Datasets:

unigram

/

FOL-nli

like 1

There is a room. Either “no one in the room creates bespoke furniture pieces from reclaimed wood or does not work on fridays” or “someone in the room neither works on fridays nor has a pet dog” but not both. If “no one outside the room does not collect comic books or collects comic books” then “everyone in the room creates bespoke furniture pieces from reclaimed wood”. Someone in the room participates in citizen science projects related to wildlife monitoring. Only one person in the room collects comic books. Everyone in the room participates in citizen science projects related to wildlife monitoring if they works on fridays and vice versa. Everyone in the room who works on fridays either collects comic books or has a pet dog but not both. If someone participates in citizen science projects related to wildlife monitoring, collects comic books and does not create bespoke furniture pieces from reclaimed wood then he/she has a pet dog.

Everyone in the room collects comic books.

contradiction

(there_is_a_room)& ((~?[X]:(room(X)=>(((does_not_work_on_fridays(X))|(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))<~>(?[X]:(room(X)&(~((works_on_fridays(X))|(has_a_pet_dog(X)))))))& ((~?[X]:(~room(X)=>(((collects_comic_books(X))|(does_not_collect_comic_books(X))))))=>(![X]:(room(X)=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X)))))& ((![X]:(room(X)=>(((reads_mystery_novels(X))|(does_not_have_a_pet_dog(X))))))=>(((?[X]:(room(X)&collects_comic_books(X))))))& ((![X]:(room(X)=>(((collects_comic_books(X))|(does_not_read_mystery_novels(X))))))=>(![X]:(room(X)=>(((does_not_read_mystery_novels(X))=>(collects_classic_novels(X)))))))& (?[X]:(room(X)&(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))& (~![X]:(room(X)=>(((reads_mystery_novels(X))=>(does_not_read_mystery_novels(X))))))& (((?[X]:(room(X)&collects_comic_books(X)))&(![X,Y]:((room(X)&room(Y)&(collects_comic_books(X))&(collects_comic_books(Y)))=>(X=Y)))))& (![X]:(room(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))<=>(works_on_fridays(X))))))& (![X]:(room(X)=>(((works_on_fridays(X))=>(((collects_comic_books(X))<~>(has_a_pet_dog(X))))))))& (![X]:(room(X)=>(is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))& ((![X]:((((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))&(collects_comic_books(X))&(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))=>(has_a_pet_dog(X)))))& (~![X]:(room(X)=>(((collects_classic_novels(X))=>(owns_an_Android_phone(X))))))& (![X]:(room(X)=>(((owns_an_Android_phone(X))=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))

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

% SZS status Unsatisfiable for 6161466551781496718302870 % SZS output start Proof for 6161466551781496718302870 45. ~? [X0] : (room(X0) => (prede(X0) | ~predf(X0))) <~> ? [X0] : (~(preda(X0) | predf(X0)) & room(X0)) [input p1] 49. ? [X0] : (predg(X0) & room(X0)) [input p5] 51. ! [X0,X1] : ((predk(X1) & predk(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predk(X0) & room(X0)) [input p7] 52. ! [X0] : (room(X0) => (predg(X0) <=> predf(X0))) [input p8] 53. ! [X0] : (room(X0) => (predf(X0) => (predk(X0) <~> preda(X0)))) [input p9] 55. ! [X0] : ((~prede(X0) & predk(X0) & predg(X0)) => preda(X0)) [input p11] 58. ! [X0] : (room(X0) => predk(X0)) & there_is_a_room [input hypothesis] 59. ~? [X0] : (room(X0) => (prede(X0) | ~predf(X0))) <~> ? [X1] : (~(preda(X1) | predf(X1)) & room(X1)) [rectify 45] 63. ! [X0,X1] : ((predk(X1) & predk(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predk(X2) & room(X2)) [rectify 51] 69. ! [X0] : (room(X0) => predk(X0)) [pure predicate removal 58] 143. ! [X0] : ((~prede(X0) & predf(X0)) & room(X0)) <~> ? [X1] : ((~preda(X1) & ~predf(X1)) & room(X1)) [ennf transformation 59] 144. ! [X0] : (~prede(X0) & predf(X0) & room(X0)) <~> ? [X1] : (~preda(X1) & ~predf(X1) & room(X1)) [flattening 143] 151. ! [X0,X1] : (X0 = X1 | (~predk(X1) | ~predk(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (predk(X2) & room(X2)) [ennf transformation 63] 152. ! [X0,X1] : (X0 = X1 | ~predk(X1) | ~predk(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (predk(X2) & room(X2)) [flattening 151] 153. ! [X0] : ((predg(X0) <=> predf(X0)) | ~room(X0)) [ennf transformation 52] 154. ! [X0] : (((predk(X0) <~> preda(X0)) | ~predf(X0)) | ~room(X0)) [ennf transformation 53] 155. ! [X0] : ((predk(X0) <~> preda(X0)) | ~predf(X0) | ~room(X0)) [flattening 154] 156. ! [X0] : (preda(X0) | (prede(X0) | ~predk(X0) | ~predg(X0))) [ennf transformation 55] 157. ! [X0] : (preda(X0) | prede(X0) | ~predk(X0) | ~predg(X0)) [flattening 156] 159. ! [X0] : (predk(X0) | ~room(X0)) [ennf transformation 69] 161. (! [X1] : (preda(X1) | predf(X1) | ~room(X1)) | ? [X0] : (prede(X0) | ~predf(X0) | ~room(X0))) & (? [X1] : (~preda(X1) & ~predf(X1) & room(X1)) | ! [X0] : (~prede(X0) & predf(X0) & room(X0))) [nnf transformation 144] 162. (! [X0] : (preda(X0) | predf(X0) | ~room(X0)) | ? [X1] : (prede(X1) | ~predf(X1) | ~room(X1))) & (? [X2] : (~preda(X2) & ~predf(X2) & room(X2)) | ! [X3] : (~prede(X3) & predf(X3) & room(X3))) [rectify 161] 163. ? [X1] : (prede(X1) | ~predf(X1) | ~room(X1)) => (prede(sK0) | ~predf(sK0) | ~room(sK0)) [choice axiom] 164. ? [X2] : (~preda(X2) & ~predf(X2) & room(X2)) => (~preda(sK1) & ~predf(sK1) & room(sK1)) [choice axiom] 165. (! [X0] : (preda(X0) | predf(X0) | ~room(X0)) | (prede(sK0) | ~predf(sK0) | ~room(sK0))) & ((~preda(sK1) & ~predf(sK1) & room(sK1)) | ! [X3] : (~prede(X3) & predf(X3) & room(X3))) [skolemisation 162,164,163] 173. ? [X0] : (predg(X0) & room(X0)) => (predg(sK5) & room(sK5)) [choice axiom] 174. predg(sK5) & room(sK5) [skolemisation 49,173] 177. ? [X2] : (predk(X2) & room(X2)) => (predk(sK7) & room(sK7)) [choice axiom] 178. ! [X0,X1] : (X0 = X1 | ~predk(X1) | ~predk(X0) | ~room(X1) | ~room(X0)) & (predk(sK7) & room(sK7)) [skolemisation 152,177] 179. ! [X0] : (((predg(X0) | ~predf(X0)) & (predf(X0) | ~predg(X0))) | ~room(X0)) [nnf transformation 153] 180. ! [X0] : (((~preda(X0) | ~predk(X0)) & (preda(X0) | predk(X0))) | ~predf(X0) | ~room(X0)) [nnf transformation 155] 265. room(sK1) | ~prede(X3) [cnf transformation 165] 268. ~predf(sK1) | ~prede(X3) [cnf transformation 165] 280. room(sK5) [cnf transformation 174] 281. predg(sK5) [cnf transformation 174] 285. room(sK7) [cnf transformation 178] 286. predk(sK7) [cnf transformation 178] 287. ~predk(X1) | X0 = X1 | ~predk(X0) | ~room(X1) | ~room(X0) [cnf transformation 178] 288. ~predg(X0) | predf(X0) | ~room(X0) [cnf transformation 179] 291. ~predk(X0) | ~preda(X0) | ~predf(X0) | ~room(X0) [cnf transformation 180] 292. ~predg(X0) | prede(X0) | ~predk(X0) | preda(X0) [cnf transformation 157] 294. ~room(X0) | predk(X0) [cnf transformation 159] 312. 5 <=> ! [X3] : ~prede(X3) [avatar definition] 313. ~prede(X3) <- (5) [avatar component clause 312] 328. 9 <=> predf(sK1) [avatar definition] 330. ~predf(sK1) <- (~9) [avatar component clause 328] 331. 5 | ~9 [avatar split clause 268,328,312] 335. 10 <=> room(sK1) [avatar definition] 337. room(sK1) <- (10) [avatar component clause 335] 338. 5 | 10 [avatar split clause 265,335,312] 371. predk(sK5) [resolution 294,280] 375. predf(sK5) | ~room(sK5) [resolution 288,281] 376. predf(sK5) [subsumption resolution 375,280] 392. prede(sK5) | ~predk(sK5) | preda(sK5) [resolution 292,281] 393. ~predk(sK5) | preda(sK5) <- (5) [subsumption resolution 392,313] 400. 18 <=> preda(sK5) [avatar definition] 404. 19 <=> predk(sK5) [avatar definition] 405. predk(sK5) <- (19) [avatar component clause 404] 407. 18 | ~19 | ~5 [avatar split clause 393,312,404,400] 408. 19 [avatar split clause 371,404] 440. ~preda(sK5) | ~predf(sK5) | ~room(sK5) <- (19) [resolution 405,291] 445. ~preda(sK5) | ~room(sK5) <- (19) [subsumption resolution 440,376] 446. ~preda(sK5) <- (19) [subsumption resolution 445,280] 447. ~18 | ~19 [avatar split clause 446,404,400] 489. sK7 = X4 | ~predk(X4) | ~room(sK7) | ~room(X4) [resolution 287,286] 499. sK7 = X4 | ~predk(X4) | ~room(X4) [subsumption resolution 489,285] 500. ~room(X4) | sK7 = X4 [subsumption resolution 499,294] 503. sK1 = sK7 <- (10) [resolution 500,337] 505. sK5 = sK7 [resolution 500,280] 522. sK1 = sK5 <- (10) [forward demodulation 505,503] 525. predf(sK1) <- (10) [backward demodulation 376,522] 530. $false <- (~9, 10) [subsumption resolution 525,330] 531. 9 | ~10 [avatar contradiction clause 530] 545. $false [avatar sat refutation 331,338,407,408,447,531] % SZS output end Proof for 6161466551781496718302870 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Judy is the only person in the room. If 'everyone in the room is not a coffee connoisseur or is not a creative tourist' then 'it is not the case that 'Judy enjoys macrame''. Judy is a client of Leon. Everyone in the room practices tai chi if they is a client of Timothy. Nicole is a sibling of Judy. Everyone in the room does not enjoy macrame or enjoys virtual reality gaming. Not everyone in the room is a coffee connoisseur if they does not enjoy macrame. Judy practices archery. Everyone in the room is a sibling of Virginia. Everyone in the room is not not not not creative only if they practices kickboxing. Someone in the room is a sibling of Leon. Everyone in the room who is a certified yoga instructor teaching classes weekly is a coffee connoisseur. Judy does not enjoy stargazing. Everyone in the room is a sibling of Nathan if they is a coffee connoisseur. Everyone in the room is not an avid mountain climber who has scaled several peaks or is not liked by Nathan. Only one person in the room is not not not not creative. No creative person is funny. Judy is a sibling of Nathan. Everyone in the room is a client of Leon if they knows morse code. No generous person is strong. Judy knows morse code. Leroy is a sibling of Judy. Not everyone in the room who bakes bread at home does not hate Virginia. Everyone in the room is not a coffee connoisseur or is not a creative tourist. It is not the case that 'Judy enjoys macrame'.

Virginia is a sibling of Judy.

entailment

room(judy)&(![X]:(room(X)=>(X='judy')))& ((![X]:(room(X)=>(((~(creative(X)&tourist(X)))|(is_not_a_coffee_connoisseur(X))))))=>(~(enjoys_macrame(judy))))& (client(leon,judy))& (![X]:(room(X)=>(((client(timothy,X))=>(practices_tai_chi(X))))))& (sibling(judy,nicole))& (![X]:(room(X)=>(((enjoys_virtual_reality_gaming(X))|(does_not_enjoy_macrame(X))))))& (~![X]:(room(X)=>(((does_not_enjoy_macrame(X))=>(is_a_coffee_connoisseur(X))))))& (practices_archery(judy))& (![X]:(room(X)=>(sibling(virginia,X))))& (![X]:(room(X)=>(((practices_kickboxing(X))<=(~~~~creative(X))))))& (?[X]:(room(X)&(sibling(leon,X))))& (![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(is_a_coffee_connoisseur(X))))))& (does_not_enjoy_stargazing(judy))& (![X]:(room(X)=>(((is_a_coffee_connoisseur(X))=>(sibling(nathan,X))))))& (![X]:(room(X)=>(((~like(X,nathan))|(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))& (((?[X]:(room(X)&~~~~creative(X)))&(![X,Y]:((room(X)&room(Y)&(~~~~creative(X))&(~~~~creative(Y)))=>(X=Y)))))& (~?[X]:(creative(X)=>funny(X)))& (sibling(nathan,judy))& (![X]:(room(X)=>(((knows_morse_code(X))=>(client(leon,X))))))& (~?[X]:(generous(X)=>strong(X)))& (knows_morse_code(judy))& (sibling(judy,leroy))& (~![X]:(room(X)=>(((bakes_bread_at_home(X))=>(~hate(virginia,X))))))& (![X]:(room(X)=>(((~(creative(X)&tourist(X)))|(is_not_a_coffee_connoisseur(X))))))& (~(enjoys_macrame(judy)))& (enjoys_bird_watching(judy))& (![X]:((room(X)&(X!=judy))=>richer(X,judy)))

room(judy)&(![X]:(room(X)=>(X='judy')))& sibling(judy,virginia)

% SZS status Unsatisfiable for 831116516512565432126576 % SZS output start Proof for 831116516512565432126576 6. ! [X0,X1] : (X0 != X1 => (sibling(X0,X1) <=> sibling(X1,X0))) [input b5] 43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42] 44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0] 52. ! [X0] : (room(X0) => sibling(fred,X0)) [input p8] 71. ~(sibling(mary,fred) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis] 100. ! [X0,X1] : ((sibling(X0,X1) <=> sibling(X1,X0)) | X0 = X1) [ennf transformation 6] 167. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44] 169. ! [X0] : (sibling(fred,X0) | ~room(X0)) [ennf transformation 52] 176. ~sibling(mary,fred) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 71] 177. ! [X0,X1] : (((sibling(X0,X1) | ~sibling(X1,X0)) & (sibling(X1,X0) | ~sibling(X0,X1))) | X0 = X1) [nnf transformation 100] 186. ? [X0] : (mary != X0 & room(X0)) => (mary != sK4 & room(sK4)) [choice axiom] 187. ~sibling(mary,fred) | (mary != sK4 & room(sK4)) | ~room(mary) [skolemisation 176,186] 189. ~sibling(X1,X0) | sibling(X0,X1) | X0 = X1 [cnf transformation 177] 238. mary != fred [cnf transformation 43] 268. room(mary) [cnf transformation 167] 269. ~room(X0) | mary = X0 [cnf transformation 167] 272. sibling(fred,X0) | ~room(X0) [cnf transformation 169] 283. ~sibling(mary,fred) | room(sK4) | ~room(mary) [cnf transformation 187] 284. ~sibling(mary,fred) | mary != sK4 | ~room(mary) [cnf transformation 187] 285. ~sibling(mary,fred) | mary != sK4 [subsumption resolution 284,268] 287. 1 <=> mary = sK4 [avatar definition] 289. mary != sK4 <- (~1) [avatar component clause 287] 291. 2 <=> sibling(mary,fred) [avatar definition] 293. ~sibling(mary,fred) <- (~2) [avatar component clause 291] 294. ~1 | ~2 [avatar split clause 285,291,287] 295. ~sibling(mary,fred) | room(sK4) [subsumption resolution 283,268] 297. 3 <=> room(sK4) [avatar definition] 299. room(sK4) <- (3) [avatar component clause 297] 300. 3 | ~2 [avatar split clause 295,291,297] 314. sibling(X0,fred) | fred = X0 | ~room(X0) [resolution 189,272] 325. mary = fred | ~room(mary) <- (~2) [resolution 314,293] 328. ~room(mary) <- (~2) [subsumption resolution 325,238] 329. $false <- (~2) [subsumption resolution 328,268] 330. 2 [avatar contradiction clause 329] 331. mary = sK4 <- (3) [resolution 299,269] 332. $false <- (~1, 3) [subsumption resolution 331,289] 333. 1 | ~3 [avatar contradiction clause 332] 334. $false [avatar sat refutation 294,300,330,333] % SZS output end Proof for 831116516512565432126576 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.036 s % ------------------------------ % ------------------------------

There is a room. If “everyone outside the room plays the drums or does not collect rare and antique scientific instruments” then “everyone in the room plays the drums if they collects rare and antique scientific instruments”. If “everyone in the room collects vintage vinyl records or does not participate in long-distance cycling events across the country” then “everyone in the room watches fantasy movies if they plays the drums”. If “everyone in the room plays the drums or does not play the drums” then “everyone in the room watches fantasy movies if they plays the drums and vice versa”. “Everyone in the room collects vintage vinyl records or does not participate in long-distance cycling events across the country” if “everyone in the room collects vintage vinyl records or does not watche fantasy movies” and vice versa. Everyone in the room who watches fantasy movies collects vintage vinyl records. Not everyone outside the room who collects vintage vinyl records participates in long-distance cycling events across the country. Everyone in the room who participates in long-distance cycling events across the country plays the drums. Everyone in the room who collects rare and antique scientific instruments collects vintage vinyl records. More than one person outside the room neither plays the drums nor collects vintage vinyl records. Everyone in the room who collects rare and antique scientific instruments watches fantasy movies. Not everyone anywhere who collects vintage vinyl records plays the drums. Only one person in the room plays the drums. Everyone anywhere who plays the drums watches fantasy movies.

