglas can play the flute”. “Douglas either collects antique clocks or watches fantasy movies but not both” unless “everyone in the room is not a member of a local theater group specializing in improv or does not frequently participates in hackathons and coding competitions”. “Douglas neither is a member of a local theater group specializing in improv nor owns a significant collection of rare gemstones and minerals” if “Douglas hosts a YouTube channel dedicated to art tutorials”. Either “at least one person in the room collects modern art” or “Douglas enjoys kayaking and exploring remote waterways” but not both. If “Douglas enjoys deep-sea diving and exploring underwater caves” then “Douglas does not host themed dinner parties featuring gourmet home-cooked meals”. Either “Douglas can play the flute” or “Douglas collects modern art” but not both. Douglas is a member of a local theater group specializing in improv. Everyone anywhere does not own a significant collection of rare gemstones and minerals or enjoys fishing. Douglas plays eSports competitively. Douglas enjoys wildlife photography. Douglas who is a member of a local theater group specializing in improv practices zumba. Douglas enjoys wildlife photography, frequently participates in hackathons and coding competitions and enjoys deep-sea diving and exploring underwater caves. It is not the case that “Douglas owns a significant collection of rare gemstones and minerals, enjoys deep-sea diving and exploring underwater caves and is an avid mountain climber who has scaled several peaks”. Douglas watches fantasy movies. Everyone in the room enjoys kayaking and exploring remote waterways or does not own a significant collection of rare gemstones and minerals. At least one person in the room does not frequently participates in hackathons and coding competitions. Douglas collects modern art. At least one person anywhere hosts a YouTube channel dedicated to art tutorials. Douglas enjoys fishing. Douglas who enjoys deep-sea diving and exploring underwater caves enjoys fishing. Douglas drives a hybrid car. Only one person in the room practices zumba, has completed a triathlon and can play the flute.

Douglas collects antique clocks.

contradiction

room(douglas)&room(cynthia)&room(carol)&(![X]:(room(X)=>(X='douglas'|X='cynthia'|X='carol')))& ((can_play_the_flute(douglas))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(douglas)))& (~(![X]:(room(X)=>(((does_not_frequently_participates_in_hackathons_and_coding_competitions(X))|(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))))))=>(((collects_antique_clocks(douglas))<~>(watches_fantasy_movies(douglas)))))& ((hosts_a_YouTube_channel_dedicated_to_art_tutorials(douglas))=>(~((is_a_member_of_a_local_theater_group_specializing_in_improv(douglas))|(owns_a_significant_collection_of_rare_gemstones_and_minerals(douglas)))))& ((((?[X]:(room(X)&collects_modern_art(X)))))<~>(enjoys_kayaking_and_exploring_remote_waterways(douglas)))& ((enjoys_deep-sea_diving_and_exploring_underwater_caves(douglas))=>(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(douglas)))& ((can_play_the_flute(douglas))<~>(collects_modern_art(douglas)))& (is_a_member_of_a_local_theater_group_specializing_in_improv(douglas))& (![X]:(anywhere(X)=>(((enjoys_fishing(X))|(does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))))))& (plays_eSports_competitively(douglas))& (enjoys_wildlife_photography(douglas))& ((is_a_member_of_a_local_theater_group_specializing_in_improv(douglas))&(practices_zumba(douglas)))& (((enjoys_wildlife_photography(douglas))&(frequently_participates_in_hackathons_and_coding_competitions(douglas))&(enjoys_deep-sea_diving_and_exploring_underwater_caves(douglas))))& (~(((owns_a_significant_collection_of_rare_gemstones_and_minerals(douglas))&(enjoys_deep-sea_diving_and_exploring_underwater_caves(douglas))&(is_an_avid_mountain_climber_who_has_scaled_several_peaks(douglas)))))& (watches_fantasy_movies(douglas))& (![X]:(room(X)=>(((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))|(enjoys_kayaking_and_exploring_remote_waterways(X))))))& (((?[X]:(room(X)&does_not_frequently_participates_in_hackathons_and_coding_competitions(X)))))& (collects_modern_art(douglas))& (((?[X]:(anywhere(X)&hosts_a_YouTube_channel_dedicated_to_art_tutorials(X)))))& (enjoys_fishing(douglas))& ((enjoys_deep-sea_diving_and_exploring_underwater_caves(douglas))&(enjoys_fishing(douglas)))& (drives_a_hybrid_car(douglas))& (((?[X]:(room(X)&((practices_zumba(X))&(has_completed_a_triathlon(X))&(can_play_the_flute(X)))))&(![X,Y]:((room(X)&room(Y)&(((practices_zumba(X))&(has_completed_a_triathlon(X))&(can_play_the_flute(X))))&(((practices_zumba(Y))&(has_completed_a_triathlon(Y))&(can_play_the_flute(Y)))))=>(X=Y)))))& (?[X]:(room(X)&(drives_a_hybrid_car(X))))

room(douglas)&room(cynthia)&room(carol)&(![X]:(room(X)=>(X='douglas'|X='cynthia'|X='carol')))& collects_antique_clocks(douglas)

% SZS status Unsatisfiable for 96050320142678138158659 % SZS output start Proof for 96050320142678138158659 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 46. ~! [X0] : (room(X0) => (~predd(X0) | ~predq(X0))) => (predz(mary) <~> predc(mary)) [input p2] 55. prede(mary) & predd(mary) [input p11] 56. predf(mary) & predq(mary) & predl(mary) [input p12] 58. predc(mary) [input p14] 68. predz(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 73. predf(mary) & predq(mary) [pure predicate removal 56] 82. predq(mary) [pure predicate removal 73] 158. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 159. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 158] 160. (predz(mary) <~> predc(mary)) | ! [X0] : ((~predd(X0) | ~predq(X0)) | ~room(X0)) [ennf transformation 46] 161. (predz(mary) <~> predc(mary)) | ! [X0] : (~predd(X0) | ~predq(X0) | ~room(X0)) [flattening 160] 165. predz(mary) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 68] 166. predz(mary) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 165] 168. ((~predc(mary) | ~predz(mary)) & (predc(mary) | predz(mary))) | ! [X0] : (~predd(X0) | ~predq(X0) | ~room(X0)) [nnf transformation 161] 262. room(mary) [cnf transformation 159] 267. ~predc(mary) | ~predz(mary) | ~predd(X0) | ~predq(X0) | ~room(X0) [cnf transformation 168] 275. predd(mary) [cnf transformation 55] 277. predq(mary) [cnf transformation 82] 278. predc(mary) [cnf transformation 58] 293. predz(mary) [cnf transformation 166] 295. 1 <=> ! [X0] : (~predd(X0) | ~room(X0) | ~predq(X0)) [avatar definition] 296. ~predd(X0) | ~room(X0) | ~predq(X0) <- (1) [avatar component clause 295] 298. 2 <=> predz(mary) [avatar definition] 302. 3 <=> predc(mary) [avatar definition] 305. 1 | ~2 | ~3 [avatar split clause 267,302,298,295] 312. 5 <=> predd(mary) [avatar definition] 313. predd(mary) <- (5) [avatar component clause 312] 345. 5 [avatar split clause 275,312] 346. 3 [avatar split clause 278,302] 348. 2 [avatar split clause 293,298] 349. ~room(mary) | ~predq(mary) <- (1, 5) [resolution 296,313] 350. ~predq(mary) <- (1, 5) [subsumption resolution 349,262] 351. $false <- (1, 5) [subsumption resolution 350,277] 352. ~1 | ~5 [avatar contradiction clause 351] 353. $false [avatar sat refutation 305,345,346,348,352] % SZS output end Proof for 96050320142678138158659 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Julio, Edwin, Katherine, Kyle, Wayne are the only persons in the room. “Everyone outside the room does not own a telescope or enjoys virtual reality gaming” only if “everyone outside the room enjoys camping and organizing outdoor survival workshops if they is a brave tall person”. If someone is tall then he/she enjoys camping and organizing outdoor survival workshops and vice versa. “A book cannot be opened only at midnight.” and “A door does not randomly teleport those who pass through it.”. At least one person in the room enjoys virtual reality gaming. Everyone in the room owns a telescope if they is not a brave person. Everyone in the room owns a telescope if they enjoys camping and organizing outdoor survival workshops. Everyone in the room neither is not a kind person nor is brave if they owns a telescope. Edwin owns a telescope. All tall persons are kind. Not everyone outside the room is not a kind person. Everyone in the room owns a telescope. At least one person outside the room is not kind. Neither “A book can be opened only at midnight.” nor “A door randomly teleports those who pass through it.”. All brave persons are tall. If someone enjoys camping and organizing outdoor survival workshops and enjoys virtual reality gaming then he/she enjoys virtual reality gaming and vice versa. “A desert does not bloom with snowdrops every year.” and “Not all swans in one park are blue.”. Julio who owns a telescope and is kind is kind.

It is not the case that “Julio enjoys camping and organizing outdoor survival workshops”.

neutral

room(julio)&room(edwin)&room(katherine)&room(kyle)&room(wayne)&(![X]:(room(X)=>(X='julio'|X='edwin'|X='katherine'|X='kyle'|X='wayne')))& ((![X]:(~room(X)=>(((enjoys_virtual_reality_gaming(X))|(does_not_own_a_telescope(X))))))=>(![X]:(~room(X)=>(((brave(X)&tall(X)&person(X))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X)))))))& ((![X]:((tall(X))<=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X)))))& (((A_book_cannot_be_opened_only_at_midnight.)&(A_door_does_not_randomly_teleport_those_who_pass_through_it.)))& (((?[X]:(room(X)&enjoys_virtual_reality_gaming(X)))))& (![X]:(room(X)=>(((~(brave(X)&person(X)))=>(owns_a_telescope(X))))))& (![X]:(room(X)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))=>(owns_a_telescope(X))))))& (![X]:(room(X)=>(((owns_a_telescope(X))=>(~((~(kind(X)&person(X)))|(brave(X))))))))& (owns_a_telescope(edwin))& (![X]:(tall(X)=>kind(X)))& (~![X]:(~room(X)=>(~(kind(X)&person(X)))))& (![X]:(room(X)=>(owns_a_telescope(X))))& (((?[X]:(~room(X)&~kind(X)))))& (~((A_book_can_be_opened_only_at_midnight.)|(A_door_randomly_teleports_those_who_pass_through_it.)))& (![X]:(brave(X)=>tall(X)))& ((![X]:((((enjoys_camping_and_organizing_outdoor_survival_workshops(X))&(enjoys_virtual_reality_gaming(X))))<=>(enjoys_virtual_reality_gaming(X)))))& (((A_desert_does_not_bloom_with_snowdrops_every_year.)&(Not_all_swans_in_one_park_are_blue.)))& ((((owns_a_telescope(julio))&(kind(julio))))&(kind(julio)))

room(julio)&room(edwin)&room(katherine)&room(kyle)&room(wayne)&(![X]:(room(X)=>(X='julio'|X='edwin'|X='katherine'|X='kyle'|X='wayne')))& ~(enjoys_camping_and_organizing_outdoor_survival_workshops(julio))

There is a room. “No one in the room does not enjoy salsa dancing or does not own an Android phone” unless ““There is no planet where the oceans are in the sky.” and “A shadow does not appear only at noon.” and “Socks disappear worldwide every full moon.””. “Not everyone in the room does not enjoy salsa dancing or does not enjoy skydiving” unless “not everyone in the room does not own an Android phone or does not participate in citizen science projects related to wildlife monitoring”. Not everyone in the room does not own an Android phone or does not participate in citizen science projects related to wildlife monitoring. Everyone anywhere does not enjoy salsa dancing. Everyone in the room does not collect rare and antique scientific instruments or does not participate in citizen science projects related to wildlife monitoring. Everyone in the room does not collect rare and antique scientific instruments or does not enjoy salsa dancing. Everyone outside the room does not enjoy skydiving or does not participate in citizen science projects related to wildlife monitoring. Everyone anywhere does not collect rare and antique scientific instruments or does not enjoy salsa dancing. Everyone in the room does not enjoy skydiving or does not own an Android phone. No wise person is strong. Someone in the room does not enjoy salsa dancing.

“There is a planet where the oceans are in the sky.” or “A shadow appears only at noon.” or both.

contradiction

(there_is_a_room)& (~(((There_is_no_planet_where_the_oceans_are_in_the_sky.)&(A_shadow_does_not_appear_only_at_noon.)&(Socks_disappear_worldwide_every_full_moon.)))=>(~?[X]:(room(X)=>(((does_not_own_an_Android_phone(X))|(does_not_enjoy_salsa_dancing(X)))))))& (~(~![X]:(room(X)=>(((does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(does_not_own_an_Android_phone(X))))))=>(~![X]:(room(X)=>(((does_not_enjoy_skydiving(X))|(does_not_enjoy_salsa_dancing(X)))))))& (~![X]:(room(X)=>(((does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(does_not_own_an_Android_phone(X))))))& (![X]:(anywhere(X)=>(does_not_enjoy_salsa_dancing(X))))& (![X]:(room(X)=>(((does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(does_not_collect_rare_and_antique_scientific_instruments(X))))))& (![X]:(room(X)=>(((does_not_enjoy_salsa_dancing(X))|(does_not_collect_rare_and_antique_scientific_instruments(X))))))& (![X]:(~room(X)=>(((does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))|(does_not_enjoy_skydiving(X))))))& (![X]:(anywhere(X)=>(((does_not_enjoy_salsa_dancing(X))|(does_not_collect_rare_and_antique_scientific_instruments(X))))))& (![X]:(room(X)=>(((does_not_own_an_Android_phone(X))|(does_not_enjoy_skydiving(X))))))& (~?[X]:(wise(X)=>strong(X)))& (?[X]:(room(X)&(does_not_enjoy_salsa_dancing(X))))

(there_is_a_room)& ((There_is_a_planet_where_the_oceans_are_in_the_sky.)|(A_shadow_appears_only_at_noon.))