Everyone outside the room plays the drums.

contradiction

(there_is_a_room)& ((![X]:(~room(X)=>(((does_not_collect_rare_and_antique_scientific_instruments(X))|(plays_the_drums(X))))))=>(![X]:(room(X)=>(((collects_rare_and_antique_scientific_instruments(X))=>(plays_the_drums(X)))))))& ((![X]:(room(X)=>(((does_not_participate_in_long-distance_cycling_events_across_the_country(X))|(collects_vintage_vinyl_records(X))))))=>(![X]:(room(X)=>(((plays_the_drums(X))=>(watches_fantasy_movies(X)))))))& ((![X]:(room(X)=>(((does_not_play_the_drums(X))|(plays_the_drums(X))))))=>(![X]:(room(X)=>(((watches_fantasy_movies(X))<=>(plays_the_drums(X)))))))& ((![X]:(room(X)=>(((does_not_watche_fantasy_movies(X))|(collects_vintage_vinyl_records(X))))))<=>(![X]:(room(X)=>(((does_not_participate_in_long-distance_cycling_events_across_the_country(X))|(collects_vintage_vinyl_records(X)))))))& (![X]:(room(X)=>(((watches_fantasy_movies(X))=>(collects_vintage_vinyl_records(X))))))& (~![X]:(~room(X)=>(((collects_vintage_vinyl_records(X))=>(participates_in_long-distance_cycling_events_across_the_country(X))))))& (![X]:(room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))=>(plays_the_drums(X))))))& (![X]:(room(X)=>(((collects_rare_and_antique_scientific_instruments(X))=>(collects_vintage_vinyl_records(X))))))& ((?[X,Y]:(~room(X)&~room(Y)&(~((plays_the_drums(X))|(collects_vintage_vinyl_records(X)))&~((plays_the_drums(Y))|(collects_vintage_vinyl_records(Y))))&(X!=Y))))& (![X]:(room(X)=>(((collects_rare_and_antique_scientific_instruments(X))=>(watches_fantasy_movies(X))))))& (~![X]:(anywhere(X)=>(((collects_vintage_vinyl_records(X))=>(plays_the_drums(X))))))& (((?[X]:(room(X)&plays_the_drums(X)))&(![X,Y]:((room(X)&room(Y)&(plays_the_drums(X))&(plays_the_drums(Y)))=>(X=Y)))))& (![X]:(anywhere(X)=>(((plays_the_drums(X))=>(watches_fantasy_movies(X))))))& (![X]:(room(X)=>(((watches_fantasy_movies(X))=>(~((participates_in_long-distance_cycling_events_across_the_country(X))|(creates_large-scale_murals_for_public_art_installations(X))))))))& (![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))=>(watches_fantasy_movies(X))))))& (![X]:(room(X)=>(((((plays_the_drums(X))|(collects_rare_and_antique_scientific_instruments(X))))=>(collects_rare_and_antique_scientific_instruments(X))))))

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

% SZS status Unsatisfiable for 1268352406033281017819033 % SZS output start Proof for 1268352406033281017819033 53. ? [X0,X1] : (X0 != X1 & ~(predd(X1) | predc(X1)) & ~(predd(X0) | predc(X0)) & ~room(X1) & ~room(X0)) [input p9] 61. ! [X0] : (~room(X0) => predc(X0)) & there_is_a_room [input hypothesis] 70. ! [X0] : (~room(X0) => predc(X0)) [pure predicate removal 61] 158. ? [X0,X1] : (X0 != X1 & (~predd(X1) & ~predc(X1)) & (~predd(X0) & ~predc(X0)) & ~room(X1) & ~room(X0)) [ennf transformation 53] 159. ? [X0,X1] : (X0 != X1 & ~predd(X1) & ~predc(X1) & ~predd(X0) & ~predc(X0) & ~room(X1) & ~room(X0)) [flattening 158] 172. ! [X0] : (predc(X0) | room(X0)) [ennf transformation 70] 191. ? [X0,X1] : (X0 != X1 & ~predd(X1) & ~predc(X1) & ~predd(X0) & ~predc(X0) & ~room(X1) & ~room(X0)) => (sK6 != sK7 & ~predd(sK7) & ~predc(sK7) & ~predd(sK6) & ~predc(sK6) & ~room(sK7) & ~room(sK6)) [choice axiom] 192. sK6 != sK7 & ~predd(sK7) & ~predc(sK7) & ~predd(sK6) & ~predc(sK6) & ~room(sK7) & ~room(sK6) [skolemisation 159,191] 302. ~room(sK6) [cnf transformation 192] 304. ~predc(sK6) [cnf transformation 192] 320. predc(X0) | room(X0) [cnf transformation 172] 414. room(sK6) [resolution 320,304] 419. $false [subsumption resolution 414,302] % SZS output end Proof for 1268352406033281017819033 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Venus, Janice are the only persons in the room. “Everyone in the room does not play the violin” if “no one in the room does not create augmented reality experiences for mobile applications or does not bake bread at home or both” and vice versa. “Everyone in the room is not a certified scuba diver with advanced underwater photography skills” if “everyone anywhere is not an expert in identifying and foraging wild edible plants or does not create augmented reality experiences for mobile applications or both”. If “everyone in the room is not a professional photographer specializing in portrait photography” then “not everyone outside the room either does not enjoy watercolor painting or is not a certified scuba diver with advanced underwater photography skills but not both” otherwise “if someone either does not regularly goes on multi-day backpacking trips in national parks or does not practice yoga but not both then he/she either does not practice yoga or does not create augmented reality experiences for mobile applications but not both and vice versa”. If “everyone in the room does not enjoy origami” then “everyone in the room is not a certified scuba diver with advanced underwater photography skills or does not play the violin or both” otherwise “everyone in the room does not create bespoke furniture pieces from reclaimed wood”. Not everyone in the room does not create bespoke furniture pieces from reclaimed wood. If someone does not practice digital art then he/she does not create bespoke furniture pieces from reclaimed wood and vice versa. Everyone outside the room is not a tea enthusiast or is not a cybersecurity expert or both. If someone is not a tea enthusiast then he/she does not enjoy origami. Venus dreamt that “everyone anywhere either does not practice digital art or is not a professional photographer specializing in portrait photography but not both”. If someone does not practice digital art, is not a tea enthusiast or does not create bespoke furniture pieces from reclaimed wood then he/she does not create augmented reality experiences for mobile applications and vice versa. Everyone in the room does not practice yoga. Everyone in the room does not bake bread at home or does not enjoy watercolor painting or both. Everyone in the room either is not an expert in identifying and foraging wild edible plants or does not enjoy watercolor painting but not both.

Venus enjoys origami.

contradiction

room(venus)&room(janice)&(![X]:(room(X)=>(X='venus'|X='janice')))& ((~?[X]:(room(X)=>(((does_not_create_augmented_reality_experiences_for_mobile_applications(X))|(does_not_bake_bread_at_home(X))))))<=>(![X]:(room(X)=>(does_not_play_the_violin(X)))))& ((![X]:(anywhere(X)=>(((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(does_not_create_augmented_reality_experiences_for_mobile_applications(X))))))=>(![X]:(room(X)=>(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))))& (((![X]:(room(X)=>(is_not_a_professional_photographer_specializing_in_portrait_photography(X))))=>(~![X]:(~room(X)=>(((does_not_enjoy_watercolor_painting(X))<~>(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))))))&((~(![X]:(room(X)=>(is_not_a_professional_photographer_specializing_in_portrait_photography(X)))))=>((![X]:((((does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))<~>(does_not_practice_yoga(X))))<=>(((does_not_practice_yoga(X))<~>(does_not_create_augmented_reality_experiences_for_mobile_applications(X)))))))))& (((![X]:(room(X)=>(does_not_enjoy_origami(X))))=>(![X]:(room(X)=>(((is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))|(does_not_play_the_violin(X)))))))&((~(![X]:(room(X)=>(does_not_enjoy_origami(X)))))=>(![X]:(room(X)=>(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))))& (~![X]:(room(X)=>(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))& ((![X]:((does_not_practice_digital_art(X))<=>(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X)))))& (![X]:(~room(X)=>(((is_not_a_tea_enthusiast(X))|(is_not_a_cybersecurity_expert(X))))))& ((![X]:((is_not_a_tea_enthusiast(X))=>(does_not_enjoy_origami(X)))))& ((venus_dream=>(![X]:(anywhere(X)=>(((does_not_practice_digital_art(X))<~>(is_not_a_professional_photographer_specializing_in_portrait_photography(X))))))))& ((![X]:((((does_not_practice_digital_art(X))|(is_not_a_tea_enthusiast(X))|(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))<=>(does_not_create_augmented_reality_experiences_for_mobile_applications(X)))))& (![X]:(room(X)=>(does_not_practice_yoga(X))))& (![X]:(room(X)=>(((does_not_bake_bread_at_home(X))|(does_not_enjoy_watercolor_painting(X))))))& (![X]:(room(X)=>(((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))<~>(does_not_enjoy_watercolor_painting(X))))))

room(venus)&room(janice)&(![X]:(room(X)=>(X='venus'|X='janice')))& enjoys_origami(venus)

% SZS status Unsatisfiable for 8263463103815564083309355 % SZS output start Proof for 8263463103815564083309355 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 48. (~! [X0] : (room(X0) => ~predo(X0)) => ! [X0] : (room(X0) => ~predn(X0))) & (! [X0] : (room(X0) => ~predo(X0)) => ! [X0] : (room(X0) => (~preda(X0) | ~predd(X0)))) [input p4] 49. ~! [X0] : (room(X0) => ~predn(X0)) [input p5] 58. predo(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis] 62. (~! [X0] : (room(X0) => ~predo(X0)) => ! [X1] : (room(X1) => ~predn(X1))) & (! [X2] : (room(X2) => ~predo(X2)) => ! [X3] : (room(X3) => (~preda(X3) | ~predd(X3)))) [rectify 48] 138. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 139. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 138] 144. (! [X1] : (~predn(X1) | ~room(X1)) | ! [X0] : (~predo(X0) | ~room(X0))) & (! [X3] : ((~preda(X3) | ~predd(X3)) | ~room(X3)) | ? [X2] : (predo(X2) & room(X2))) [ennf transformation 62] 145. (! [X1] : (~predn(X1) | ~room(X1)) | ! [X0] : (~predo(X0) | ~room(X0))) & (! [X3] : (~preda(X3) | ~predd(X3) | ~room(X3)) | ? [X2] : (predo(X2) & room(X2))) [flattening 144] 146. ? [X0] : (predn(X0) & room(X0)) [ennf transformation 49] 152. predo(mary) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 58] 153. predo(mary) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 152] 169. (! [X0] : (~predn(X0) | ~room(X0)) | ! [X1] : (~predo(X1) | ~room(X1))) & (! [X2] : (~preda(X2) | ~predd(X2) | ~room(X2)) | ? [X3] : (predo(X3) & room(X3))) [rectify 145] 170. ? [X3] : (predo(X3) & room(X3)) => (predo(sK5) & room(sK5)) [choice axiom] 171. (! [X0] : (~predn(X0) | ~room(X0)) | ! [X1] : (~predo(X1) | ~room(X1))) & (! [X2] : (~preda(X2) | ~predd(X2) | ~room(X2)) | (predo(sK5) & room(sK5))) [skolemisation 169,170] 172. ? [X0] : (predn(X0) & room(X0)) => (predn(sK6) & room(sK6)) [choice axiom] 173. predn(sK6) & room(sK6) [skolemisation 146,172] 258. room(mary) [cnf transformation 139] 286. ~predn(X0) | ~room(X0) | ~predo(X1) | ~room(X1) [cnf transformation 171] 287. room(sK6) [cnf transformation 173] 288. predn(sK6) [cnf transformation 173] 303. predo(mary) [cnf transformation 153] 406. 23 <=> ! [X1] : (~predo(X1) | ~room(X1)) [avatar definition] 407. ~predo(X1) | ~room(X1) <- (23) [avatar component clause 406] 409. 24 <=> ! [X0] : (~predn(X0) | ~room(X0)) [avatar definition] 410. ~predn(X0) | ~room(X0) <- (24) [avatar component clause 409] 411. 23 | 24 [avatar split clause 286,409,406] 438. ~room(mary) <- (23) [resolution 407,303] 439. $false <- (23) [subsumption resolution 438,258] 440. ~23 [avatar contradiction clause 439] 454. ~room(sK6) <- (24) [resolution 410,288] 456. $false <- (24) [subsumption resolution 454,287] 457. ~24 [avatar contradiction clause 456] 458. $false [avatar sat refutation 411,440,457] % SZS output end Proof for 8263463103815564083309355 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

If “everyone in the room does not practice zumba and is not a client of Meta” then “everyone in the room does not create YouTube content” otherwise “if someone is not a dedicated advocate for digital privacy and encryption and does not have completed a triathlon then he/she neither does not host a YouTube channel dedicated to art tutorials nor does not collect modern art”. No one in the room either is not an enthusiastic bird watcher who travels for rare sightings or does not have completed a triathlon but not both. Everyone in the room is not an enthusiastic bird watcher who travels for rare sightings. At least one person in the room is not a dedicated advocate for digital privacy and encryption. Someone in the room neither does not collect comic books nor does not create YouTube content. Everyone in the room does not practice pilates.

Everyone in the room does not collect modern art or practices pilates.

contradiction

(there_is_a_room)& (((![X]:(room(X)=>(((is_not_right-handed(X))&(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))=>(![X]:(room(X)=>(is_not_right-handed(X)))))&((~(![X]:(room(X)=>(((is_not_right-handed(X))&(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X)))))))=>(![X]:(room(X)=>(((does_not_practice_zumba(X))|(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))|(is_not_a_client_of_Meta(X))))))))& ((![X]:(room(X)=>(((does_not_own_a_3D_printer(X))<~>(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))<~>(![X]:(room(X)=>(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X)))))& ((?[X]:(~room(X)&(does_not_practice_urban_gardening(X))))=>(![X]:(room(X)=>(does_not_know_morse_code(X)))))& (((![X]:(room(X)=>(((does_not_practice_zumba(X))&(is_not_a_client_of_Meta(X))))))=>(![X]:(room(X)=>(does_not_create_YouTube_content(X)))))&((~(![X]:(room(X)=>(((does_not_practice_zumba(X))&(is_not_a_client_of_Meta(X)))))))=>((![X]:((((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))&(does_not_have_completed_a_triathlon(X))))=>(~((does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))|(does_not_collect_modern_art(X)))))))))& (?[X]:(room(X)&(((does_not_create_YouTube_content(X))<~>(is_not_a_client_of_Meta(X))))))& ((![X]:((does_not_practice_urban_gardening(X))=>(does_not_know_morse_code(X)))))& (~?[X]:(room(X)=>(((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))<~>(does_not_have_completed_a_triathlon(X))))))& (![X]:(room(X)=>(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))& (![X]:(~room(X)=>(does_not_collect_modern_art(X))))& (((?[X]:(room(X)&is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X)))))& (![X]:(room(X)=>(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))))& (~?[X]:(anywhere(X)=>(((does_not_practice_zumba(X))<~>(does_not_know_morse_code(X))))))& ((![X]:((does_not_have_a_tattoo(X))<=>(does_not_play_video_games(X)))))& (![X]:(room(X)=>(((is_not_a_cybersecurity_expert(X))<~>(does_not_collect_modern_art(X))))))& (?[X]:(room(X)&(~((does_not_collect_comic_books(X))|(does_not_create_YouTube_content(X))))))& (![X]:(room(X)=>(does_not_practice_pilates(X))))& (?[X]:(room(X)&(is_not_right-handed(X))))& (![X]:(room(X)=>(is_not_a_dedicated_volunteer_for_local_community_service_projects(X))))& (![X]:(room(X)=>(does_not_have_a_tattoo(X))))

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

% SZS status Unsatisfiable for 3745235541861482545306448 % SZS output start Proof for 3745235541861482545306448 48. (~! [X0] : (room(X0) => (~predu(X0) & ~predx(X0))) => ! [X0] : ((~prede(X0) & ~preds(X0)) => ~(~predd(X0) | ~predg(X0)))) & (! [X0] : (room(X0) => (~predu(X0) & ~predx(X0))) => ! [X0] : (room(X0) => ~predm(X0))) [input p4] 51. ~? [X0] : (room(X0) => (~preda(X0) <~> ~prede(X0))) [input p7] 52. ! [X0] : (room(X0) => ~preda(X0)) [input p8] 54. ? [X0] : (~preds(X0) & room(X0)) [input p10] 59. ? [X0] : (~(~predm(X0) | ~predi(X0)) & room(X0)) [input p15] 60. ! [X0] : (room(X0) => ~predj(X0)) [input p16] 64. ! [X0] : (room(X0) => (~predd(X0) | predj(X0))) & there_is_a_room [input hypothesis] 68. (~! [X0] : (room(X0) => (~predu(X0) & ~predx(X0))) => ! [X1] : ((~prede(X1) & ~preds(X1)) => ~(~predd(X1) | ~predg(X1)))) & (! [X2] : (room(X2) => (~predu(X2) & ~predx(X2))) => ! [X3] : (room(X3) => ~predm(X3))) [rectify 48] 73. ? [X0] : (~~predm(X0) & room(X0)) [pure predicate removal 59] 74. (~! [X0] : (room(X0) => (~predu(X0) & ~predx(X0))) => ! [X1] : ((~prede(X1) & ~preds(X1)) => ~~predd(X1))) & (! [X2] : (room(X2) => (~predu(X2) & ~predx(X2))) => ! [X3] : (room(X3) => ~predm(X3))) [pure predicate removal 68] 78. ! [X0] : (room(X0) => (~predd(X0) | predj(X0))) [pure predicate removal 64] 155. (! [X1] : (predd(X1) | (prede(X1) | preds(X1))) | ! [X0] : ((~predu(X0) & ~predx(X0)) | ~room(X0))) & (! [X3] : (~predm(X3) | ~room(X3)) | ? [X2] : ((predu(X2) | predx(X2)) & room(X2))) [ennf transformation 74] 156. (! [X1] : (predd(X1) | prede(X1) | preds(X1)) | ! [X0] : ((~predu(X0) & ~predx(X0)) | ~room(X0))) & (! [X3] : (~predm(X3) | ~room(X3)) | ? [X2] : ((predu(X2) | predx(X2)) & room(X2))) [flattening 155] 157. ! [X0] : ((~preda(X0) <=> ~prede(X0)) & room(X0)) [ennf transformation 51] 158. ! [X0] : (~preda(X0) | ~room(X0)) [ennf transformation 52] 163. ? [X0] : (predm(X0) & room(X0)) [ennf transformation 73] 164. ! [X0] : (~predj(X0) | ~room(X0)) [ennf transformation 60] 165. ! [X0] : ((~predd(X0) | predj(X0)) | ~room(X0)) [ennf transformation 78] 166. ! [X0] : (~predd(X0) | predj(X0) | ~room(X0)) [flattening 165] 177. (! [X0] : (predd(X0) | prede(X0) | preds(X0)) | ! [X1] : ((~predu(X1) & ~predx(X1)) | ~room(X1))) & (! [X2] : (~predm(X2) | ~room(X2)) | ? [X3] : ((predu(X3) | predx(X3)) & room(X3))) [rectify 156] 178. ? [X3] : ((predu(X3) | predx(X3)) & room(X3)) => ((predu(sK3) | predx(sK3)) & room(sK3)) [choice axiom] 179. (! [X0] : (predd(X0) | prede(X0) | preds(X0)) | ! [X1] : ((~predu(X1) & ~predx(X1)) | ~room(X1))) & (! [X2] : (~predm(X2) | ~room(X2)) | ((predu(sK3) | predx(sK3)) & room(sK3))) [skolemisation 177,178] 184. ! [X0] : (((~preda(X0) | prede(X0)) & (~prede(X0) | preda(X0))) & room(X0)) [nnf transformation 157] 185. ! [X0] : ((~preda(X0) | prede(X0)) & (~prede(X0) | preda(X0)) & room(X0)) [flattening 184] 186. ? [X0] : (~preds(X0) & room(X0)) => (~preds(sK5) & room(sK5)) [choice axiom] 187. ~preds(sK5) & room(sK5) [skolemisation 54,186] 190. ? [X0] : (predm(X0) & room(X0)) => (predm(sK6) & room(sK6)) [choice axiom] 191. predm(sK6) & room(sK6) [skolemisation 163,190] 287. ~predm(X2) | ~room(X2) | predu(sK3) | predx(sK3) [cnf transformation 179] 288. predd(X0) | prede(X0) | preds(X0) | ~predx(X1) | ~room(X1) [cnf transformation 179] 289. predd(X0) | prede(X0) | preds(X0) | ~predu(X1) | ~room(X1) [cnf transformation 179] 293. room(X0) [cnf transformation 185] 294. ~prede(X0) | preda(X0) [cnf transformation 185] 296. ~preda(X0) | ~room(X0) [cnf transformation 158] 299. ~preds(sK5) [cnf transformation 187] 306. predm(sK6) [cnf transformation 191] 307. ~predj(X0) | ~room(X0) [cnf transformation 164] 310. ~predd(X0) | predj(X0) | ~room(X0) [cnf transformation 166] 374. 15 <=> ! [X1] : (~predu(X1) | ~room(X1)) [avatar definition] 375. ~predu(X1) | ~room(X1) <- (15) [avatar component clause 374] 377. 16 <=> ! [X0] : (predd(X0) | preds(X0) | prede(X0)) [avatar definition] 378. predd(X0) | preds(X0) | prede(X0) <- (16) [avatar component clause 377] 379. 15 | 16 [avatar split clause 289,377,374] 381. 17 <=> ! [X1] : (~predx(X1) | ~room(X1)) [avatar definition] 382. ~predx(X1) | ~room(X1) <- (17) [avatar component clause 381] 383. 17 | 16 [avatar split clause 288,377,381] 385. 18 <=> predx(sK3) [avatar definition] 387. predx(sK3) <- (18) [avatar component clause 385] 389. 19 <=> predu(sK3) [avatar definition] 391. predu(sK3) <- (19) [avatar component clause 389] 393. 20 <=> ! [X2] : (~predm(X2) | ~room(X2)) [avatar definition] 394. ~predm(X2) | ~room(X2) <- (20) [avatar component clause 393] 395. 18 | 19 | 20 [avatar split clause 287,393,389,385] 411. ~preda(X0) [subsumption resolution 296,293] 415. ~predj(X0) [subsumption resolution 307,293] 416. ~predd(X0) | ~room(X0) [subsumption resolution 310,415] 417. ~predd(X0) [subsumption resolution 416,293] 418. ~predm(X2) <- (20) [subsumption resolution 394,293] 419. prede(X0) | preds(X0) <- (16) [subsumption resolution 378,417] 422. $false <- (20) [resolution 418,306] 425. ~20 [avatar contradiction clause 422] 429. preds(X0) | preda(X0) <- (16) [resolution 419,294] 430. preds(X0) <- (16) [subsumption resolution 429,411] 431. $false <- (16) [resolution 430,299] 432. ~16 [avatar contradiction clause 431] 433. ~predx(X1) <- (17) [subsumption resolution 382,293] 434. ~predu(X1) <- (15) [subsumption resolution 375,293] 435. $false <- (17, 18) [resolution 433,387] 436. ~17 | ~18 [avatar contradiction clause 435] 437. $false <- (15, 19) [subsumption resolution 391,434] 438. ~15 | ~19 [avatar contradiction clause 437] 439. $false [avatar sat refutation 379,383,395,425,432,436,438] % SZS output end Proof for 3745235541861482545306448 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Tabatha, Alene, Ramona are the only persons in the room. “Tabatha either collects antique jewelry or practices tai chi but not both” if “Tabatha practices tai chi”. If “Tabatha plays the drums” then “Alene either has completed a triathlon or designs and sews custom cosplay costumes for conventions but not both”. Tabatha plays the drums and is a Linux enthusiast. Alene owns a smart tv. Someone in the room either is a Linux enthusiast or enjoys camping and organizing outdoor survival workshops but not both. Alene either has completed a triathlon or designs and sews custom cosplay costumes for conventions but not both. Alene streams on Twitch. Tabatha is a Linux enthusiast. Alene collects rare minerals. Alene practices tai chi. Tabatha develops open-source software projects in their free time. Tabatha is an avid mountain climber who has scaled several peaks. Tabatha creates bespoke furniture pieces from reclaimed wood. Tabatha either streams on Twitch or collects rare minerals but not both. Tabatha plays video games and is a client of LVMH. At least one person in the room creates bespoke furniture pieces from reclaimed wood. More than one person in the room plays the drums or creates YouTube content or both. At least one person in the room owns a smart tv and enjoys origami. Only one person in the room develops open-source software projects in their free time. Tabatha collects antique jewelry. Tabatha designs and sews custom cosplay costumes for conventions. Tabatha is a client of LVMH. Tabatha participates in citizen science projects related to wildlife monitoring. At least one person in the room plays video games, practices tai chi or enjoys making ceramics. Tabatha is a cybersecurity expert. Alene is a cybersecurity expert. More than one person in the room has completed a triathlon.

Tabatha is a client of LVMH.

entailment

room(tabatha)&room(alene)&room(ramona)&(![X]:(room(X)=>(X='tabatha'|X='alene'|X='ramona')))& ((practices_tai_chi(tabatha))=>(((collects_antique_jewelry(tabatha))<~>(practices_tai_chi(tabatha)))))& ((plays_the_drums(tabatha))=>(((has_completed_a_triathlon(alene))<~>(designs_and_sews_custom_cosplay_costumes_for_conventions(alene)))))& (((plays_the_drums(tabatha))&(is_a_Linux_enthusiast(tabatha))))& (owns_a_smart_tv(alene))& (?[X]:(room(X)&(((is_a_Linux_enthusiast(X))<~>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))& (((has_completed_a_triathlon(alene))<~>(designs_and_sews_custom_cosplay_costumes_for_conventions(alene))))& (streams_on_Twitch(alene))& (is_a_Linux_enthusiast(tabatha))& (collects_rare_minerals(alene))& (practices_tai_chi(alene))& (develops_open-source_software_projects_in_their_free_time(tabatha))& (is_an_avid_mountain_climber_who_has_scaled_several_peaks(tabatha))& (creates_bespoke_furniture_pieces_from_reclaimed_wood(tabatha))& (((streams_on_Twitch(tabatha))<~>(collects_rare_minerals(tabatha))))& (((plays_video_games(tabatha))&(is_a_client_of_LVMH(tabatha))))& (((?[X]:(room(X)&creates_bespoke_furniture_pieces_from_reclaimed_wood(X)))))& ((?[X,Y]:(room(X)&room(Y)&(((plays_the_drums(X))|(creates_YouTube_content(X)))&((plays_the_drums(Y))|(creates_YouTube_content(Y))))&(X!=Y))))& (((?[X]:(room(X)&((owns_a_smart_tv(X))&(enjoys_origami(X)))))))& (((?[X]:(room(X)&develops_open-source_software_projects_in_their_free_time(X)))&(![X,Y]:((room(X)&room(Y)&(develops_open-source_software_projects_in_their_free_time(X))&(develops_open-source_software_projects_in_their_free_time(Y)))=>(X=Y)))))& (collects_antique_jewelry(tabatha))& (designs_and_sews_custom_cosplay_costumes_for_conventions(tabatha))& (is_a_client_of_LVMH(tabatha))& (participates_in_citizen_science_projects_related_to_wildlife_monitoring(tabatha))& (((?[X]:(room(X)&((plays_video_games(X))|(practices_tai_chi(X))|(enjoys_making_ceramics(X)))))))& (is_a_cybersecurity_expert(tabatha))& (is_a_cybersecurity_expert(alene))& ((?[X,Y]:(room(X)&room(Y)&(has_completed_a_triathlon(X)&has_completed_a_triathlon(Y))&(X!=Y))))& (enjoys_origami(alene))

room(tabatha)&room(alene)&room(ramona)&(![X]:(room(X)=>(X='tabatha'|X='alene'|X='ramona')))& is_a_client_of_LVMH(tabatha)

% SZS status Unsatisfiable for 7612163299534762987352966 % SZS output start Proof for 7612163299534762987352966 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 59. predh(mary) & predd(mary) [input p15] 73. ~(predh(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis] 82. predh(mary) [pure predicate removal 59] 160. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 161. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 160] 166. ~predh(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 73] 167. ~predh(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 166] 189. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK9 & paul != sK9 & mary != sK9 & room(sK9)) [choice axiom] 190. ~predh(mary) | (fred != sK9 & paul != sK9 & mary != sK9 & room(sK9)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 167,189] 271. room(mary) [cnf transformation 161] 272. room(paul) [cnf transformation 161] 273. room(fred) [cnf transformation 161] 274. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 161] 293. predh(mary) [cnf transformation 82] 311. ~predh(mary) | room(sK9) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 190] 312. ~predh(mary) | mary != sK9 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 190] 313. ~predh(mary) | paul != sK9 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 190] 314. ~predh(mary) | fred != sK9 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 190] 363. fred != sK9 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 314,293] 364. fred != sK9 | ~room(paul) | ~room(mary) [subsumption resolution 363,273] 365. fred != sK9 | ~room(mary) [subsumption resolution 364,272] 366. fred != sK9 [subsumption resolution 365,271] 367. paul != sK9 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 313,293] 368. paul != sK9 | ~room(paul) | ~room(mary) [subsumption resolution 367,273] 369. paul != sK9 | ~room(mary) [subsumption resolution 368,272] 370. paul != sK9 [subsumption resolution 369,271] 371. mary != sK9 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 312,293] 372. mary != sK9 | ~room(paul) | ~room(mary) [subsumption resolution 371,273] 373. mary != sK9 | ~room(mary) [subsumption resolution 372,272] 374. mary != sK9 [subsumption resolution 373,271] 375. room(sK9) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 311,293] 376. room(sK9) | ~room(paul) | ~room(mary) [subsumption resolution 375,273] 377. room(sK9) | ~room(mary) [subsumption resolution 376,272] 378. room(sK9) [subsumption resolution 377,271] 433. paul = sK9 | mary = sK9 | fred = sK9 [resolution 274,378] 551. mary = sK9 | fred = sK9 [subsumption resolution 433,370] 552. fred = sK9 [subsumption resolution 551,374] 553. $false [subsumption resolution 552,366] % SZS output end Proof for 7612163299534762987352966 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.020 s % ------------------------------ % ------------------------------

Jane, Janet, Mary, Carley, Alice are the only persons in the room. “It is true that “Jane is the richest outside the room”” unless “Janet hosts regular workshops on creative writing”. “More than one person in the room enjoys making ceramics” unless ““A book can be opened only at midnight.” and “A pen exists that only writes secrets.” and “A tower leans significantly but never falls.””. If “Jane is a tea enthusiast” then “Janet is not a old person, streams on Twitch and is not hated by Janet”. If “Janet is not a old person, streams on Twitch and is not hated by Janet” then “Alice composes and performs experimental electronic music, is a certified scuba diver with advanced underwater photography skills and streams on Twitch”. If “Janet and Carley like each other” then “Alice collects classic novels” otherwise “no strong person is happy”. “Alice is the least young outside the room” unless “Mary and Carley are respectively brave and creative”.