% SZS status Unsatisfiable for 2999313390434051577986181 % SZS output start Proof for 2999313390434051577986181 5. ! [X0] : anywhere(X0) [input b4] 45. ~(propositione & ~propositionb & ~propositiond) => ~? [X0] : (room(X0) => (~predr(X0) | ~predx(X0))) [input p1] 48. ! [X0] : (anywhere(X0) => ~predr(X0)) [input p4] 56. (propositionb | propositiond) & there_is_a_room [input hypothesis] 64. ~(~propositionb & ~propositiond) => ~? [X0] : (room(X0) => (~predr(X0) | ~predx(X0))) [pure predicate removal 45] 65. propositionb | propositiond [pure predicate removal 56] 138. ! [X0] : ((predr(X0) & predx(X0)) & room(X0)) | (~propositionb & ~propositiond) [ennf transformation 64] 139. ! [X0] : (predr(X0) & predx(X0) & room(X0)) | (~propositionb & ~propositiond) [flattening 138] 144. ! [X0] : (~predr(X0) | ~anywhere(X0)) [ennf transformation 48] 162. anywhere(X0) [cnf transformation 5] 247. predr(X0) | ~propositiond [cnf transformation 139] 248. predr(X0) | ~propositionb [cnf transformation 139] 258. ~predr(X0) | ~anywhere(X0) [cnf transformation 144] 263. propositionb | propositiond [cnf transformation 65] 265. 1 <=> propositionb [avatar definition] 269. 2 <=> ! [X0] : predr(X0) [avatar definition] 270. predr(X0) <- (2) [avatar component clause 269] 271. ~1 | 2 [avatar split clause 248,269,265] 273. 3 <=> propositiond [avatar definition] 276. ~3 | 2 [avatar split clause 247,269,273] 321. ~predr(X0) [subsumption resolution 258,162] 322. 3 | 1 [avatar split clause 263,265,273] 323. $false <- (2) [subsumption resolution 270,321] 324. ~2 [avatar contradiction clause 323] 325. $false [avatar sat refutation 271,276,322,324] % SZS output end Proof for 2999313390434051577986181 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Melissa is the only person in the room. If “Elaine and Melissa hate each other” then “Melissa is not hated by Ronald”. Someone in the room does not like Ronald. If someone does not like Shawn then he/she is not liked by Elaine and vice versa. Elaine and Melissa like each other. Someone who does not like Ronald hate someone who likes Shawn. Someone who does not like Shawn hate someone who does not like Elaine.

Melissa is liked by Shawn.

neutral

room(melissa)&(![X]:(room(X)=>(X='melissa')))& (((hate(elaine,melissa) & hate(melissa,elaine)))=>(~hate(melissa,ronald)))& (?[X]:(room(X)&(~like(ronald,X))))& ((![X]:((~like(shawn,X))<=>(~like(X,elaine)))))& ((like(elaine,melissa) & like(melissa,elaine)))& (?[X,Y]:((~like(ronald,X))&(like(shawn,Y))&(hate(X,Y))))& (?[X,Y]:((~like(shawn,X))&(~like(elaine,Y))&(hate(X,Y))))

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

Jenny is the only person in the room. If “no one in the room does not have a specialized collection of handmade artisan pottery or does not enjoy logic puzzles” then “if someone neither owns a microscope nor practices urban gardening then he/she builds model airplanes”. If “Jenny owns a high-end gaming PC with custom-built components” then “if someone participates in citizen science projects related to wildlife monitoring then he/she enjoys rooftop gardening”. Everyone in the room maintains a large, organic vegetable garden year-round or collects rare and antique scientific instruments or both only if they does not own a high-end gaming PC with custom-built components. Jenny does not host a YouTube channel dedicated to art tutorials. Everyone in the room owns a 3D printer if they does not participate in citizen science projects related to wildlife monitoring. Jenny maintains a large, organic vegetable garden year-round or collects rare and antique scientific instruments or both. If someone is an expert in identifying and foraging wild edible plants then he/she enjoys logic puzzles. Jenny practices urban gardening, owns a 3D printer or collects rare and antique scientific instruments. Everyone anywhere is right-handed if they neither does not practice and performs acrobatic dance routines nor maintains a large, organic vegetable garden year-round. Everyone in the room plays the violin if they is right-handed. If someone participates in citizen science projects related to wildlife monitoring then he/she enjoys rooftop gardening. Everyone anywhere watches fantasy movies, maintains a large, organic vegetable garden year-round and owns a high-end gaming PC with custom-built components if they participates in citizen science projects related to wildlife monitoring. Jenny builds model airplanes. It is not the case that “Jenny plays the violin, practices urban gardening or watches fantasy movies”. Jenny does not have a specialized collection of handmade artisan pottery. Jenny is a client of Costco. Not everyone outside the room is a dedicated advocate for digital privacy and encryption if they either is a Linux enthusiast or hosts a YouTube channel dedicated to art tutorials but not both. Everyone in the room enjoys logic puzzles only if they is a dedicated advocate for digital privacy and encryption. Everyone in the room who has a specialized collection of handmade artisan pottery is a skilled home brewer experimenting with craft beer recipes. Jenny does not participate in citizen science projects related to wildlife monitoring.

Jenny is right-handed.

contradiction

room(jenny)&(![X]:(room(X)=>(X='jenny')))& ((~?[X]:(room(X)=>(((does_not_enjoy_logic_puzzles(X))|(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))))))=>((![X]:((~((owns_a_microscope(X))|(practices_urban_gardening(X))))=>(builds_model_airplanes(X))))))& ((owns_a_high-end_gaming_PC_with_custom-built_components(jenny))=>((![X]:((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))=>(enjoys_rooftop_gardening(X))))))& (![X]:(room(X)=>(((does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))<=(((maintains_a_large,_organic_vegetable_garden_year-round(X))|(collects_rare_and_antique_scientific_instruments(X))))))))& (does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(jenny))& (![X]:(room(X)=>(((does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))=>(owns_a_3D_printer(X))))))& (((maintains_a_large,_organic_vegetable_garden_year-round(jenny))|(collects_rare_and_antique_scientific_instruments(jenny))))& ((![X]:((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))=>(enjoys_logic_puzzles(X)))))& (((practices_urban_gardening(jenny))|(owns_a_3D_printer(jenny))|(collects_rare_and_antique_scientific_instruments(jenny))))& (![X]:(anywhere(X)=>(((~((does_not_practice_and_performs_acrobatic_dance_routines(X))|(maintains_a_large,_organic_vegetable_garden_year-round(X))))=>(is_right-handed(X))))))& (![X]:(room(X)=>(((is_right-handed(X))=>(plays_the_violin(X))))))& ((![X]:((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))=>(enjoys_rooftop_gardening(X)))))& (![X]:(anywhere(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))=>(((watches_fantasy_movies(X))&(maintains_a_large,_organic_vegetable_garden_year-round(X))&(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))))& (builds_model_airplanes(jenny))& (~(((plays_the_violin(jenny))|(practices_urban_gardening(jenny))|(watches_fantasy_movies(jenny)))))& (does_not_have_a_specialized_collection_of_handmade_artisan_pottery(jenny))& (is_a_client_of_Costco(jenny))& (~![X]:(~room(X)=>(((((is_a_Linux_enthusiast(X))<~>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))& (![X]:(room(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))<=(enjoys_logic_puzzles(X))))))& (![X]:(room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))& (does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(jenny))

room(jenny)&(![X]:(room(X)=>(X='jenny')))& is_right-handed(jenny)