Mary enjoys macrame.

entailment

room(jane)&room(janet)&room(mary)&room(carley)&room(alice)&(![X]:(room(X)=>(X='jane'|X='janet'|X='mary'|X='carley'|X='alice')))& (~(hosts_regular_workshops_on_creative_writing(janet))=>(![X]:((~room(X)&(X!=jane))=>richer(X,jane))))& (~(((A_book_can_be_opened_only_at_midnight.)&(A_pen_exists_that_only_writes_secrets.)&(A_tower_leans_significantly_but_never_falls.)))=>((?[X,Y]:(room(X)&room(Y)&(enjoys_making_ceramics(X)&enjoys_making_ceramics(Y))&(X!=Y)))))& (((is_a_tea_enthusiast(jane))=>(((~(old(janet)&person(janet)))&(streams_on_Twitch(janet))&(~hate(janet,janet)))))& ((((~(old(janet)&person(janet)))&(streams_on_Twitch(janet))&(~hate(janet,janet))))=>(((composes_and_performs_experimental_electronic_music(alice))&(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(alice))&(streams_on_Twitch(alice))))))& ((((like(janet,carley) & like(carley,janet)))=>(collects_classic_novels(alice)))&((~((like(janet,carley) & like(carley,janet))))=>(~?[X]:(strong(X)=>happy(X)))))& (~((brave(mary))&(creative(carley)))=>(![X]:((~room(X)&(X!=alice))=>younger(alice,X))))& (~(((A_tower_does_not_lean_significantly_without_falling.)|(A_tower_leans_significantly_but_never_falls.)))=>(is_a_tea_enthusiast(jane)))& (~hate(alice,darlene))& (hosts_regular_game_nights_featuring_complex_strategy_games(carley))& ((?[X,Y]:(room(X)&room(Y)&(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))&(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))&(enjoys_macrame(X)))&((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(Y))&(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(Y))&(enjoys_macrame(Y))))&(X!=Y))))& (((enjoys_macrame(mary))&(~like(mary,darlene))))& ((writes_and_illustrates_their_own_graphic_novels(mary))&(collects_classic_novels(mary)))& (collects_classic_novels(carley))& (((?[X]:(~room(X)&uses_contact_lenses(X)))&(![X,Y]:((~room(X)&~room(Y)&(uses_contact_lenses(X))&(uses_contact_lenses(Y)))=>(X=Y)))))& (~?[X]:(calm(X)=>quiet(X)))& (((?[X]:(~room(X)&plays_eSports_competitively(X)))))& ((like(janet,carley) & like(carley,janet)))& (hosts_regular_game_nights_featuring_complex_strategy_games(janet))& (?[X,Y]:((((plays_eSports_competitively(X))&(practices_digital_art(X))&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))&(owns_a_3D_printer(Y))&(sibling(X,Y))))& (((A_book_cannot_be_opened_only_at_midnight.)|(A_door_does_not_randomly_teleport_those_who_pass_through_it.)))& (((A_tower_leans_significantly_but_never_falls.)|(A_pen_exists_that_only_writes_secrets.)))& (~((A_door_does_not_randomly_teleport_those_who_pass_through_it.)|(A_clock_measures_time_in_various_colors.)))& (((?[X]:(room(X)&enjoys_stand-up_paddleboarding(X)))&(![X,Y]:((room(X)&room(Y)&(enjoys_stand-up_paddleboarding(X))&(enjoys_stand-up_paddleboarding(Y)))=>(X=Y)))))

room(jane)&room(janet)&room(mary)&room(carley)&room(alice)&(![X]:(room(X)=>(X='jane'|X='janet'|X='mary'|X='carley'|X='alice')))& enjoys_macrame(mary)

% SZS status Unsatisfiable for 6730050746082751065634477 % SZS output start Proof for 6730050746082751065634477 44. ! [X0,X1] : ((predv(X1) & predv(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predv(X0) & room(X0)) & ~(propositione | ~propositionc) & (propositionb | propositiond) & (~propositionc | ~propositiona) & ? [X0,X1] : (sibling(X0,X1) & predp(X1) & predk(X0) & predg(X0) & preda(X0)) & predd(paul) & like(alice,susan) & like(susan,alice) & ? [X0] : (preda(X0) & ~room(X0)) & ~? [X0] : (calm(X0) => quiet(X0)) & ! [X0,X1] : ((preds(X1) & preds(X0) & ~room(X1) & ~room(X0)) => X0 = X1) & ? [X0] : (preds(X0) & ~room(X0)) & predc(alice) & predc(fred) & predu(fred) & ~like(fred,lucy) & prede(fred) & ? [X0,X1] : (X0 != X1 & prede(X1) & predz(X1) & predk(X1) & prede(X0) & predz(X0) & predk(X0) & room(X1) & room(X0)) & predd(alice) & ~hate(john,lucy) & (~(propositiond | ~propositiond) => predx(mary)) & (~(creative(alice) & brave(fred)) => ! [X0] : ((john != X0 & ~room(X0)) => younger(john,X0))) & (~(like(alice,susan) & like(susan,alice)) => ~? [X0] : (strong(X0) => happy(X0))) & ((like(alice,susan) & like(susan,alice)) => predc(john)) & ((~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul))) => (predb(john) & predz(john) & predo(john))) & (predx(mary) => (~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul)))) & (~(propositiond & propositionb & propositiona) => ? [X0,X1] : (X0 != X1 & predi(X1) & predi(X0) & room(X1) & room(X0))) & (~predh(paul) => ! [X0] : ((mary != X0 & ~room(X0)) => richer(X0,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 p0] 45. ~(prede(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. ! [X0,X1] : ((predv(X1) & predv(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predv(X2) & room(X2)) & ~(propositione | ~propositionc) & (propositionb | propositiond) & (~propositionc | ~propositiona) & ? [X3,X4] : (sibling(X3,X4) & predp(X4) & predk(X3) & predg(X3) & preda(X3)) & predd(paul) & like(alice,susan) & like(susan,alice) & ? [X5] : (preda(X5) & ~room(X5)) & ~? [X6] : (calm(X6) => quiet(X6)) & ! [X7,X8] : ((preds(X8) & preds(X7) & ~room(X8) & ~room(X7)) => X7 = X8) & ? [X9] : (preds(X9) & ~room(X9)) & predc(alice) & predc(fred) & predu(fred) & ~like(fred,lucy) & prede(fred) & ? [X10,X11] : (X10 != X11 & prede(X11) & predz(X11) & predk(X11) & prede(X10) & predz(X10) & predk(X10) & room(X11) & room(X10)) & predd(alice) & ~hate(john,lucy) & (~(propositiond | ~propositiond) => predx(mary)) & (~(creative(alice) & brave(fred)) => ! [X12] : ((john != X12 & ~room(X12)) => younger(john,X12))) & (~(like(alice,susan) & like(susan,alice)) => ~? [X13] : (strong(X13) => happy(X13))) & ((like(alice,susan) & like(susan,alice)) => predc(john)) & ((~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul))) => (predb(john) & predz(john) & predo(john))) & (predx(mary) => (~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul)))) & (~(propositiond & propositionb & propositiona) => ? [X14,X15] : (X14 != X15 & predi(X15) & predi(X14) & room(X15) & room(X14))) & (~predh(paul) => ! [X16] : ((mary != X16 & ~room(X16)) => richer(X16,mary))) & ! [X17] : (room(X17) => (john = X17 | alice = X17 | fred = X17 | paul = X17 | mary = X17)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 44] 47. ! [X0,X1] : ((predv(X1) & predv(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predv(X2) & room(X2)) & ~~propositionc & (propositionb | propositiond) & (~propositionc | ~propositiona) & ? [X3,X4] : (sibling(X3,X4) & predp(X4) & predk(X3) & predg(X3) & preda(X3)) & predd(paul) & like(alice,susan) & like(susan,alice) & ? [X5] : (preda(X5) & ~room(X5)) & ~? [X6] : (calm(X6) => quiet(X6)) & ! [X7,X8] : ((preds(X8) & preds(X7) & ~room(X8) & ~room(X7)) => X7 = X8) & ? [X9] : (preds(X9) & ~room(X9)) & predc(alice) & predc(fred) & predu(fred) & ~like(fred,lucy) & prede(fred) & ? [X10,X11] : (X10 != X11 & prede(X11) & predz(X11) & predk(X11) & prede(X10) & predz(X10) & predk(X10) & room(X11) & room(X10)) & predd(alice) & ~hate(john,lucy) & (~(propositiond | ~propositiond) => predx(mary)) & (~(creative(alice) & brave(fred)) => ! [X12] : ((john != X12 & ~room(X12)) => younger(john,X12))) & (~(like(alice,susan) & like(susan,alice)) => ~? [X13] : (strong(X13) => happy(X13))) & ((like(alice,susan) & like(susan,alice)) => predc(john)) & ((~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul))) => (predb(john) & predz(john) & predo(john))) & (predx(mary) => (~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul)))) & (~(propositiond & propositionb & propositiona) => ? [X14,X15] : (X14 != X15 & predi(X15) & predi(X14) & room(X15) & room(X14))) & (~predh(paul) => ! [X16] : ((mary != X16 & ~room(X16)) => richer(X16,mary))) & ! [X17] : (room(X17) => (john = X17 | alice = X17 | fred = X17 | paul = X17 | mary = X17)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 46] 48. ! [X0,X1] : ((predv(X1) & predv(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predv(X2) & room(X2)) & ~~propositionc & (propositionb | propositiond) & (~propositionc | ~propositiona) & ? [X3,X4] : (sibling(X3,X4) & predk(X3) & predg(X3) & preda(X3)) & predd(paul) & like(alice,susan) & like(susan,alice) & ? [X5] : (preda(X5) & ~room(X5)) & ~? [X6] : (calm(X6) => quiet(X6)) & ! [X7,X8] : ((preds(X8) & preds(X7) & ~room(X8) & ~room(X7)) => X7 = X8) & ? [X9] : (preds(X9) & ~room(X9)) & predc(alice) & predc(fred) & predu(fred) & ~like(fred,lucy) & prede(fred) & ? [X10,X11] : (X10 != X11 & prede(X11) & predz(X11) & predk(X11) & prede(X10) & predz(X10) & predk(X10) & room(X11) & room(X10)) & predd(alice) & ~hate(john,lucy) & (~(propositiond | ~propositiond) => predx(mary)) & (~(creative(alice) & brave(fred)) => ! [X12] : ((john != X12 & ~room(X12)) => younger(john,X12))) & (~(like(alice,susan) & like(susan,alice)) => ~? [X13] : (strong(X13) => happy(X13))) & ((like(alice,susan) & like(susan,alice)) => predc(john)) & ((~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul))) => (predb(john) & predz(john) & predo(john))) & (predx(mary) => (~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul)))) & (~(propositiond & propositionb & propositiona) => ? [X14,X15] : (X14 != X15 & predi(X15) & predi(X14) & room(X15) & room(X14))) & (~predh(paul) => ! [X16] : ((mary != X16 & ~room(X16)) => richer(X16,mary))) & ! [X17] : (room(X17) => (john = X17 | alice = X17 | fred = X17 | paul = X17 | mary = X17)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 47] 49. ! [X0,X1] : ((predv(X1) & predv(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predv(X2) & room(X2)) & ~~propositionc & (propositionb | propositiond) & (~propositionc | ~propositiona) & ? [X3,X4] : (sibling(X3,X4) & predk(X3) & preda(X3)) & predd(paul) & like(alice,susan) & like(susan,alice) & ? [X5] : (preda(X5) & ~room(X5)) & ~? [X6] : (calm(X6) => quiet(X6)) & ! [X7,X8] : ((preds(X8) & preds(X7) & ~room(X8) & ~room(X7)) => X7 = X8) & ? [X9] : (preds(X9) & ~room(X9)) & predc(alice) & predc(fred) & predu(fred) & ~like(fred,lucy) & prede(fred) & ? [X10,X11] : (X10 != X11 & prede(X11) & predz(X11) & predk(X11) & prede(X10) & predz(X10) & predk(X10) & room(X11) & room(X10)) & predd(alice) & ~hate(john,lucy) & (~(propositiond | ~propositiond) => predx(mary)) & (~(creative(alice) & brave(fred)) => ! [X12] : ((john != X12 & ~room(X12)) => younger(john,X12))) & (~(like(alice,susan) & like(susan,alice)) => ~? [X13] : (strong(X13) => happy(X13))) & ((like(alice,susan) & like(susan,alice)) => predc(john)) & ((~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul))) => (predb(john) & predz(john) & predo(john))) & (predx(mary) => (~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul)))) & (~(propositiond & propositionb & propositiona) => ? [X14,X15] : (X14 != X15 & predi(X15) & predi(X14) & room(X15) & room(X14))) & (~predh(paul) => ! [X16] : ((mary != X16 & ~room(X16)) => richer(X16,mary))) & ! [X17] : (room(X17) => (john = X17 | alice = X17 | fred = X17 | paul = X17 | mary = X17)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 48] 50. ! [X0,X1] : ((predv(X1) & predv(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predv(X2) & room(X2)) & ~~propositionc & (propositionb | propositiond) & (~propositionc | ~propositiona) & ? [X3,X4] : (sibling(X3,X4) & predk(X3)) & predd(paul) & like(alice,susan) & like(susan,alice) & ? [X5] : ~room(X5) & ~? [X6] : (calm(X6) => quiet(X6)) & ! [X7,X8] : ((preds(X8) & preds(X7) & ~room(X8) & ~room(X7)) => X7 = X8) & ? [X9] : (preds(X9) & ~room(X9)) & predc(alice) & predc(fred) & predu(fred) & ~like(fred,lucy) & prede(fred) & ? [X10,X11] : (X10 != X11 & prede(X11) & predz(X11) & predk(X11) & prede(X10) & predz(X10) & predk(X10) & room(X11) & room(X10)) & predd(alice) & ~hate(john,lucy) & (~(propositiond | ~propositiond) => predx(mary)) & (~(creative(alice) & brave(fred)) => ! [X12] : ((john != X12 & ~room(X12)) => younger(john,X12))) & (~(like(alice,susan) & like(susan,alice)) => ~? [X13] : (strong(X13) => happy(X13))) & ((like(alice,susan) & like(susan,alice)) => predc(john)) & ((~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul))) => (predb(john) & predz(john) & predo(john))) & (predx(mary) => (~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul)))) & (~(propositiond & propositionb & propositiona) => ? [X14,X15] : (X14 != X15 & predi(X15) & predi(X14) & room(X15) & room(X14))) & (~predh(paul) => ! [X16] : ((mary != X16 & ~room(X16)) => richer(X16,mary))) & ! [X17] : (room(X17) => (john = X17 | alice = X17 | fred = X17 | paul = X17 | mary = X17)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 49] 51. ! [X0,X1] : ((predv(X1) & predv(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predv(X2) & room(X2)) & ~~propositionc & (propositionb | propositiond) & (~propositionc | ~propositiona) & ? [X3,X4] : (sibling(X3,X4) & predk(X3)) & predd(paul) & like(alice,susan) & like(susan,alice) & ? [X5] : ~room(X5) & ~? [X6] : quiet(X6) & ! [X7,X8] : ((preds(X8) & preds(X7) & ~room(X8) & ~room(X7)) => X7 = X8) & ? [X9] : (preds(X9) & ~room(X9)) & predc(alice) & predc(fred) & predu(fred) & ~like(fred,lucy) & prede(fred) & ? [X10,X11] : (X10 != X11 & prede(X11) & predz(X11) & predk(X11) & prede(X10) & predz(X10) & predk(X10) & room(X11) & room(X10)) & predd(alice) & ~hate(john,lucy) & (~(propositiond | ~propositiond) => predx(mary)) & (~(creative(alice) & brave(fred)) => ! [X12] : ((john != X12 & ~room(X12)) => younger(john,X12))) & (~(like(alice,susan) & like(susan,alice)) => ~? [X13] : (strong(X13) => happy(X13))) & ((like(alice,susan) & like(susan,alice)) => predc(john)) & ((~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul))) => (predb(john) & predz(john) & predo(john))) & (predx(mary) => (~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul)))) & (~(propositiond & propositionb & propositiona) => ? [X14,X15] : (X14 != X15 & predi(X15) & predi(X14) & room(X15) & room(X14))) & (~predh(paul) => ! [X16] : ((mary != X16 & ~room(X16)) => richer(X16,mary))) & ! [X17] : (room(X17) => (john = X17 | alice = X17 | fred = X17 | paul = X17 | mary = X17)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 50] 52. ! [X0,X1] : ((predv(X1) & predv(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predv(X2) & room(X2)) & ~~propositionc & (propositionb | propositiond) & (~propositionc | ~propositiona) & ? [X3,X4] : (sibling(X3,X4) & predk(X3)) & predd(paul) & like(alice,susan) & like(susan,alice) & ? [X5] : ~room(X5) & ~? [X6] : quiet(X6) & ! [X7,X8] : ((preds(X8) & preds(X7) & ~room(X8) & ~room(X7)) => X7 = X8) & ? [X9] : (preds(X9) & ~room(X9)) & predc(alice) & predc(fred) & ~like(fred,lucy) & prede(fred) & ? [X10,X11] : (X10 != X11 & prede(X11) & predz(X11) & predk(X11) & prede(X10) & predz(X10) & predk(X10) & room(X11) & room(X10)) & predd(alice) & ~hate(john,lucy) & (~(propositiond | ~propositiond) => predx(mary)) & (~(creative(alice) & brave(fred)) => ! [X12] : ((john != X12 & ~room(X12)) => younger(john,X12))) & (~(like(alice,susan) & like(susan,alice)) => ~? [X13] : (strong(X13) => happy(X13))) & ((like(alice,susan) & like(susan,alice)) => predc(john)) & ((~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul))) => (predb(john) & predz(john) & predo(john))) & (predx(mary) => (~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul)))) & (~(propositiond & propositionb & propositiona) => ? [X14,X15] : (X14 != X15 & predi(X15) & predi(X14) & room(X15) & room(X14))) & (~predh(paul) => ! [X16] : ((mary != X16 & ~room(X16)) => richer(X16,mary))) & ! [X17] : (room(X17) => (john = X17 | alice = X17 | fred = X17 | paul = X17 | mary = X17)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 51] 53. ! [X0,X1] : ((predv(X1) & predv(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predv(X2) & room(X2)) & ~~propositionc & (propositionb | propositiond) & (~propositionc | ~propositiona) & ? [X3,X4] : sibling(X3,X4) & predd(paul) & like(alice,susan) & like(susan,alice) & ? [X5] : ~room(X5) & ~? [X6] : quiet(X6) & ! [X7,X8] : ((preds(X8) & preds(X7) & ~room(X8) & ~room(X7)) => X7 = X8) & ? [X9] : (preds(X9) & ~room(X9)) & predc(alice) & predc(fred) & ~like(fred,lucy) & prede(fred) & ? [X10,X11] : (X10 != X11 & prede(X11) & predz(X11) & prede(X10) & predz(X10) & room(X11) & room(X10)) & predd(alice) & ~hate(john,lucy) & (~(propositiond | ~propositiond) => predx(mary)) & (~(creative(alice) & brave(fred)) => ! [X12] : ((john != X12 & ~room(X12)) => younger(john,X12))) & (~(like(alice,susan) & like(susan,alice)) => ~? [X13] : (strong(X13) => happy(X13))) & ((like(alice,susan) & like(susan,alice)) => predc(john)) & ((~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul))) => (predb(john) & predz(john) & predo(john))) & (predx(mary) => (~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul)))) & (~(propositiond & propositionb & propositiona) => ? [X14,X15] : (X14 != X15 & predi(X15) & predi(X14) & room(X15) & room(X14))) & (~predh(paul) => ! [X16] : ((mary != X16 & ~room(X16)) => richer(X16,mary))) & ! [X17] : (room(X17) => (john = X17 | alice = X17 | fred = X17 | paul = X17 | mary = X17)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 52] 54. ! [X0,X1] : ((predv(X1) & predv(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predv(X2) & room(X2)) & ~~propositionc & (propositionb | propositiond) & (~propositionc | ~propositiona) & ? [X3,X4] : sibling(X3,X4) & like(alice,susan) & like(susan,alice) & ? [X5] : ~room(X5) & ~? [X6] : quiet(X6) & ! [X7,X8] : ((preds(X8) & preds(X7) & ~room(X8) & ~room(X7)) => X7 = X8) & ? [X9] : (preds(X9) & ~room(X9)) & predc(alice) & predc(fred) & ~like(fred,lucy) & prede(fred) & ? [X10,X11] : (X10 != X11 & prede(X11) & predz(X11) & prede(X10) & predz(X10) & room(X11) & room(X10)) & ~hate(john,lucy) & (~(propositiond | ~propositiond) => predx(mary)) & (~(creative(alice) & brave(fred)) => ! [X12] : ((john != X12 & ~room(X12)) => younger(john,X12))) & (~(like(alice,susan) & like(susan,alice)) => ~? [X13] : (strong(X13) => happy(X13))) & ((like(alice,susan) & like(susan,alice)) => predc(john)) & ((~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul))) => (predb(john) & predz(john) & predo(john))) & (predx(mary) => (~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul)))) & (~(propositiond & propositionb & propositiona) => ? [X14,X15] : (X14 != X15 & predi(X15) & predi(X14) & room(X15) & room(X14))) & (~predh(paul) => ! [X16] : ((mary != X16 & ~room(X16)) => richer(X16,mary))) & ! [X17] : (room(X17) => (john = X17 | alice = X17 | fred = X17 | paul = X17 | mary = X17)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 53] 55. ! [X0,X1] : ((predv(X1) & predv(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predv(X2) & room(X2)) & ~~propositionc & (propositionb | propositiond) & (~propositionc | ~propositiona) & ? [X3,X4] : sibling(X3,X4) & like(alice,susan) & like(susan,alice) & ? [X5] : ~room(X5) & ~? [X6] : quiet(X6) & ! [X7,X8] : ((preds(X8) & preds(X7) & ~room(X8) & ~room(X7)) => X7 = X8) & ? [X9] : (preds(X9) & ~room(X9)) & predc(alice) & predc(fred) & ~like(fred,lucy) & prede(fred) & ? [X10,X11] : (X10 != X11 & prede(X11) & predz(X11) & prede(X10) & predz(X10) & room(X11) & room(X10)) & ~hate(john,lucy) & (~(propositiond | ~propositiond) => predx(mary)) & (~brave(fred) => ! [X12] : ((john != X12 & ~room(X12)) => younger(john,X12))) & (~(like(alice,susan) & like(susan,alice)) => ~? [X13] : (strong(X13) => happy(X13))) & ((like(alice,susan) & like(susan,alice)) => predc(john)) & ((~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul))) => (predb(john) & predz(john) & predo(john))) & (predx(mary) => (~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul)))) & (~(propositiond & propositionb & propositiona) => ? [X14,X15] : (X14 != X15 & predi(X15) & predi(X14) & room(X15) & room(X14))) & (~predh(paul) => ! [X16] : ((mary != X16 & ~room(X16)) => richer(X16,mary))) & ! [X17] : (room(X17) => (john = X17 | alice = X17 | fred = X17 | paul = X17 | mary = X17)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 54] 56. ! [X0,X1] : ((predv(X1) & predv(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predv(X2) & room(X2)) & ~~propositionc & (propositionb | propositiond) & (~propositionc | ~propositiona) & ? [X3,X4] : sibling(X3,X4) & like(alice,susan) & like(susan,alice) & ? [X5] : ~room(X5) & ~? [X6] : quiet(X6) & ! [X7,X8] : ((preds(X8) & preds(X7) & ~room(X8) & ~room(X7)) => X7 = X8) & ? [X9] : (preds(X9) & ~room(X9)) & predc(alice) & predc(fred) & ~like(fred,lucy) & prede(fred) & ? [X10,X11] : (X10 != X11 & prede(X11) & predz(X11) & prede(X10) & predz(X10) & room(X11) & room(X10)) & ~hate(john,lucy) & (~(propositiond | ~propositiond) => predx(mary)) & (~(like(alice,susan) & like(susan,alice)) => ~? [X13] : (strong(X13) => happy(X13))) & ((like(alice,susan) & like(susan,alice)) => predc(john)) & ((~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul))) => (predb(john) & predz(john) & predo(john))) & (predx(mary) => (~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul)))) & (~(propositiond & propositionb & propositiona) => ? [X14,X15] : (X14 != X15 & predi(X15) & predi(X14) & room(X15) & room(X14))) & (~predh(paul) => ! [X16] : ((mary != X16 & ~room(X16)) => richer(X16,mary))) & ! [X17] : (room(X17) => (john = X17 | alice = X17 | fred = X17 | paul = X17 | mary = X17)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 55] 57. ! [X0,X1] : ((predv(X1) & predv(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predv(X2) & room(X2)) & ~~propositionc & (propositionb | propositiond) & (~propositionc | ~propositiona) & ? [X3,X4] : sibling(X3,X4) & like(alice,susan) & like(susan,alice) & ? [X5] : ~room(X5) & ~? [X6] : quiet(X6) & ! [X7,X8] : ((preds(X8) & preds(X7) & ~room(X8) & ~room(X7)) => X7 = X8) & ? [X9] : (preds(X9) & ~room(X9)) & predc(alice) & predc(fred) & ~like(fred,lucy) & prede(fred) & ? [X10,X11] : (X10 != X11 & prede(X11) & predz(X11) & prede(X10) & predz(X10) & room(X11) & room(X10)) & ~hate(john,lucy) & (~(propositiond | ~propositiond) => predx(mary)) & (~(like(alice,susan) & like(susan,alice)) => ~? [X13] : ~strong(X13)) & ((like(alice,susan) & like(susan,alice)) => predc(john)) & ((~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul))) => (predb(john) & predz(john) & predo(john))) & (predx(mary) => (~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul)))) & (~(propositiond & propositionb & propositiona) => ? [X14,X15] : (X14 != X15 & predi(X15) & predi(X14) & room(X15) & room(X14))) & (~predh(paul) => ! [X16] : ((mary != X16 & ~room(X16)) => richer(X16,mary))) & ! [X17] : (room(X17) => (john = X17 | alice = X17 | fred = X17 | paul = X17 | mary = X17)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 56] 58. ! [X0,X1] : ((predv(X1) & predv(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predv(X2) & room(X2)) & ~~propositionc & (propositionb | propositiond) & (~propositionc | ~propositiona) & ? [X3,X4] : sibling(X3,X4) & like(alice,susan) & like(susan,alice) & ? [X5] : ~room(X5) & ~? [X6] : quiet(X6) & ! [X7,X8] : ((preds(X8) & preds(X7) & ~room(X8) & ~room(X7)) => X7 = X8) & ? [X9] : (preds(X9) & ~room(X9)) & predc(alice) & predc(fred) & ~like(fred,lucy) & prede(fred) & ? [X10,X11] : (X10 != X11 & prede(X11) & predz(X11) & prede(X10) & predz(X10) & room(X11) & room(X10)) & ~hate(john,lucy) & (~(propositiond | ~propositiond) => predx(mary)) & ((like(alice,susan) & like(susan,alice)) => predc(john)) & ((~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul))) => (predb(john) & predz(john) & predo(john))) & (predx(mary) => (~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul)))) & (~(propositiond & propositionb & propositiona) => ? [X14,X15] : (X14 != X15 & predi(X15) & predi(X14) & room(X15) & room(X14))) & (~predh(paul) => ! [X16] : ((mary != X16 & ~room(X16)) => richer(X16,mary))) & ! [X17] : (room(X17) => (john = X17 | alice = X17 | fred = X17 | paul = X17 | mary = X17)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 57] 59. ! [X0,X1] : ((predv(X1) & predv(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predv(X2) & room(X2)) & ~~propositionc & (propositionb | propositiond) & (~propositionc | ~propositiona) & ? [X3,X4] : sibling(X3,X4) & like(alice,susan) & like(susan,alice) & ? [X5] : ~room(X5) & ~? [X6] : quiet(X6) & ! [X7,X8] : ((preds(X8) & preds(X7) & ~room(X8) & ~room(X7)) => X7 = X8) & ? [X9] : (preds(X9) & ~room(X9)) & ~like(fred,lucy) & prede(fred) & ? [X10,X11] : (X10 != X11 & prede(X11) & predz(X11) & prede(X10) & predz(X10) & room(X11) & room(X10)) & ~hate(john,lucy) & (~(propositiond | ~propositiond) => predx(mary)) & ((~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul))) => (predb(john) & predz(john) & predo(john))) & (predx(mary) => (~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul)))) & (~(propositiond & propositionb & propositiona) => ? [X14,X15] : (X14 != X15 & predi(X15) & predi(X14) & room(X15) & room(X14))) & (~predh(paul) => ! [X16] : ((mary != X16 & ~room(X16)) => richer(X16,mary))) & ! [X17] : (room(X17) => (john = X17 | alice = X17 | fred = X17 | paul = X17 | mary = X17)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 58] 60. ! [X0,X1] : ((predv(X1) & predv(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predv(X2) & room(X2)) & ~~propositionc & (propositionb | propositiond) & (~propositionc | ~propositiona) & ? [X3,X4] : sibling(X3,X4) & like(alice,susan) & like(susan,alice) & ? [X5] : ~room(X5) & ~? [X6] : quiet(X6) & ! [X7,X8] : ((preds(X8) & preds(X7) & ~room(X8) & ~room(X7)) => X7 = X8) & ? [X9] : (preds(X9) & ~room(X9)) & ~like(fred,lucy) & prede(fred) & ? [X10,X11] : (X10 != X11 & prede(X11) & prede(X10) & room(X11) & room(X10)) & ~hate(john,lucy) & (~(propositiond | ~propositiond) => predx(mary)) & ((~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul))) => (predb(john) & predo(john))) & (predx(mary) => (~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul)))) & (~(propositiond & propositionb & propositiona) => ? [X14,X15] : (X14 != X15 & predi(X15) & predi(X14) & room(X15) & room(X14))) & (~predh(paul) => ! [X16] : ((mary != X16 & ~room(X16)) => richer(X16,mary))) & ! [X17] : (room(X17) => (john = X17 | alice = X17 | fred = X17 | paul = X17 | mary = X17)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 59] 61. ! [X0,X1] : ((predv(X1) & predv(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predv(X2) & room(X2)) & ~~propositionc & (propositionb | propositiond) & (~propositionc | ~propositiona) & ? [X3,X4] : sibling(X3,X4) & like(alice,susan) & like(susan,alice) & ? [X5] : ~room(X5) & ~? [X6] : quiet(X6) & ! [X7,X8] : ((preds(X8) & preds(X7) & ~room(X8) & ~room(X7)) => X7 = X8) & ? [X9] : (preds(X9) & ~room(X9)) & ~like(fred,lucy) & prede(fred) & ? [X10,X11] : (X10 != X11 & prede(X11) & prede(X10) & room(X11) & room(X10)) & ~hate(john,lucy) & (~(propositiond | ~propositiond) => predx(mary)) & ((~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul))) => predb(john)) & (predx(mary) => (~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul)))) & (~(propositiond & propositionb & propositiona) => ? [X14,X15] : (X14 != X15 & predi(X15) & predi(X14) & room(X15) & room(X14))) & (~predh(paul) => ! [X16] : ((mary != X16 & ~room(X16)) => richer(X16,mary))) & ! [X17] : (room(X17) => (john = X17 | alice = X17 | fred = X17 | paul = X17 | mary = X17)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 60] 62. ! [X0,X1] : ((predv(X1) & predv(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predv(X2) & room(X2)) & ~~propositionc & (propositionb | propositiond) & (~propositionc | ~propositiona) & ? [X3,X4] : sibling(X3,X4) & like(alice,susan) & like(susan,alice) & ? [X5] : ~room(X5) & ~? [X6] : quiet(X6) & ! [X7,X8] : ((preds(X8) & preds(X7) & ~room(X8) & ~room(X7)) => X7 = X8) & ? [X9] : (preds(X9) & ~room(X9)) & ~like(fred,lucy) & prede(fred) & ? [X10,X11] : (X10 != X11 & prede(X11) & prede(X10) & room(X11) & room(X10)) & ~hate(john,lucy) & (~(propositiond | ~propositiond) => predx(mary)) & ((~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul))) => predb(john)) & (predx(mary) => (~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul)))) & (~(propositiond & propositionb & propositiona) => ? [X14,X15] : (X14 != X15 & room(X15) & room(X14))) & (~predh(paul) => ! [X16] : ((mary != X16 & ~room(X16)) => richer(X16,mary))) & ! [X17] : (room(X17) => (john = X17 | alice = X17 | fred = X17 | paul = X17 | mary = X17)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 61] 63. ! [X0,X1] : ((predv(X1) & predv(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predv(X2) & room(X2)) & ~~propositionc & (~propositionc | ~propositiona) & ? [X3,X4] : sibling(X3,X4) & like(alice,susan) & like(susan,alice) & ? [X5] : ~room(X5) & ~? [X6] : quiet(X6) & ! [X7,X8] : ((preds(X8) & preds(X7) & ~room(X8) & ~room(X7)) => X7 = X8) & ? [X9] : (preds(X9) & ~room(X9)) & ~like(fred,lucy) & prede(fred) & ? [X10,X11] : (X10 != X11 & prede(X11) & prede(X10) & room(X11) & room(X10)) & ~hate(john,lucy) & (~(propositiond | ~propositiond) => predx(mary)) & ((~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul))) => predb(john)) & (predx(mary) => (~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul)))) & (~(propositiond & propositiona) => ? [X14,X15] : (X14 != X15 & room(X15) & room(X14))) & (~predh(paul) => ! [X16] : ((mary != X16 & ~room(X16)) => richer(X16,mary))) & ! [X17] : (room(X17) => (john = X17 | alice = X17 | fred = X17 | paul = X17 | mary = X17)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 62] 64. ! [X0,X1] : ((predv(X1) & predv(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predv(X2) & room(X2)) & ~~propositionc & (~propositionc | ~propositiona) & ? [X3,X4] : sibling(X3,X4) & like(alice,susan) & like(susan,alice) & ? [X5] : ~room(X5) & ~? [X6] : quiet(X6) & ! [X7,X8] : ((preds(X8) & preds(X7) & ~room(X8) & ~room(X7)) => X7 = X8) & ? [X9] : (preds(X9) & ~room(X9)) & ~like(fred,lucy) & prede(fred) & ? [X10,X11] : (X10 != X11 & prede(X11) & prede(X10) & room(X11) & room(X10)) & ~hate(john,lucy) & (~(propositiond | ~propositiond) => predx(mary)) & ((~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul))) => predb(john)) & (predx(mary) => (~hate(paul,susan) & predb(paul) & ~(person(paul) & old(paul)))) & (~(propositiond & propositiona) => ? [X14,X15] : (X14 != X15 & room(X15) & room(X14))) & ! [X17] : (room(X17) => (john = X17 | alice = X17 | fred = X17 | paul = X17 | mary = X17)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [pure predicate removal 63] 139. ! [X0,X1] : (X0 = X1 | (~predv(X1) | ~predv(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (predv(X2) & room(X2)) & propositionc & (~propositionc | ~propositiona) & ? [X3,X4] : sibling(X3,X4) & like(alice,susan) & like(susan,alice) & ? [X5] : ~room(X5) & ! [X6] : ~quiet(X6) & ! [X7,X8] : (X7 = X8 | (~preds(X8) | ~preds(X7) | room(X8) | room(X7))) & ? [X9] : (preds(X9) & ~room(X9)) & ~like(fred,lucy) & prede(fred) & ? [X10,X11] : (X10 != X11 & prede(X11) & prede(X10) & room(X11) & room(X10)) & ~hate(john,lucy) & (predx(mary) | (propositiond | ~propositiond)) & (predb(john) | (hate(paul,susan) | ~predb(paul) | (person(paul) & old(paul)))) & ((~hate(paul,susan) & predb(paul) & (~person(paul) | ~old(paul))) | ~predx(mary)) & (? [X14,X15] : (X14 != X15 & room(X15) & room(X14)) | (propositiond & propositiona)) & ! [X17] : ((john = X17 | alice = X17 | fred = X17 | paul = X17 | mary = X17) | ~room(X17)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 64] 140. ! [X0,X1] : (X0 = X1 | ~predv(X1) | ~predv(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (predv(X2) & room(X2)) & propositionc & (~propositionc | ~propositiona) & ? [X3,X4] : sibling(X3,X4) & like(alice,susan) & like(susan,alice) & ? [X5] : ~room(X5) & ! [X6] : ~quiet(X6) & ! [X7,X8] : (X7 = X8 | ~preds(X8) | ~preds(X7) | room(X8) | room(X7)) & ? [X9] : (preds(X9) & ~room(X9)) & ~like(fred,lucy) & prede(fred) & ? [X10,X11] : (X10 != X11 & prede(X11) & prede(X10) & room(X11) & room(X10)) & ~hate(john,lucy) & (predx(mary) | propositiond | ~propositiond) & (predb(john) | hate(paul,susan) | ~predb(paul) | (person(paul) & old(paul))) & ((~hate(paul,susan) & predb(paul) & (~person(paul) | ~old(paul))) | ~predx(mary)) & (? [X14,X15] : (X14 != X15 & room(X15) & room(X14)) | (propositiond & propositiona)) & ! [X17] : (john = X17 | alice = X17 | fred = X17 | paul = X17 | mary = X17 | ~room(X17)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 139] 141. ~prede(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] 142. ~prede(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 141] 144. ! [X0,X1] : (X0 = X1 | ~predv(X1) | ~predv(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (predv(X2) & room(X2)) & propositionc & (~propositionc | ~propositiona) & ? [X3,X4] : sibling(X3,X4) & like(alice,susan) & like(susan,alice) & ? [X5] : ~room(X5) & ! [X6] : ~quiet(X6) & ! [X7,X8] : (X7 = X8 | ~preds(X8) | ~preds(X7) | room(X8) | room(X7)) & ? [X9] : (preds(X9) & ~room(X9)) & ~like(fred,lucy) & prede(fred) & ? [X10,X11] : (X10 != X11 & prede(X11) & prede(X10) & room(X11) & room(X10)) & ~hate(john,lucy) & (predx(mary) | propositiond | ~propositiond) & (predb(john) | hate(paul,susan) | ~predb(paul) | (person(paul) & old(paul))) & ((~hate(paul,susan) & predb(paul) & (~person(paul) | ~old(paul))) | ~predx(mary)) & (? [X12,X13] : (X12 != X13 & room(X13) & room(X12)) | (propositiond & propositiona)) & ! [X14] : (john = X14 | alice = X14 | fred = X14 | paul = X14 | mary = X14 | ~room(X14)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 140] 145. ? [X2] : (predv(X2) & room(X2)) => (predv(sK0) & room(sK0)) [choice axiom] 146. ? [X3,X4] : sibling(X3,X4) => sibling(sK1,sK2) [choice axiom] 147. ? [X5] : ~room(X5) => ~room(sK3) [choice axiom] 148. ? [X9] : (preds(X9) & ~room(X9)) => (preds(sK4) & ~room(sK4)) [choice axiom] 149. ? [X10,X11] : (X10 != X11 & prede(X11) & prede(X10) & room(X11) & room(X10)) => (sK5 != sK6 & prede(sK6) & prede(sK5) & room(sK6) & room(sK5)) [choice axiom] 150. ? [X12,X13] : (X12 != X13 & room(X13) & room(X12)) => (sK7 != sK8 & room(sK8) & room(sK7)) [choice axiom] 151. ! [X0,X1] : (X0 = X1 | ~predv(X1) | ~predv(X0) | ~room(X1) | ~room(X0)) & (predv(sK0) & room(sK0)) & propositionc & (~propositionc | ~propositiona) & sibling(sK1,sK2) & like(alice,susan) & like(susan,alice) & ~room(sK3) & ! [X6] : ~quiet(X6) & ! [X7,X8] : (X7 = X8 | ~preds(X8) | ~preds(X7) | room(X8) | room(X7)) & (preds(sK4) & ~room(sK4)) & ~like(fred,lucy) & prede(fred) & (sK5 != sK6 & prede(sK6) & prede(sK5) & room(sK6) & room(sK5)) & ~hate(john,lucy) & (predx(mary) | propositiond | ~propositiond) & (predb(john) | hate(paul,susan) | ~predb(paul) | (person(paul) & old(paul))) & ((~hate(paul,susan) & predb(paul) & (~person(paul) | ~old(paul))) | ~predx(mary)) & ((sK7 != sK8 & room(sK8) & room(sK7)) | (propositiond & propositiona)) & ! [X14] : (john = X14 | alice = X14 | fred = X14 | paul = X14 | mary = X14 | ~room(X14)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [skolemisation 144,150,149,148,147,146,145] 152. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK9 & alice != sK9 & fred != sK9 & paul != sK9 & mary != sK9 & room(sK9)) [choice axiom] 153. ~prede(fred) | (john != sK9 & alice != sK9 & fred != sK9 & paul != sK9 & mary != sK9 & room(sK9)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 142,152] 236. room(mary) [cnf transformation 151] 237. room(paul) [cnf transformation 151] 238. room(fred) [cnf transformation 151] 239. room(alice) [cnf transformation 151] 240. room(john) [cnf transformation 151] 241. ~room(X14) | alice = X14 | fred = X14 | paul = X14 | mary = X14 | john = X14 [cnf transformation 151] 260. prede(fred) [cnf transformation 151] 275. ~prede(fred) | room(sK9) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 153] 276. ~prede(fred) | mary != sK9 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 153] 277. ~prede(fred) | paul != sK9 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 153] 278. ~prede(fred) | fred != sK9 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 153] 279. ~prede(fred) | alice != sK9 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 153] 280. ~prede(fred) | john != sK9 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 153] 336. john != sK9 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 280,260] 337. john != sK9 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 336,240] 338. john != sK9 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 337,239] 339. john != sK9 | ~room(paul) | ~room(mary) [subsumption resolution 338,238] 340. john != sK9 | ~room(mary) [subsumption resolution 339,237] 341. john != sK9 [subsumption resolution 340,236] 342. alice != sK9 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 279,260] 343. alice != sK9 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 342,240] 344. alice != sK9 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 343,239] 345. alice != sK9 | ~room(paul) | ~room(mary) [subsumption resolution 344,238] 346. alice != sK9 | ~room(mary) [subsumption resolution 345,237] 347. alice != sK9 [subsumption resolution 346,236] 348. fred != sK9 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 278,260] 349. fred != sK9 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 348,240] 350. fred != sK9 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 349,239] 351. fred != sK9 | ~room(paul) | ~room(mary) [subsumption resolution 350,238] 352. fred != sK9 | ~room(mary) [subsumption resolution 351,237] 353. fred != sK9 [subsumption resolution 352,236] 354. paul != sK9 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 277,260] 355. paul != sK9 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 354,240] 356. paul != sK9 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 355,239] 357. paul != sK9 | ~room(paul) | ~room(mary) [subsumption resolution 356,238] 358. paul != sK9 | ~room(mary) [subsumption resolution 357,237] 359. paul != sK9 [subsumption resolution 358,236] 360. mary != sK9 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 276,260] 361. mary != sK9 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 360,240] 362. mary != sK9 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 361,239] 363. mary != sK9 | ~room(paul) | ~room(mary) [subsumption resolution 362,238] 364. mary != sK9 | ~room(mary) [subsumption resolution 363,237] 365. mary != sK9 [subsumption resolution 364,236] 366. room(sK9) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 275,260] 367. room(sK9) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 366,240] 368. room(sK9) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 367,239] 369. room(sK9) | ~room(paul) | ~room(mary) [subsumption resolution 368,238] 370. room(sK9) | ~room(mary) [subsumption resolution 369,237] 371. room(sK9) [subsumption resolution 370,236] 436. alice = sK9 | fred = sK9 | paul = sK9 | mary = sK9 | john = sK9 [resolution 241,371] 542. fred = sK9 | paul = sK9 | mary = sK9 | john = sK9 [subsumption resolution 436,347] 543. paul = sK9 | mary = sK9 | john = sK9 [subsumption resolution 542,353] 544. mary = sK9 | john = sK9 [subsumption resolution 543,359] 545. john = sK9 [subsumption resolution 544,365] 546. $false [subsumption resolution 545,341] % SZS output end Proof for 6730050746082751065634477 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.019 s % ------------------------------ % ------------------------------