% SZS status Unsatisfiable for 5760852130493160321488125 % SZS output start Proof for 5760852130493160321488125 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 54. ! [X0] : (room(X0) => (predt(X0) => predx(X0))) [input p10] 58. ~(prede(mary) | preda(mary) | predx(mary)) [input p14] 65. predt(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 76. ~(prede(mary) | predx(mary)) [pure predicate removal 58] 83. ~predx(mary) [pure predicate removal 76] 158. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 159. ! [X0] : ((predx(X0) | ~predt(X0)) | ~room(X0)) [ennf transformation 54] 160. ! [X0] : (predx(X0) | ~predt(X0) | ~room(X0)) [flattening 159] 161. ~predx(mary) [ennf transformation 83] 163. predt(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 65] 249. room(mary) [cnf transformation 158] 252. ~predt(X0) | predx(X0) | ~room(X0) [cnf transformation 160] 253. ~predx(mary) [cnf transformation 161] 259. predt(mary) [cnf transformation 163] 271. predx(mary) | ~room(mary) [resolution 252,259] 272. ~room(mary) [subsumption resolution 271,253] 273. $false [subsumption resolution 272,249] % SZS output end Proof for 5760852130493160321488125 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.039 s % ------------------------------ % ------------------------------

Joseph, Sonja, Ashley are the only persons in the room. Everyone in the room who creates augmented reality experiences for mobile applications neither owns a significant collection of rare gemstones and minerals nor enjoys writing detailed reviews of new and classic board games. Everyone in the room creates augmented reality experiences for mobile applications if they practices urban gardening. Someone in the room enjoys cross-country skiing. Sonja enjoys writing detailed reviews of new and classic board games. Joseph practices urban gardening.

Joseph owns a significant collection of rare gemstones and minerals.

contradiction

room(joseph)&room(sonja)&room(ashley)&(![X]:(room(X)=>(X='joseph'|X='sonja'|X='ashley')))& (![X]:(room(X)=>(((creates_augmented_reality_experiences_for_mobile_applications(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)=>(((practices_urban_gardening(X))=>(creates_augmented_reality_experiences_for_mobile_applications(X))))))& (?[X]:(room(X)&(enjoys_cross-country_skiing(X))))& (enjoys_writing_detailed_reviews_of_new_and_classic_board_games(sonja))& (![X]:(room(X)=>(((enjoys_cross-country_skiing(X))=>(does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))))))& (~![X]:(room(X)=>(is_a_cybersecurity_expert(X))))& (has_completed_a_triathlon(ashley))& (~![X]:(room(X)=>(((((enjoys_stand-up_paddleboarding(X))&(practices_archery(X))&(has_completed_a_triathlon(X))))=>(~((plays_the_violin(X))|(owns_an_Android_phone(X))))))))& (collects_limited-edition_art_prints_from_contemporary_artists(joseph))& (![X]:(room(X)=>(((((collects_limited-edition_art_prints_from_contemporary_artists(X))<~>(plays_the_violin(X))))<=(creates_augmented_reality_experiences_for_mobile_applications(X))))))& (![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))<=(((collects_limited-edition_art_prints_from_contemporary_artists(X))<~>(plays_the_violin(X))))))))& (![X]:(room(X)=>(((enjoys_cross-country_skiing(X))=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))<~>(owns_an_Android_phone(X))))))))& (~![X]:(room(X)=>(((((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))<~>(owns_an_Android_phone(X))))|(is_not_an_avid_hiker(X))))))& (enjoys_cross-country_skiing(joseph))& (~((has_completed_a_triathlon(joseph))|(practices_archery(joseph))))& (enjoys_writing_detailed_reviews_of_new_and_classic_board_games(ashley))& (hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(joseph))& (![X]:(room(X)=>(((is_a_cybersecurity_expert(X))=>(~((has_completed_a_triathlon(X))|(enjoys_stand-up_paddleboarding(X))))))))& (practices_urban_gardening(joseph))& (((?[X]:(room(X)&has_completed_a_triathlon(X)))&(![X,Y]:((room(X)&room(Y)&(has_completed_a_triathlon(X))&(has_completed_a_triathlon(Y)))=>(X=Y)))))& (![X]:(anywhere(X)=>(((enjoys_stand-up_paddleboarding(X))<=(~((plays_the_violin(X))|(collects_vintage_vinyl_records(X))))))))& (~(~(owns_a_significant_collection_of_rare_gemstones_and_minerals(sonja))))& (owns_an_Android_phone(ashley))& (![X]:(~room(X)=>(((practices_archery(X))=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))))& (![X]:(room(X)=>(((is_a_scotch_connoisseur(X))=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))& (![X]:(~room(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))<=>(creates_augmented_reality_experiences_for_mobile_applications(X))))))

room(joseph)&room(sonja)&room(ashley)&(![X]:(room(X)=>(X='joseph'|X='sonja'|X='ashley')))& owns_a_significant_collection_of_rare_gemstones_and_minerals(joseph)

% SZS status Unsatisfiable for 311680898640051984652278 % SZS output start Proof for 311680898640051984652278 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 45. ! [X0] : (room(X0) => (predi(X0) => ~(predh(X0) | predc(X0)))) [input p1] 46. ! [X0] : (room(X0) => (predf(X0) => predi(X0))) [input p2] 63. predf(mary) [input p19] 71. predc(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 152. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 153. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 152] 154. ! [X0] : (((~predh(X0) & ~predc(X0)) | ~predi(X0)) | ~room(X0)) [ennf transformation 45] 155. ! [X0] : ((~predh(X0) & ~predc(X0)) | ~predi(X0) | ~room(X0)) [flattening 154] 156. ! [X0] : ((predi(X0) | ~predf(X0)) | ~room(X0)) [ennf transformation 46] 157. ! [X0] : (predi(X0) | ~predf(X0) | ~room(X0)) [flattening 156] 176. predc(mary) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 71] 177. predc(mary) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 176] 275. room(mary) [cnf transformation 153] 279. ~predc(X0) | ~predi(X0) | ~room(X0) [cnf transformation 155] 281. ~predf(X0) | predi(X0) | ~room(X0) [cnf transformation 157] 306. predf(mary) [cnf transformation 63] 319. predc(mary) [cnf transformation 177] 341. ~predi(mary) | ~room(mary) [resolution 279,319] 343. ~predi(mary) [subsumption resolution 341,275] 347. predi(mary) | ~room(mary) [resolution 281,306] 348. ~room(mary) [subsumption resolution 347,343] 349. $false [subsumption resolution 348,275] % SZS output end Proof for 311680898640051984652278 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Juana is the only person in the room. “Everyone in the room is not kind if they is a curious person” unless “at least one person in the room is poorer than Randy”. Everyone anywhere is not kind if they is not a curious person and vice versa. Charles is poorer than Juana. Someone who either is kind or is poorer than Randy but not both is poorer than someone who is not a kind curious person. Everyone in the room is not kind, not curious if and only if they is poorer than Randy. Everyone in the room who is poorer than Sarah is a kind curious person. Sarah is poorer than Juana. Juana either is poorer than Sarah or is not a kind person but not both.