Sandra, Patrice, Isabel are the only persons in the room. If it is not the case that at least one person in the room enjoys kayaking then everyone anywhere who practices archery reads mystery novels. Not everyone in the room who is a dedicated volunteer for local community service projects enjoys stand-up paddleboarding. If someone collects classic novels then he/she is an active member of a local robotics club or does practice yoga or both and vice versa. Everyone in the room who enjoys camping and organizing outdoor survival workshops practices archery. Everyone in the room who is a dedicated volunteer for local community service projects practices archery. If someone practices archery then he/she does practice yoga and vice versa. Everyone anywhere who practices archery reads mystery novels. Everyone in the room is not an active member of a local robotics club or maintains a large, organic vegetable garden year-round. At least one person in the room practices archery. Everyone in the room who enjoys stand-up paddleboarding makes intricate hand-cut paper art for exhibitions. Everyone in the room who makes intricate hand-cut paper art for exhibitions watches fantasy movies. Everyone in the room watches fantasy movies only if they is an active member of a local robotics club. Everyone in the room who maintains a large, organic vegetable garden year-round enjoys kayaking. Everyone in the room enjoys kayaking only if they either watches fantasy movies or maintains a large, organic vegetable garden year-round but not both. Everyone outside the room who either watches fantasy movies or maintains a large, organic vegetable garden year-round but not both enjoys stand-up paddleboarding. Everyone in the room reads mystery novels only if they does enjoy trail running. Everyone in the room who does enjoy trail running collects classic novels.

Isabel watches fantasy movies.

contradiction

room(sandra)&room(patrice)&room(isabel)&(![X]:(room(X)=>(X='sandra'|X='patrice'|X='isabel')))& ((~(((?[X]:(room(X)&enjoys_kayaking(X))))))=>(![X]:(anywhere(X)=>(((practices_archery(X))=>(reads_mystery_novels(X)))))))& (~![X]:(room(X)=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))=>(enjoys_stand-up_paddleboarding(X))))))& ((![X]:((collects_classic_novels(X))<=>(((is_an_active_member_of_a_local_robotics_club(X))|(does_practice_yoga(X)))))))& (![X]:(room(X)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))=>(practices_archery(X))))))& (![X]:(room(X)=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))=>(practices_archery(X))))))& ((![X]:((practices_archery(X))<=>(does_practice_yoga(X)))))& (![X]:(anywhere(X)=>(((practices_archery(X))=>(reads_mystery_novels(X))))))& (![X]:(room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))|(is_not_an_active_member_of_a_local_robotics_club(X))))))& (((?[X]:(room(X)&practices_archery(X)))))& (![X]:(room(X)=>(((enjoys_stand-up_paddleboarding(X))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))& (![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))=>(watches_fantasy_movies(X))))))& (![X]:(room(X)=>(((is_an_active_member_of_a_local_robotics_club(X))<=(watches_fantasy_movies(X))))))& (![X]:(room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))=>(enjoys_kayaking(X))))))& (![X]:(room(X)=>(((((watches_fantasy_movies(X))<~>(maintains_a_large,_organic_vegetable_garden_year-round(X))))<=(enjoys_kayaking(X))))))& (![X]:(~room(X)=>(((((watches_fantasy_movies(X))<~>(maintains_a_large,_organic_vegetable_garden_year-round(X))))=>(enjoys_stand-up_paddleboarding(X))))))& (![X]:(room(X)=>(((does_enjoy_trail_running(X))<=(reads_mystery_novels(X))))))& (![X]:(room(X)=>(((does_enjoy_trail_running(X))=>(collects_classic_novels(X))))))

room(sandra)&room(patrice)&room(isabel)&(![X]:(room(X)=>(X='sandra'|X='patrice'|X='isabel')))& watches_fantasy_movies(isabel)

% SZS status Unsatisfiable for 462806600639822603903188 % SZS output start Proof for 462806600639822603903188 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 52. ! [X0] : (room(X0) => (~predh(X0) | predi(X0))) [input p8] 56. ! [X0] : (room(X0) => (predp(X0) => predh(X0))) [input p12] 57. ! [X0] : (room(X0) => (predi(X0) => predm(X0))) [input p13] 58. ! [X0] : (room(X0) => (predm(X0) => (predp(X0) <~> predi(X0)))) [input p14] 62. predp(fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 137. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 138. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 137] 149. ! [X0] : ((~predh(X0) | predi(X0)) | ~room(X0)) [ennf transformation 52] 150. ! [X0] : (~predh(X0) | predi(X0) | ~room(X0)) [flattening 149] 155. ! [X0] : ((predh(X0) | ~predp(X0)) | ~room(X0)) [ennf transformation 56] 156. ! [X0] : (predh(X0) | ~predp(X0) | ~room(X0)) [flattening 155] 157. ! [X0] : ((predm(X0) | ~predi(X0)) | ~room(X0)) [ennf transformation 57] 158. ! [X0] : (predm(X0) | ~predi(X0) | ~room(X0)) [flattening 157] 159. ! [X0] : (((predp(X0) <~> predi(X0)) | ~predm(X0)) | ~room(X0)) [ennf transformation 58] 160. ! [X0] : ((predp(X0) <~> predi(X0)) | ~predm(X0) | ~room(X0)) [flattening 159] 167. predp(fred) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 62] 168. predp(fred) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 167] 178. ! [X0] : (((~predi(X0) | ~predp(X0)) & (predi(X0) | predp(X0))) | ~predm(X0) | ~room(X0)) [nnf transformation 160] 263. room(fred) [cnf transformation 138] 275. ~predh(X0) | predi(X0) | ~room(X0) [cnf transformation 150] 280. ~predp(X0) | predh(X0) | ~room(X0) [cnf transformation 156] 281. ~predi(X0) | predm(X0) | ~room(X0) [cnf transformation 158] 283. ~predi(X0) | ~predp(X0) | ~predm(X0) | ~room(X0) [cnf transformation 178] 292. predp(fred) [cnf transformation 168] 310. ~predp(X0) | ~predi(X0) | ~room(X0) [subsumption resolution 283,281] 319. predh(fred) | ~room(fred) [resolution 280,292] 320. predh(fred) [subsumption resolution 319,263] 321. predi(fred) | ~room(fred) [resolution 320,275] 322. predi(fred) [subsumption resolution 321,263] 331. ~predi(fred) | ~room(fred) [resolution 310,292] 332. ~room(fred) [subsumption resolution 331,322] 333. $false [subsumption resolution 332,263] % SZS output end Proof for 462806600639822603903188 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.032 s % ------------------------------ % ------------------------------

Dolores, Rose, Samantha, Harold are the only persons in the room. Dolores trains for and competes in international triathlons. Someone in the room is a certified yoga instructor teaching classes weekly. It is not the case that “Dolores hosts regular game nights featuring complex strategy games”. If someone neither is a professional photographer specializing in portrait photography nor enjoys landscape photography then he/she is right-handed and vice versa. If someone hosts regular game nights featuring complex strategy games then he/she owns a 3D printer and vice versa. Someone outside the room is a certified yoga instructor teaching classes weekly. Everyone in the room who either is a certified yoga instructor teaching classes weekly or trains for and competes in international triathlons but not both neither is a professional photographer specializing in portrait photography nor hosts regular game nights featuring complex strategy games. Everyone in the room is a certified scuba diver with advanced underwater photography skills or does not enjoy origami. Everyone outside the room who is a certified scuba diver with advanced underwater photography skills hosts regular game nights featuring complex strategy games. If someone is an avid mountain climber who has scaled several peaks then he/she has a curated collection of mid-century modern furniture and vice versa. No one anywhere hosts regular game nights featuring complex strategy games or does not use an ios phone. Dolores practices urban gardening. Rose is a certified scuba diver with advanced underwater photography skills, is a certified yoga instructor teaching classes weekly and enjoys landscape photography. At least one person in the room has a curated collection of mid-century modern furniture. Not everyone in the room does not enjoy origami or practices urban gardening. Dolores is a certified scuba diver with advanced underwater photography skills.

Rose owns a 3D printer.

contradiction

room(dolores)&room(rose)&room(samantha)&room(harold)&(![X]:(room(X)=>(X='dolores'|X='rose'|X='samantha'|X='harold')))& (trains_for_and_competes_in_international_triathlons(dolores))& (?[X]:(room(X)&(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))& (~(hosts_regular_game_nights_featuring_complex_strategy_games(dolores)))& ((![X]:((~((is_a_professional_photographer_specializing_in_portrait_photography(X))|(enjoys_landscape_photography(X))))<=>(is_right-handed(X)))))& ((![X]:((hosts_regular_game_nights_featuring_complex_strategy_games(X))<=>(owns_a_3D_printer(X)))))& (?[X]:(~room(X)&(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))& (![X]:(room(X)=>(((((is_a_certified_yoga_instructor_teaching_classes_weekly(X))<~>(trains_for_and_competes_in_international_triathlons(X))))=>(~((is_a_professional_photographer_specializing_in_portrait_photography(X))|(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))))& (![X]:(room(X)=>(((does_not_enjoy_origami(X))|(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))& (![X]:(~room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))& ((![X]:((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))<=>(has_a_curated_collection_of_mid-century_modern_furniture(X)))))& (~?[X]:(anywhere(X)=>(((does_not_use_an_ios_phone(X))|(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))& (practices_urban_gardening(dolores))& (((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(rose))&(is_a_certified_yoga_instructor_teaching_classes_weekly(rose))&(enjoys_landscape_photography(rose))))& (((?[X]:(room(X)&has_a_curated_collection_of_mid-century_modern_furniture(X)))))& (~![X]:(room(X)=>(((practices_urban_gardening(X))|(does_not_enjoy_origami(X))))))& (is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(dolores))

room(dolores)&room(rose)&room(samantha)&room(harold)&(![X]:(room(X)=>(X='dolores'|X='rose'|X='samantha'|X='harold')))& owns_a_3D_printer(rose)

% SZS status Unsatisfiable for 4430592393961281851827527 % SZS output start Proof for 4430592393961281851827527 49. ! [X0] : (predm(X0) <=> predd(X0)) [input p5] 55. ~? [X0] : (anywhere(X0) => (predm(X0) | ~predp(X0))) [input p11] 61. predd(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 65. ~? [X0] : (anywhere(X0) => predm(X0)) [pure predicate removal 55] 66. ~? [X0] : predm(X0) [pure predicate removal 65] 147. ! [X0] : ~predm(X0) [ennf transformation 66] 150. predd(paul) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 61] 151. predd(paul) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 150] 155. ! [X0] : ((predm(X0) | ~predd(X0)) & (predd(X0) | ~predm(X0))) [nnf transformation 49] 253. ~predd(X0) | predm(X0) [cnf transformation 155] 260. ~predm(X0) [cnf transformation 147] 274. predd(paul) [cnf transformation 151] 275. predm(paul) [resolution 253,274] 276. $false [subsumption resolution 275,260] % SZS output end Proof for 4430592393961281851827527 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Julie, Maureen, David, Sarah, Janice are the only persons in the room. "Everyone in the room does not own a telescope or volunteers for local environmental conservation projects" only if "Sarah is a quiet person". "Not everyone in the room who owns a telescope either plays video games or is quieter than Joann but not both" unless "Julie is a client of Meta". If "everyone in the room does not volunteer for local environmental conservation projects or is not a client of Meta" then "everyone in the room is a skilled home brewer experimenting with craft beer recipes if they does not volunteer for local environmental conservation projects". "Everyone in the room who is quieter than Joann is a quiet person" unless "everyone outside the room volunteers for local environmental conservation projects or does not own a telescope". "Sarah is not not quiet" if "Joann is quieter than Julie". "Everyone in the room does not volunteer for local environmental conservation projects or is quieter than Joann" unless "everyone in the room is not a client of Meta or is quiet". David is a client of Meta. If someone is a client of Meta then he/she is quiet and vice versa. Someone who is not a quiet person is quieter than someone who is quieter than Joann. Everyone in the room neither owns a telescope nor is quieter than Joann only if they is a quiet person. Everyone in the room who is a quiet person owns a telescope. Joann is quieter than Sarah.

Sarah owns a telescope.

entailment

room(julie)&room(maureen)&room(david)&room(sarah)&room(janice)&(![X]:(room(X)=>(X='julie'|X='maureen'|X='david'|X='sarah'|X='janice')))& ((![X]:(room(X)=>(((volunteers_for_local_environmental_conservation_projects(X))|(does_not_own_a_telescope(X))))))=>(quiet(sarah)&person(sarah)))& (~(is_a_client_of_Meta(julie))=>(~![X]:(room(X)=>(((owns_a_telescope(X))=>(((plays_video_games(X))<~>(quieter(joann,X)))))))))& ((![X]:(room(X)=>(((is_not_a_client_of_Meta(X))|(does_not_volunteer_for_local_environmental_conservation_projects(X))))))=>(![X]:(room(X)=>(((does_not_volunteer_for_local_environmental_conservation_projects(X))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X)))))))& (~(![X]:(~room(X)=>(((does_not_own_a_telescope(X))|(volunteers_for_local_environmental_conservation_projects(X))))))=>(![X]:(room(X)=>(((quieter(joann,X))=>(quiet(X)&person(X)))))))& ((quieter(julie,joann))=>(~~quiet(sarah)))& (~(![X]:(room(X)=>(((quiet(X))|(is_not_a_client_of_Meta(X))))))=>(![X]:(room(X)=>(((quieter(joann,X))|(does_not_volunteer_for_local_environmental_conservation_projects(X)))))))& (is_a_client_of_Meta(david))& ((![X]:((is_a_client_of_Meta(X))<=>(quiet(X)))))& (?[X,Y]:((~(quiet(X)&person(X)))&(quieter(joann,Y))&(quieter(X,Y))))& (quiet(maureen))& (![X]:(room(X)=>(((quiet(X)&person(X))<=(~((owns_a_telescope(X))|(quieter(joann,X))))))))& (?[X]:(room(X)&(is_a_client_of_LVMH(X))))& (![X]:(~room(X)=>(((quieter(joann,X))=>(does_not_own_a_telescope(X))))))& (~![X]:(room(X)=>(((quiet(X)&person(X))<=(does_not_own_a_telescope(X))))))& (![X]:((anywhere(X)&(X!=maureen))=>quieter(maureen,X)))& (![X]:(room(X)=>(((quiet(X)&person(X))=>(owns_a_telescope(X))))))& (volunteers_for_local_environmental_conservation_projects(david))& (quieter(sarah,joann))& (![X]:(room(X)=>(((plays_video_games(X))<=>(quieter(joann,X))))))& (is_a_client_of_LVMH(sarah))& (quieter(joann,david))

room(julie)&room(maureen)&room(david)&room(sarah)&room(janice)&(![X]:(room(X)=>(X='julie'|X='maureen'|X='david'|X='sarah'|X='janice')))& owns_a_telescope(sarah)

% SZS status Unsatisfiable for 4956216663872770574240568 % SZS output start Proof for 4956216663872770574240568 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] 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 55. ! [X0] : (room(X0) => (~(quieter(lucy,X0) | prede(X0)) => (person(X0) & quiet(X0)))) [input p11] 60. ! [X0] : (room(X0) => ((person(X0) & quiet(X0)) => prede(X0))) [input p16] 62. quieter(alice,lucy) [input p18] 66. ~(prede(alice) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis] 91. ! [X0,X1] : ((~quieter(X1,X0) | ~quieter(X0,X1)) | X0 = X1) [ennf transformation 14] 92. ! [X0,X1] : (~quieter(X1,X0) | ~quieter(X0,X1) | X0 = X1) [flattening 91] 144. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 145. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 144] 156. ! [X0] : (((person(X0) & quiet(X0)) | (quieter(lucy,X0) | prede(X0))) | ~room(X0)) [ennf transformation 55] 157. ! [X0] : ((person(X0) & quiet(X0)) | quieter(lucy,X0) | prede(X0) | ~room(X0)) [flattening 156] 164. ! [X0] : ((prede(X0) | (~person(X0) | ~quiet(X0))) | ~room(X0)) [ennf transformation 60] 165. ! [X0] : (prede(X0) | ~person(X0) | ~quiet(X0) | ~room(X0)) [flattening 164] 167. ~prede(alice) | ? [X0] : ((john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 66] 168. ~prede(alice) | ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 167] 186. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK6 & alice != sK6 & fred != sK6 & paul != sK6 & mary != sK6 & room(sK6)) [choice axiom] 187. ~prede(alice) | (john != sK6 & alice != sK6 & fred != sK6 & paul != sK6 & mary != sK6 & room(sK6)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 168,186] 198. ~quieter(X1,X0) | ~quieter(X0,X1) | X0 = X1 [cnf transformation 92] 266. alice != lucy [cnf transformation 43] 269. room(mary) [cnf transformation 145] 270. room(paul) [cnf transformation 145] 271. room(fred) [cnf transformation 145] 272. room(alice) [cnf transformation 145] 273. room(john) [cnf transformation 145] 274. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 145] 296. quieter(lucy,X0) | quiet(X0) | prede(X0) | ~room(X0) [cnf transformation 157] 297. quieter(lucy,X0) | person(X0) | prede(X0) | ~room(X0) [cnf transformation 157] 304. ~room(X0) | ~person(X0) | ~quiet(X0) | prede(X0) [cnf transformation 165] 306. quieter(alice,lucy) [cnf transformation 62] 310. ~prede(alice) | room(sK6) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 187] 311. ~prede(alice) | mary != sK6 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 187] 312. ~prede(alice) | paul != sK6 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 187] 313. ~prede(alice) | fred != sK6 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 187] 314. ~prede(alice) | alice != sK6 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 187] 315. ~prede(alice) | john != sK6 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 187] 321. 2 <=> person(alice) [avatar definition] 336. 5 <=> quiet(alice) [avatar definition] 408. ~prede(alice) | john != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 315,273] 409. ~prede(alice) | john != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 408,272] 410. ~prede(alice) | john != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 409,271] 411. ~prede(alice) | john != sK6 | ~room(mary) [subsumption resolution 410,270] 412. ~prede(alice) | john != sK6 [subsumption resolution 411,269] 414. 21 <=> john = sK6 [avatar definition] 416. john != sK6 <- (~21) [avatar component clause 414] 418. 22 <=> prede(alice) [avatar definition] 420. ~prede(alice) <- (~22) [avatar component clause 418] 421. ~21 | ~22 [avatar split clause 412,418,414] 422. ~prede(alice) | alice != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 314,273] 423. ~prede(alice) | alice != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 422,272] 424. ~prede(alice) | alice != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 423,271] 425. ~prede(alice) | alice != sK6 | ~room(mary) [subsumption resolution 424,270] 426. ~prede(alice) | alice != sK6 [subsumption resolution 425,269] 428. 23 <=> alice = sK6 [avatar definition] 430. alice != sK6 <- (~23) [avatar component clause 428] 431. ~23 | ~22 [avatar split clause 426,418,428] 432. ~prede(alice) | fred != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 313,273] 433. ~prede(alice) | fred != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 432,272] 434. ~prede(alice) | fred != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 433,271] 435. ~prede(alice) | fred != sK6 | ~room(mary) [subsumption resolution 434,270] 436. ~prede(alice) | fred != sK6 [subsumption resolution 435,269] 438. 24 <=> fred = sK6 [avatar definition] 440. fred != sK6 <- (~24) [avatar component clause 438] 441. ~24 | ~22 [avatar split clause 436,418,438] 442. ~prede(alice) | paul != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 312,273] 443. ~prede(alice) | paul != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 442,272] 444. ~prede(alice) | paul != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 443,271] 445. ~prede(alice) | paul != sK6 | ~room(mary) [subsumption resolution 444,270] 446. ~prede(alice) | paul != sK6 [subsumption resolution 445,269] 448. 25 <=> paul = sK6 [avatar definition] 450. paul != sK6 <- (~25) [avatar component clause 448] 451. ~25 | ~22 [avatar split clause 446,418,448] 452. ~prede(alice) | mary != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 311,273] 453. ~prede(alice) | mary != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 452,272] 454. ~prede(alice) | mary != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 453,271] 455. ~prede(alice) | mary != sK6 | ~room(mary) [subsumption resolution 454,270] 456. ~prede(alice) | mary != sK6 [subsumption resolution 455,269] 458. 26 <=> mary = sK6 [avatar definition] 460. mary != sK6 <- (~26) [avatar component clause 458] 461. ~26 | ~22 [avatar split clause 456,418,458] 462. ~prede(alice) | room(sK6) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 310,273] 463. ~prede(alice) | room(sK6) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 462,272] 464. ~prede(alice) | room(sK6) | ~room(paul) | ~room(mary) [subsumption resolution 463,271] 465. ~prede(alice) | room(sK6) | ~room(mary) [subsumption resolution 464,270] 466. ~prede(alice) | room(sK6) [subsumption resolution 465,269] 468. 27 <=> room(sK6) [avatar definition] 470. room(sK6) <- (27) [avatar component clause 468] 471. 27 | ~22 [avatar split clause 466,418,468] 505. ~person(alice) | ~quiet(alice) | prede(alice) [resolution 304,272] 588. ~quieter(lucy,alice) | alice = lucy [resolution 198,306] 593. ~quieter(lucy,alice) [subsumption resolution 588,266] 666. quiet(alice) | prede(alice) | ~room(alice) [resolution 296,593] 672. person(alice) | prede(alice) | ~room(alice) [resolution 297,593] 797. alice = sK6 | fred = sK6 | paul = sK6 | mary = sK6 | john = sK6 <- (27) [resolution 274,470] 840. fred = sK6 | paul = sK6 | mary = sK6 | john = sK6 <- (~23, 27) [subsumption resolution 797,430] 841. paul = sK6 | mary = sK6 | john = sK6 <- (~23, ~24, 27) [subsumption resolution 840,440] 842. mary = sK6 | john = sK6 <- (~23, ~24, ~25, 27) [subsumption resolution 841,450] 843. john = sK6 <- (~23, ~24, ~25, ~26, 27) [subsumption resolution 842,460] 844. $false <- (~21, ~23, ~24, ~25, ~26, 27) [subsumption resolution 843,416] 845. 21 | 23 | 24 | 25 | 26 | ~27 [avatar contradiction clause 844] 846. person(alice) | prede(alice) [subsumption resolution 672,272] 847. 22 | 2 [avatar split clause 846,321,418] 859. ~person(alice) | ~quiet(alice) <- (~22) [subsumption resolution 505,420] 860. ~5 | ~2 | 22 [avatar split clause 859,418,321,336] 890. quiet(alice) | ~room(alice) <- (~22) [subsumption resolution 666,420] 891. quiet(alice) <- (~22) [subsumption resolution 890,272] 892. 5 | 22 [avatar split clause 891,418,336] 901. $false [avatar sat refutation 421,431,441,451,461,471,845,847,860,892] % SZS output end Proof for 4956216663872770574240568 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5500 % Time elapsed: 0.041 s % ------------------------------ % ------------------------------

Bert, Elizabeth are the only persons in the room. Everyone in the room does not host a popular podcast about emerging technologies if they is a dedicated advocate for digital privacy and encryption and uses contact lenses. Everyone in the room who does not host a popular podcast about emerging technologies practices tai chi. Bert does not use contact lenses. Everyone anywhere who practices digital art does not volunteer for local environmental conservation projects. Everyone in the room regularly goes on multi-day backpacking trips in national parks if they does not volunteer for local environmental conservation projects. Everyone in the room practices tai chi if they regularly goes on multi-day backpacking trips in national parks. Elizabeth does not write poetry and travels domestically frequently. Elizabeth who maintains a large, organic vegetable garden year-round is a dedicated advocate for digital privacy and encryption and uses contact lenses. Bert practices tai chi. Everyone in the room who watches fantasy movies is not a client of LVMH, is a client of LVMH and has a curated collection of mid-century modern furniture. Elizabeth is a dedicated advocate for digital privacy and encryption and uses contact lenses. Everyone in the room can play the guitar only if they creates large-scale murals for public art installations. If someone is a wine connoisseur with a private cellar of vintage wines then he/she enjoys rooftop gardening. Elizabeth volunteers for local environmental conservation projects, has a curated collection of mid-century modern furniture or writes poetry.