Juana is poorer than Sarah.

contradiction

room(juana)&(![X]:(room(X)=>(X='juana')))& (~(((?[X]:(room(X)&poorer(randy,X)))))=>(![X]:(room(X)=>(((curious(X)&person(X))=>(~kind(X)))))))& (![X]:(anywhere(X)=>(((~kind(X))<=>(~(curious(X)&person(X)))))))& (poorer(juana,charles))& (?[X,Y]:((((kind(X))<~>(poorer(randy,X))))&(~(kind(Y)&curious(Y)&person(Y)))&(poorer(X,Y))))& (![X]:(room(X)=>(((~kind(X)&~curious(X))<=>(poorer(randy,X))))))& (![X]:(room(X)=>(((poorer(sarah,X))=>(kind(X)&curious(X)&person(X))))))& (poorer(juana,sarah))& (((poorer(sarah,juana))<~>(~(kind(juana)&person(juana)))))

room(juana)&(![X]:(room(X)=>(X='juana')))& poorer(sarah,juana)

% SZS status Unsatisfiable for 7717228916315317695858005 % SZS output start Proof for 7717228916315317695858005 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 45. ~? [X0] : (poorer(paul,X0) & room(X0)) => ! [X0] : (room(X0) => ((person(X0) & curious(X0)) => ~kind(X0))) [input p1] 46. ! [X0] : (anywhere(X0) => (~kind(X0) <=> ~(person(X0) & curious(X0)))) [input p2] 49. ! [X0] : (room(X0) => ((~curious(X0) & ~kind(X0)) <=> poorer(paul,X0))) [input p5] 52. poorer(fred,mary) <~> ~(person(mary) & kind(mary)) [input p8] 53. poorer(fred,mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis] 54. ~? [X0] : (poorer(paul,X0) & room(X0)) => ! [X1] : (room(X1) => ((person(X1) & curious(X1)) => ~kind(X1))) [rectify 45] 126. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 127. ! [X1] : ((~kind(X1) | (~person(X1) | ~curious(X1))) | ~room(X1)) | ? [X0] : (poorer(paul,X0) & room(X0)) [ennf transformation 54] 128. ! [X1] : (~kind(X1) | ~person(X1) | ~curious(X1) | ~room(X1)) | ? [X0] : (poorer(paul,X0) & room(X0)) [flattening 127] 129. ! [X0] : ((~kind(X0) <=> (~person(X0) | ~curious(X0))) | ~anywhere(X0)) [ennf transformation 46] 131. ! [X0] : (((~curious(X0) & ~kind(X0)) <=> poorer(paul,X0)) | ~room(X0)) [ennf transformation 49] 134. poorer(fred,mary) <~> (~person(mary) | ~kind(mary)) [ennf transformation 52] 135. poorer(fred,mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 53] 137. ! [X0] : (~kind(X0) | ~person(X0) | ~curious(X0) | ~room(X0)) | ? [X1] : (poorer(paul,X1) & room(X1)) [rectify 128] 138. ? [X1] : (poorer(paul,X1) & room(X1)) => (poorer(paul,sK0) & room(sK0)) [choice axiom] 139. ! [X0] : (~kind(X0) | ~person(X0) | ~curious(X0) | ~room(X0)) | (poorer(paul,sK0) & room(sK0)) [skolemisation 137,138] 140. ! [X0] : (((~kind(X0) | (person(X0) & curious(X0))) & ((~person(X0) | ~curious(X0)) | kind(X0))) | ~anywhere(X0)) [nnf transformation 129] 141. ! [X0] : (((~kind(X0) | (person(X0) & curious(X0))) & (~person(X0) | ~curious(X0) | kind(X0))) | ~anywhere(X0)) [flattening 140] 146. ! [X0] : ((((~curious(X0) & ~kind(X0)) | ~poorer(paul,X0)) & (poorer(paul,X0) | (curious(X0) | kind(X0)))) | ~room(X0)) [nnf transformation 131] 147. ! [X0] : ((((~curious(X0) & ~kind(X0)) | ~poorer(paul,X0)) & (poorer(paul,X0) | curious(X0) | kind(X0))) | ~room(X0)) [flattening 146] 148. ((person(mary) & kind(mary)) | ~poorer(fred,mary)) & ((~person(mary) | ~kind(mary)) | poorer(fred,mary)) [nnf transformation 134] 149. ((person(mary) & kind(mary)) | ~poorer(fred,mary)) & (~person(mary) | ~kind(mary) | poorer(fred,mary)) [flattening 148] 150. anywhere(X0) [cnf transformation 5] 231. room(mary) [cnf transformation 126] 232. ~room(X0) | mary = X0 [cnf transformation 126] 233. ~kind(X0) | ~person(X0) | ~curious(X0) | ~room(X0) | room(sK0) [cnf transformation 139] 234. ~kind(X0) | ~person(X0) | ~curious(X0) | ~room(X0) | poorer(paul,sK0) [cnf transformation 139] 235. ~person(X0) | ~curious(X0) | kind(X0) | ~anywhere(X0) [cnf transformation 141] 236. ~kind(X0) | curious(X0) | ~anywhere(X0) [cnf transformation 141] 244. ~poorer(paul,X0) | ~kind(X0) | ~room(X0) [cnf transformation 147] 251. kind(mary) | ~poorer(fred,mary) [cnf transformation 149] 252. person(mary) | ~poorer(fred,mary) [cnf transformation 149] 255. poorer(fred,mary) [cnf transformation 135] 257. 1 <=> poorer(paul,sK0) [avatar definition] 259. poorer(paul,sK0) <- (1) [avatar component clause 257] 261. 2 <=> ! [X0] : (~kind(X0) | ~room(X0) | ~curious(X0) | ~person(X0)) [avatar definition] 262. ~kind(X0) | ~room(X0) | ~curious(X0) | ~person(X0) <- (2) [avatar component clause 261] 263. 1 | 2 [avatar split clause 234,261,257] 265. 3 <=> room(sK0) [avatar definition] 267. room(sK0) <- (3) [avatar component clause 265] 268. 3 | 2 [avatar split clause 233,261,265] 270. ~kind(X0) | curious(X0) [subsumption resolution 236,150] 271. ~curious(X0) | ~person(X0) | kind(X0) [subsumption resolution 235,150] 286. 6 <=> poorer(fred,mary) [avatar definition] 290. 7 <=> person(mary) [avatar definition] 292. person(mary) <- (7) [avatar component clause 290] 293. ~6 | 7 [avatar split clause 252,290,286] 295. 8 <=> kind(mary) [avatar definition] 297. kind(mary) <- (8) [avatar component clause 295] 298. ~6 | 8 [avatar split clause 251,295,286] 301. 6 [avatar split clause 255,286] 302. ~curious(X0) | ~room(X0) | ~person(X0) <- (2) [subsumption resolution 262,271] 306. curious(mary) <- (8) [resolution 270,297] 311. ~room(mary) | ~person(mary) <- (2, 8) [resolution 302,306] 313. ~person(mary) <- (2, 8) [subsumption resolution 311,231] 314. $false <- (2, 7, 8) [subsumption resolution 313,292] 315. ~2 | ~7 | ~8 [avatar contradiction clause 314] 316. mary = sK0 <- (3) [resolution 267,232] 317. poorer(paul,mary) <- (1, 3) [backward demodulation 259,316] 319. ~kind(mary) | ~room(mary) <- (1, 3) [resolution 244,317] 320. ~room(mary) <- (1, 3, 8) [subsumption resolution 319,297] 321. $false <- (1, 3, 8) [subsumption resolution 320,231] 322. ~1 | ~3 | ~8 [avatar contradiction clause 321] 323. $false [avatar sat refutation 263,268,293,298,301,315,322] % SZS output end Proof for 7717228916315317695858005 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

There is a room. “Everyone in the room does not create large-scale murals for public art installations” unless “everyone in the room does not use an ios phone”. “Everyone in the room is not allergic to anything” unless “not everyone anywhere is not a member of a local theater group specializing in improv”. “Only one person in the room does not use a Windows laptop” unless “everyone outside the room does not enjoy kayaking”. Everyone in the room is not a dedicated volunteer for local community service projects. Not everyone in the room does not create large-scale murals for public art installations. Everyone outside the room does not work on fridays. Everyone in the room does not have a vast collection of first-edition science fiction novels. Everyone anywhere does not collect action figures. Everyone outside the room does not collect rare and antique scientific instruments. Everyone outside the room is not an enthusiastic bird watcher who travels for rare sightings. Everyone in the room does not own a television. Everyone in the room does not enjoy deep-sea diving and exploring underwater caves. Everyone in the room does not enjoy watercolor painting, does not practice kickboxing and is not a member of a local theater group specializing in improv.

Everyone in the room does not create large-scale murals for public art installations or is allergic to anything.

neutral

(there_is_a_room)& (~(![X]:(room(X)=>(does_not_use_an_ios_phone(X))))=>(![X]:(room(X)=>(does_not_create_large-scale_murals_for_public_art_installations(X)))))& (~(~![X]:(anywhere(X)=>(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))))=>(![X]:(room(X)=>(is_not_allergic_to_anything(X)))))& (~(![X]:(~room(X)=>(does_not_enjoy_kayaking(X))))=>(((?[X]:(room(X)&does_not_use_a_Windows_laptop(X)))&(![X,Y]:((room(X)&room(Y)&(does_not_use_a_Windows_laptop(X))&(does_not_use_a_Windows_laptop(Y)))=>(X=Y))))))& (![X]:(room(X)=>(is_not_a_dedicated_volunteer_for_local_community_service_projects(X))))& (~![X]:(room(X)=>(does_not_create_large-scale_murals_for_public_art_installations(X))))& (![X]:(~room(X)=>(does_not_work_on_fridays(X))))& (![X]:(room(X)=>(does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))))& (![X]:(anywhere(X)=>(does_not_collect_action_figures(X))))& (![X]:(~room(X)=>(does_not_collect_rare_and_antique_scientific_instruments(X))))& (![X]:(~room(X)=>(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))& (![X]:(room(X)=>(does_not_own_a_television(X))))& (![X]:(room(X)=>(does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))))& (![X]:(room(X)=>(((does_not_enjoy_watercolor_painting(X))&(does_not_practice_kickboxing(X))&(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))))))

(there_is_a_room)& ![X]:(room(X)=>(((is_allergic_to_anything(X))|(does_not_create_large-scale_murals_for_public_art_installations(X)))))

There is a room. If “everyone in the room is an avid collector of autographed memorabilia from famous musicians or does not practice graffiti art” then “everyone in the room who is an avid collector of autographed memorabilia from famous musicians practices graffiti art”. If “not everyone in the room is an avid collector of autographed memorabilia from famous musicians or is not an avid collector of autographed memorabilia from famous musicians” then “everyone anywhere is an avid collector of autographed memorabilia from famous musicians only if they is an expert in identifying and foraging wild edible plants”. Everyone in the room who is an expert in identifying and foraging wild edible plants is an avid collector of autographed memorabilia from famous musicians. Everyone anywhere is an avid collector of autographed memorabilia from famous musicians only if they is an expert in identifying and foraging wild edible plants. Everyone in the room either is an expert in identifying and foraging wild edible plants or practices graffiti art but not both only if they is an expert in identifying and foraging wild edible plants. Everyone in the room who is an expert in identifying and foraging wild edible plants practices graffiti art. Everyone anywhere who practices graffiti art is an avid collector of autographed memorabilia from famous musicians. Someone in the room is an expert in identifying and foraging wild edible plants. Everyone outside the room who either is an avid collector of autographed memorabilia from famous musicians or is an expert in identifying and foraging wild edible plants but not both is an avid collector of autographed memorabilia from famous musicians.

Everyone in the room is an avid collector of autographed memorabilia from famous musicians.

neutral

(there_is_a_room)& ((![X]:(room(X)=>(((does_not_practice_graffiti_art(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))=>(practices_graffiti_art(X)))))))& ((~![X]:(room(X)=>(((is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))|(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))=>(![X]:(anywhere(X)=>(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))<=(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X)))))))& (![X]:(room(X)=>(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))=>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))& (![X]:(anywhere(X)=>(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))<=(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))& (![X]:(room(X)=>(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))<=(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))<~>(practices_graffiti_art(X))))))))& (![X]:(room(X)=>(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))=>(practices_graffiti_art(X))))))& (![X]:(anywhere(X)=>(((practices_graffiti_art(X))=>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))& (?[X]:(room(X)&(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))& (![X]:(~room(X)=>(((((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))<~>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))=>(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))

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

Carole, Donald, Martha, Jon are the only persons in the room. “Carole trains for and competes in international triathlons” unless “Martha is strong”. “Donald either is strong or is a quiet tourist but not both” only if “someone in the room is an enthusiastic bird watcher who travels for rare sightings”. Either “Martha hosts themed dinner parties featuring gourmet home-cooked meals” or “Martha enjoys landscape photography” but not both. “Donald hosts themed dinner parties featuring gourmet home-cooked meals” if “Carole is a strong person and is a quiet tourist” and vice versa. “Donald hosts themed dinner parties featuring gourmet home-cooked meals” if “Martha trains for and competes in international triathlons” and vice versa. “Carole trains for and competes in international triathlons” unless “Carole hosts themed dinner parties featuring gourmet home-cooked meals”. “Someone in the room hosts themed dinner parties featuring gourmet home-cooked meals” only if “at least one person in the room is a strong tourist”. “Martha is strong” unless “Carole is an enthusiastic bird watcher who travels for rare sightings”.

Carole trains for and competes in international triathlons.

neutral

room(carole)&room(donald)&room(martha)&room(jon)&(![X]:(room(X)=>(X='carole'|X='donald'|X='martha'|X='jon')))& (~(strong(martha))=>(trains_for_and_competes_in_international_triathlons(carole)))& ((((strong(donald))<~>(quiet(donald)&tourist(donald))))=>(?[X]:(room(X)&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X)))))& ((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(martha))<~>(enjoys_landscape_photography(martha)))& ((((strong(carole)&person(carole))&(quiet(carole)&tourist(carole))))<=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(donald)))& ((trains_for_and_competes_in_international_triathlons(martha))<=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(donald)))& (~(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(carole))=>(trains_for_and_competes_in_international_triathlons(carole)))& ((?[X]:(room(X)&(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))=>(((?[X]:(room(X)&strong(X)&tourist(X))))))& (~(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(carole))=>(strong(martha)))& (~(?[X]:(anywhere(X)&(quiet(X))))=>(![X]:(quiet(X)=>strong(X))))& (~(((strong(carole)&tourist(carole))<~>(trains_for_and_competes_in_international_triathlons(carole))))=>(strong(carole)&person(carole)))& (quiet(carole))& (hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(martha))& (![X]:((anywhere(X)&(X!=donald))=>quieter(X,donald)))& (quiet(martha))& (?[X]:(room(X)&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))& (strong(martha)&person(martha))& ((quiet(martha))&(trains_for_and_competes_in_international_triathlons(martha)))& (~(enjoys_landscape_photography(martha)))& (trains_for_and_competes_in_international_triathlons(martha))& (hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(donald))& (strong(martha)&tourist(martha))& (((?[X]:(room(X)&trains_for_and_competes_in_international_triathlons(X)))))

room(carole)&room(donald)&room(martha)&room(jon)&(![X]:(room(X)=>(X='carole'|X='donald'|X='martha'|X='jon')))& trains_for_and_competes_in_international_triathlons(carole)

Alex, Larry, David, Irene, Allen are the only persons in the room. Virginia and Alex hate each other. Everyone in the room who is a sibling of Virginia is calm. Everyone in the room is not calm, not kind, not old if they is calm. Everyone in the room enjoys snowboarding if they is not calm, not kind, not old. Everyone in the room is a kind quiet calm tall person if they has a vast collection of first-edition science fiction novels.

Larry has a vast collection of first-edition science fiction novels.

contradiction

room(alex)&room(larry)&room(david)&room(irene)&room(allen)&(![X]:(room(X)=>(X='alex'|X='larry'|X='david'|X='irene'|X='allen')))& ((hate(virginia,alex) & hate(alex,virginia)))& (![X]:(room(X)=>(((sibling(virginia,X))=>(calm(X))))))& (![X]:(room(X)=>(((calm(X))=>(~calm(X)&~kind(X)&~old(X))))))& (![X]:(room(X)=>(((~calm(X)&~kind(X)&~old(X))=>(enjoys_snowboarding(X))))))& (![X]:(anywhere(X)=>(((enjoys_snowboarding(X))=>(~like(X,virginia))))))& (![X]:(anywhere(X)=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))<=(collects_comic_books(X))))))& (![X]:(room(X)=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))=>(kind(X)&quiet(X)&calm(X)&tall(X)&person(X))))))& (client(alex,virginia))& (![X]:(anywhere(X)=>(((((client(virginia,X))&(cannot_play_the_harmonica(X))&(sibling(virginia,X))))<=>(wise(X)&european(X))))))& (louder(alex,virginia))

room(alex)&room(larry)&room(david)&room(irene)&room(allen)&(![X]:(room(X)=>(X='alex'|X='larry'|X='david'|X='irene'|X='allen')))& has_a_vast_collection_of_first-edition_science_fiction_novels(larry)

% SZS status Unsatisfiable for 2528087614815376394606533 % SZS output start Proof for 2528087614815376394606533 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) => (calm(X0) => (~old(X0) & ~kind(X0) & ~calm(X0)))) [input p3] 51. ! [X0] : (room(X0) => (predk(X0) => (person(X0) & tall(X0) & calm(X0) & quiet(X0) & kind(X0)))) [input p7] 55. predk(paul) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 56. ! [X0] : (room(X0) => (predk(X0) => (person(X0) & calm(X0) & quiet(X0) & kind(X0)))) [pure predicate removal 51] 60. ! [X0] : (room(X0) => (predk(X0) => (calm(X0) & quiet(X0) & kind(X0)))) [pure predicate removal 56] 133. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 134. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 133] 137. ! [X0] : (((~old(X0) & ~kind(X0) & ~calm(X0)) | ~calm(X0)) | ~room(X0)) [ennf transformation 47] 138. ! [X0] : ((~old(X0) & ~kind(X0) & ~calm(X0)) | ~calm(X0) | ~room(X0)) [flattening 137] 139. ! [X0] : (((calm(X0) & quiet(X0) & kind(X0)) | ~predk(X0)) | ~room(X0)) [ennf transformation 60] 140. ! [X0] : ((calm(X0) & quiet(X0) & kind(X0)) | ~predk(X0) | ~room(X0)) [flattening 139] 142. predk(paul) & ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 55] 143. predk(paul) & ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 142] 229. room(paul) [cnf transformation 134] 235. ~calm(X0) | ~calm(X0) | ~room(X0) [cnf transformation 138] 240. calm(X0) | ~predk(X0) | ~room(X0) [cnf transformation 140] 254. predk(paul) [cnf transformation 143] 255. ~calm(X0) | ~room(X0) [duplicate literal removal 235] 256. ~predk(X0) | ~room(X0) [subsumption resolution 240,255] 262. ~room(paul) [resolution 256,254] 263. $false [subsumption resolution 262,229] % SZS output end Proof for 2528087614815376394606533 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Eleanor, James are the only persons in the room. If “James owns a smart tv” then “more than one person in the room streams on Twitch”. Someone in the room hosts regular workshops on creative writing. Someone in the room can play the guitar. If someone enjoys logic puzzles then he/she does not own a smart tv. More than one person in the room is an amateur astronomer who builds and uses custom telescopes. Someone anywhere enjoys salsa dancing. Someone in the room builds model airplanes. Everyone in the room who collects vintage vinyl records collects historical artifacts related to ancient civilizations. Someone in the room collects vintage vinyl records. Everyone in the room who streams on Twitch collects vintage vinyl records. Everyone in the room who collects vintage vinyl records regularly goes on multi-day backpacking trips in national parks. Someone in the room does not regularly contributes to tech forums and online communities, regularly contributes to tech forums and online communities or competes in national level swimming championships. Someone in the room regularly contributes to tech forums and online communities. Everyone in the room who practices digital art has a tattoo.

Everyone in the room does not collect vintage vinyl records or has a tattoo.

neutral

room(eleanor)&room(james)&(![X]:(room(X)=>(X='eleanor'|X='james')))& ((owns_a_smart_tv(james))=>((?[X,Y]:(room(X)&room(Y)&(streams_on_Twitch(X)&streams_on_Twitch(Y))&(X!=Y)))))& (?[X]:(room(X)&(hosts_regular_workshops_on_creative_writing(X))))& (?[X]:(room(X)&(can_play_the_guitar(X))))& ((![X]:((enjoys_logic_puzzles(X))=>(does_not_own_a_smart_tv(X)))))& ((?[X,Y]:(room(X)&room(Y)&(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X)&is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(Y))&(X!=Y))))& (?[X]:(anywhere(X)&(enjoys_salsa_dancing(X))))& (?[X]:(room(X)&(builds_model_airplanes(X))))& (![X]:(room(X)=>(((collects_vintage_vinyl_records(X))=>(collects_historical_artifacts_related_to_ancient_civilizations(X))))))& (?[X]:(room(X)&(collects_vintage_vinyl_records(X))))& (![X]:(room(X)=>(((streams_on_Twitch(X))=>(collects_vintage_vinyl_records(X))))))& (![X]:(room(X)=>(((collects_vintage_vinyl_records(X))=>(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))& (?[X]:(room(X)&(((does_not_regularly_contributes_to_tech_forums_and_online_communities(X))|(regularly_contributes_to_tech_forums_and_online_communities(X))|(competes_in_national_level_swimming_championships(X))))))& (?[X]:(room(X)&(regularly_contributes_to_tech_forums_and_online_communities(X))))& (![X]:(room(X)=>(((practices_digital_art(X))=>(has_a_tattoo(X))))))

room(eleanor)&room(james)&(![X]:(room(X)=>(X='eleanor'|X='james')))& ![X]:(room(X)=>(((has_a_tattoo(X))|(does_not_collect_vintage_vinyl_records(X)))))

Melissa, Vera are the only persons in the room. Either 'at least one person in the room is a night owl' or 'it is not the case that 'Vera enjoys making ceramics'' but not both. If 'it is not the case that 'it is not the case that 'Vera has a tattoo''' then 'Vera has a tattoo'. If someone is a certified scuba diver with advanced underwater photography skills then he/she maintains a personal blog focused on cybersecurity tips. Melissa is a certified scuba diver with advanced underwater photography skills.

Melissa maintains a personal blog focused on cybersecurity tips.

entailment

room(melissa)&room(vera)&(![X]:(room(X)=>(X='melissa'|X='vera')))& ((((?[X]:(room(X)&is_a_night_owl(X)))))<~>(~(enjoys_making_ceramics(vera))))& ((~(~(has_a_tattoo(vera))))=>(has_a_tattoo(vera)))& ((~(~(is_a_night_owl(vera))))=>(~(has_a_tattoo(vera))))& ((maintains_a_personal_blog_focused_on_cybersecurity_tips(vera))=>(has_a_vast_collection_of_first-edition_science_fiction_novels(vera)))& (maintains_a_personal_blog_focused_on_cybersecurity_tips(vera))& ((![X]:((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(X)))))& ((![X]:((develops_open-source_software_projects_in_their_free_time(X))<=>(has_a_tattoo(X)))))& (is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(melissa))& (has_a_tattoo(vera))& ((![X]:((can_play_the_guitar(X))<=>(develops_open-source_software_projects_in_their_free_time(X)))))& (is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(vera))& (has_lived_in_exactly_three_countries(vera))& (enjoys_macrame(melissa))& (enjoys_making_ceramics(vera))

room(melissa)&room(vera)&(![X]:(room(X)=>(X='melissa'|X='vera')))& maintains_a_personal_blog_focused_on_cybersecurity_tips(melissa)

% SZS status Unsatisfiable for 3345960797004429883704966 % SZS output start Proof for 3345960797004429883704966 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 50. ! [X0] : (prede(X0) => predc(X0)) [input p6] 52. prede(mary) [input p8] 59. ~(predc(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 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] : (predc(X0) | ~prede(X0)) [ennf transformation 50] 140. ~predc(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 59] 141. ~predc(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 140] 147. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK1 & mary != sK1 & room(sK1)) [choice axiom] 148. ~predc(mary) | (paul != sK1 & mary != sK1 & room(sK1)) | ~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] 238. ~prede(X0) | predc(X0) [cnf transformation 139] 239. prede(mary) [cnf transformation 52] 243. ~predc(mary) | room(sK1) | ~room(paul) | ~room(mary) [cnf transformation 148] 244. ~predc(mary) | mary != sK1 | ~room(paul) | ~room(mary) [cnf transformation 148] 245. ~predc(mary) | paul != sK1 | ~room(paul) | ~room(mary) [cnf transformation 148] 275. ~predc(mary) | paul != sK1 | ~room(mary) [subsumption resolution 245,230] 276. ~predc(mary) | paul != sK1 [subsumption resolution 275,229] 278. 7 <=> paul = sK1 [avatar definition] 280. paul != sK1 <- (~7) [avatar component clause 278] 282. 8 <=> predc(mary) [avatar definition] 285. ~7 | ~8 [avatar split clause 276,282,278] 286. ~predc(mary) | mary != sK1 | ~room(mary) [subsumption resolution 244,230] 287. ~predc(mary) | mary != sK1 [subsumption resolution 286,229] 289. 9 <=> mary = sK1 [avatar definition] 291. mary != sK1 <- (~9) [avatar component clause 289] 292. ~9 | ~8 [avatar split clause 287,282,289] 293. ~predc(mary) | room(sK1) | ~room(mary) [subsumption resolution 243,230] 294. ~predc(mary) | room(sK1) [subsumption resolution 293,229] 296. 10 <=> room(sK1) [avatar definition] 298. room(sK1) <- (10) [avatar component clause 296] 299. 10 | ~8 [avatar split clause 294,282,296] 300. predc(mary) [resolution 238,239] 304. 8 [avatar split clause 300,282] 308. mary = sK1 | paul = sK1 <- (10) [resolution 231,298] 318. paul = sK1 <- (~9, 10) [subsumption resolution 308,291] 319. $false <- (~7, ~9, 10) [subsumption resolution 318,280] 320. 7 | 9 | ~10 [avatar contradiction clause 319] 321. $false [avatar sat refutation 285,292,299,304,320] % SZS output end Proof for 3345960797004429883704966 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------