Elizabeth does not watche fantasy movies.

entailment

room(bert)&room(elizabeth)&(![X]:(room(X)=>(X='bert'|X='elizabeth')))& (![X]:(room(X)=>(((((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))&(uses_contact_lenses(X))))=>(does_not_host_a_popular_podcast_about_emerging_technologies(X))))))& (![X]:(room(X)=>(((does_not_host_a_popular_podcast_about_emerging_technologies(X))=>(practices_tai_chi(X))))))& (does_not_use_contact_lenses(bert))& (![X]:(anywhere(X)=>(((practices_digital_art(X))=>(does_not_volunteer_for_local_environmental_conservation_projects(X))))))& (![X]:(room(X)=>(((does_not_volunteer_for_local_environmental_conservation_projects(X))=>(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))& (![X]:(room(X)=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))=>(practices_tai_chi(X))))))& (((does_not_write_poetry(elizabeth))&(travels_domestically_frequently(elizabeth))))& ((maintains_a_large,_organic_vegetable_garden_year-round(elizabeth))&(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(elizabeth))&(uses_contact_lenses(elizabeth)))))& (practices_tai_chi(bert))& (![X]:(room(X)=>(((watches_fantasy_movies(X))=>(((is_not_a_client_of_LVMH(X))&(is_a_client_of_LVMH(X))&(has_a_curated_collection_of_mid-century_modern_furniture(X))))))))& (((is_a_dedicated_advocate_for_digital_privacy_and_encryption(elizabeth))&(uses_contact_lenses(elizabeth))))& (![X]:(room(X)=>(((creates_large-scale_murals_for_public_art_installations(X))<=(can_play_the_guitar(X))))))& ((![X]:((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(enjoys_rooftop_gardening(X)))))& (((volunteers_for_local_environmental_conservation_projects(elizabeth))|(has_a_curated_collection_of_mid-century_modern_furniture(elizabeth))|(writes_poetry(elizabeth))))

room(bert)&room(elizabeth)&(![X]:(room(X)=>(X='bert'|X='elizabeth')))& does_not_watche_fantasy_movies(elizabeth)

% SZS status Unsatisfiable for 2210331073251987863220113 % SZS output start Proof for 2210331073251987863220113 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 54. ! [X0] : (room(X0) => (predn(X0) => (predq(X0) & predz(X0) & ~predz(X0)))) [input p10] 59. ~(~predn(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 63. ! [X0] : (room(X0) => (predn(X0) => (predz(X0) & ~predz(X0)))) [pure predicate removal 54] 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] 149. ! [X0] : (((predz(X0) & ~predz(X0)) | ~predn(X0)) | ~room(X0)) [ennf transformation 63] 150. ! [X0] : ((predz(X0) & ~predz(X0)) | ~predn(X0) | ~room(X0)) [flattening 149] 151. predn(paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 59] 152. predn(paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 151] 154. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK0 & mary != sK0 & room(sK0)) [choice axiom] 155. predn(paul) | (paul != sK0 & mary != sK0 & room(sK0)) | ~room(paul) | ~room(mary) [skolemisation 152,154] 236. room(mary) [cnf transformation 148] 237. room(paul) [cnf transformation 148] 238. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 148] 241. ~predz(X0) | ~predn(X0) | ~room(X0) [cnf transformation 150] 242. ~predn(X0) | predz(X0) | ~room(X0) [cnf transformation 150] 244. predn(paul) | room(sK0) | ~room(paul) | ~room(mary) [cnf transformation 155] 245. predn(paul) | mary != sK0 | ~room(paul) | ~room(mary) [cnf transformation 155] 246. predn(paul) | paul != sK0 | ~room(paul) | ~room(mary) [cnf transformation 155] 247. ~predn(X0) | ~room(X0) [subsumption resolution 241,242] 248. predn(paul) | paul != sK0 | ~room(mary) [subsumption resolution 246,237] 249. predn(paul) | paul != sK0 [subsumption resolution 248,236] 251. 1 <=> paul = sK0 [avatar definition] 253. paul != sK0 <- (~1) [avatar component clause 251] 255. 2 <=> predn(paul) [avatar definition] 257. predn(paul) <- (2) [avatar component clause 255] 258. ~1 | 2 [avatar split clause 249,255,251] 259. predn(paul) | mary != sK0 | ~room(mary) [subsumption resolution 245,237] 260. predn(paul) | mary != sK0 [subsumption resolution 259,236] 262. 3 <=> mary = sK0 [avatar definition] 264. mary != sK0 <- (~3) [avatar component clause 262] 265. ~3 | 2 [avatar split clause 260,255,262] 266. predn(paul) | room(sK0) | ~room(mary) [subsumption resolution 244,237] 267. predn(paul) | room(sK0) [subsumption resolution 266,236] 269. 4 <=> room(sK0) [avatar definition] 271. room(sK0) <- (4) [avatar component clause 269] 272. 4 | 2 [avatar split clause 267,255,269] 273. ~room(paul) <- (2) [resolution 247,257] 274. $false <- (2) [subsumption resolution 273,237] 275. ~2 [avatar contradiction clause 274] 278. mary = sK0 | paul = sK0 <- (4) [resolution 238,271] 279. paul = sK0 <- (~3, 4) [subsumption resolution 278,264] 280. $false <- (~1, ~3, 4) [subsumption resolution 279,253] 281. 1 | 3 | ~4 [avatar contradiction clause 280] 282. $false [avatar sat refutation 258,265,272,275,281] % SZS output end Proof for 2210331073251987863220113 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Marcus, Frank are the only persons in the room. Everyone in the room does not mentor a youth basketball team on weekends or collects comic books. Everyone in the room collects comic books if they enjoys making ceramics. Everyone in the room who collects comic books is an expert in identifying and foraging wild edible plants. Marcus collects classic novels. Frank who either enjoys windsurfing or practices kickboxing but not both enjoys making ceramics. More than one person in the room is a certified scuba diver with advanced underwater photography skills.

Frank collects comic books.

entailment

room(marcus)&room(frank)&(![X]:(room(X)=>(X='marcus'|X='frank')))& (![X]:(room(X)=>(((collects_comic_books(X))|(does_not_mentor_a_youth_basketball_team_on_weekends(X))))))& (![X]:(room(X)=>(((enjoys_making_ceramics(X))=>(collects_comic_books(X))))))& (![X]:(room(X)=>(((collects_comic_books(X))=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))& (collects_classic_novels(marcus))& ((((enjoys_windsurfing(frank))<~>(practices_kickboxing(frank))))&(enjoys_making_ceramics(frank)))& ((?[X,Y]:(room(X)&room(Y)&(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)&is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(Y))&(X!=Y))))& ((?[X,Y]:(anywhere(X)&anywhere(Y)&(((has_a_specialized_collection_of_handmade_artisan_pottery(X))|(is_a_wine_connoisseur(X))|(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))&((has_a_specialized_collection_of_handmade_artisan_pottery(Y))|(is_a_wine_connoisseur(Y))|(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(Y))))&(X!=Y))))& (![X]:(room(X)=>(((enjoys_making_ceramics(X))<=>(regularly_contributes_to_tech_forums_and_online_communities(X))))))& (is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(frank))& ((![X]:((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))<=>(enjoys_windsurfing(X)))))& ((?[X,Y]:(room(X)&room(Y)&(((enjoys_coding_in_Python(X))&(enjoys_stargazing(X))&(writes_a_travel_blog(X)))&((enjoys_coding_in_Python(Y))&(enjoys_stargazing(Y))&(writes_a_travel_blog(Y))))&(X!=Y))))& (![X]:(room(X)=>(((collects_comic_books(X))=>(((enjoys_stargazing(X))|(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))|(enjoys_watercolor_painting(X))))))))& ((enjoys_wildlife_photography(frank))&(enjoys_stargazing(frank)))& ((?[X,Y]:(room(X)&room(Y)&(((enjoys_stargazing(X))<~>(practices_kickboxing(X)))&((enjoys_stargazing(Y))<~>(practices_kickboxing(Y))))&(X!=Y))))& (![X]:(room(X)=>(((((can_play_the_piano(X))|(enjoys_salsa_dancing(X))|(is_a_Linux_enthusiast(X))))=>(enjoys_stargazing(X))))))& (![X]:(room(X)=>(((enjoys_stargazing(X))=>(enjoys_salsa_dancing(X))))))& (![X]:(room(X)=>(((((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))<~>(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))=>(does_not_stream_on_Twitch(X))))))

room(marcus)&room(frank)&(![X]:(room(X)=>(X='marcus'|X='frank')))& collects_comic_books(frank)

% SZS status Unsatisfiable for 7898075941631781501159034 % SZS output start Proof for 7898075941631781501159034 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 46. ! [X0] : (room(X0) => (predv(X0) => predf(X0))) [input p2] 49. predv(paul) & (predd(paul) <~> prede(paul)) [input p5] 62. ~(predf(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 149. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 150. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 149] 151. ! [X0] : ((predf(X0) | ~predv(X0)) | ~room(X0)) [ennf transformation 46] 152. ! [X0] : (predf(X0) | ~predv(X0) | ~room(X0)) [flattening 151] 159. ~predf(paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 62] 160. ~predf(paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 159] 162. predv(paul) & ((~prede(paul) | ~predd(paul)) & (prede(paul) | predd(paul))) [nnf transformation 49] 163. predv(paul) & (~prede(paul) | ~predd(paul)) & (prede(paul) | predd(paul)) [flattening 162] 175. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK8 & mary != sK8 & room(sK8)) [choice axiom] 176. ~predf(paul) | (paul != sK8 & mary != sK8 & room(sK8)) | ~room(paul) | ~room(mary) [skolemisation 160,175] 257. room(mary) [cnf transformation 150] 258. room(paul) [cnf transformation 150] 259. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 150] 260. ~predv(X0) | predf(X0) | ~room(X0) [cnf transformation 152] 263. predv(paul) [cnf transformation 163] 287. ~predf(paul) | room(sK8) | ~room(paul) | ~room(mary) [cnf transformation 176] 288. ~predf(paul) | mary != sK8 | ~room(paul) | ~room(mary) [cnf transformation 176] 289. ~predf(paul) | paul != sK8 | ~room(paul) | ~room(mary) [cnf transformation 176] 320. ~predf(paul) | paul != sK8 | ~room(mary) [subsumption resolution 289,258] 321. ~predf(paul) | paul != sK8 [subsumption resolution 320,257] 323. 7 <=> paul = sK8 [avatar definition] 325. paul != sK8 <- (~7) [avatar component clause 323] 327. 8 <=> predf(paul) [avatar definition] 330. ~7 | ~8 [avatar split clause 321,327,323] 331. ~predf(paul) | mary != sK8 | ~room(mary) [subsumption resolution 288,258] 332. ~predf(paul) | mary != sK8 [subsumption resolution 331,257] 334. 9 <=> mary = sK8 [avatar definition] 336. mary != sK8 <- (~9) [avatar component clause 334] 337. ~9 | ~8 [avatar split clause 332,327,334] 338. ~predf(paul) | room(sK8) | ~room(mary) [subsumption resolution 287,258] 339. ~predf(paul) | room(sK8) [subsumption resolution 338,257] 341. 10 <=> room(sK8) [avatar definition] 343. room(sK8) <- (10) [avatar component clause 341] 344. 10 | ~8 [avatar split clause 339,327,341] 349. predf(paul) | ~room(paul) [resolution 260,263] 353. predf(paul) [subsumption resolution 349,258] 354. 8 [avatar split clause 353,327] 376. mary = sK8 | paul = sK8 <- (10) [resolution 259,343] 431. paul = sK8 <- (~9, 10) [subsumption resolution 376,336] 432. $false <- (~7, ~9, 10) [subsumption resolution 431,325] 433. 7 | 9 | ~10 [avatar contradiction clause 432] 434. $false [avatar sat refutation 330,337,344,354,433] % SZS output end Proof for 7898075941631781501159034 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5245 % Time elapsed: 0.028 s % ------------------------------ % ------------------------------

There is a room. All calm persons are old. No generous person is funny. Everyone in the room is tall. Everyone outside the room is generous, is funny and is quiet.

All wise persons are tall.

entailment

(there_is_a_room)& (![X]:(calm(X)=>old(X)))& (~?[X]:(generous(X)=>funny(X)))& (![X]:(room(X)=>(tall(X))))& (![X]:(room(X)=>(((patient(X)&person(X))|(old(X)&person(X))|(curious(X))))))& (![X]:(room(X)=>(((funny(X))|(generous(X)&person(X))|(strong(X)&person(X))))))& (![X]:(room(X)=>(calm(X))))& (![X]:(~room(X)=>(((generous(X))&(funny(X))&(quiet(X))))))& (~?[X]:(wise(X)=>patient(X)))& (![X]:(room(X)=>(((humble(X))|(quiet(X)&person(X))|(curious(X)&person(X))))))& (~?[X]:(room(X)=>(~((curious(X))|(calm(X)&person(X))))))& (![X]:(funny(X)=>quiet(X)))

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

% SZS status Unsatisfiable for 2295920786014361885783361 % SZS output start Proof for 2295920786014361885783361 44. there_is_a_room [input p0] 46. ~? [X0] : (generous(X0) => funny(X0)) [input p2] 47. ! [X0] : (room(X0) => tall(X0)) [input p3] 51. ! [X0] : (~room(X0) => (quiet(X0) & funny(X0) & generous(X0))) [input p7] 56. ~(! [X0] : (wise(X0) => tall(X0)) & there_is_a_room) [input hypothesis] 58. ~(! [X0] : tall(X0) & there_is_a_room) [pure predicate removal 56] 64. ! [X0] : (~room(X0) => (quiet(X0) & funny(X0))) [pure predicate removal 51] 65. ~? [X0] : funny(X0) [pure predicate removal 46] 141. ! [X0] : ~funny(X0) [ennf transformation 65] 142. ! [X0] : (tall(X0) | ~room(X0)) [ennf transformation 47] 144. ! [X0] : ((quiet(X0) & funny(X0)) | room(X0)) [ennf transformation 64] 147. ? [X0] : ~tall(X0) | ~there_is_a_room [ennf transformation 58] 149. ? [X0] : ~tall(X0) => ~tall(sK0) [choice axiom] 150. ~tall(sK0) | ~there_is_a_room [skolemisation 147,149] 231. there_is_a_room [cnf transformation 44] 233. ~funny(X0) [cnf transformation 141] 234. ~room(X0) | tall(X0) [cnf transformation 142] 236. funny(X0) | room(X0) [cnf transformation 144] 240. ~tall(sK0) | ~there_is_a_room [cnf transformation 150] 241. room(X0) [subsumption resolution 236,233] 242. ~tall(sK0) [subsumption resolution 240,231] 243. tall(X0) [resolution 234,241] 244. $false [resolution 243,242] % SZS output end Proof for 2295920786014361885783361 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5117 % Time elapsed: 0.033 s % ------------------------------ % ------------------------------

Barbara, Ida, Anthony, Andy, Leo are the only persons in the room. It is not the case that "Barbara neither is an enthusiastic bird watcher who travels for rare sightings nor is not a wine connoisseur with a private cellar of vintage wines". Barbara own a television. Barbara neither uses an ios phone nor travels domestically frequently.

Barbara travels domestically frequently.

contradiction

room(barbara)&room(ida)&room(anthony)&room(andy)&room(leo)&(![X]:(room(X)=>(X='barbara'|X='ida'|X='anthony'|X='andy'|X='leo')))& (~(~((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(barbara))|(is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(barbara)))))& (own_a_television(barbara))& ((barbara_dream=>((barbara_dream=>(is_right-handed(barbara))))))& (has_completed_a_triathlon(barbara))& (does_not_enjoy_kayaking(barbara))& (uses_contact_lenses(barbara))& ((![X]:((is_not_a_tea_enthusiast(X))=>(owns_a_3D_printer(X)))))& ((![X]:((designs_and_sews_custom_cosplay_costumes_for_conventions(X))=>(is_a_tea_enthusiast(X)))))& ((![X]:((((does_not_own_a_television(X))<~>(collects_comic_books(X))))<=>(uses_contact_lenses(X)))))& (is_not_a_tea_enthusiast(barbara))& (makes_homemade_pastries(barbara))& (composes_and_performs_experimental_electronic_music(barbara))& (does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(barbara))& (~((uses_an_ios_phone(barbara))|(travels_domestically_frequently(barbara))))& (~(?[X]:(anywhere(X)&(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X)))))& ((![X]:((enjoys_kayaking(X))=>(does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X)))))& (((own_a_television(barbara))<~>(travels_domestically_frequently(barbara))))

room(barbara)&room(ida)&room(anthony)&room(andy)&room(leo)&(![X]:(room(X)=>(X='barbara'|X='ida'|X='anthony'|X='andy'|X='leo')))& travels_domestically_frequently(barbara)

% SZS status Unsatisfiable for 7758657993756158767919272 % SZS output start Proof for 7758657993756158767919272 58. ~(predb(mary) | predf(mary)) [input p14] 62. predb(mary) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis] 65. ~predb(mary) [pure predicate removal 58] 153. ~predb(mary) [ennf transformation 65] 154. predb(mary) & ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 62] 155. predb(mary) & ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 154] 249. ~predb(mary) [cnf transformation 153] 258. predb(mary) [cnf transformation 155] 259. $false [subsumption resolution 258,249] % SZS output end Proof for 7758657993756158767919272 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Regena, Jerry, Kina are the only persons in the room. If someone does not practice yoga, does not watche fantasy movies or is not a wine connoisseur then he/she does not play eSports competitively. Everyone in the room does not play eSports competitively. If someone does not enjoy deep-sea diving and exploring underwater caves, does not build model airplanes or does not play eSports competitively then he/she does not have lived in exactly three countries.

Regena has lived in exactly three countries.

contradiction

room(regena)&room(jerry)&room(kina)&(![X]:(room(X)=>(X='regena'|X='jerry'|X='kina')))& ((![X]:((((does_not_practice_yoga(X))|(does_not_watche_fantasy_movies(X))|(is_not_a_wine_connoisseur(X))))=>(does_not_play_eSports_competitively(X)))))& (![X]:(room(X)=>(does_not_play_eSports_competitively(X))))& ((![X]:((does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))=>(does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X)))))& (![X]:(room(X)=>(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))))& (![X]:(room(X)=>(((does_not_play_eSports_competitively(X))|(does_not_build_model_airplanes(X))|(does_not_practice_yoga(X))))))& ((![X]:((((does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))|(does_not_build_model_airplanes(X))|(does_not_play_eSports_competitively(X))))=>(does_not_have_lived_in_exactly_three_countries(X)))))& (![X]:(room(X)=>(does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))))& (![X]:(room(X)=>(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))))& (![X]:(room(X)=>(((does_not_enjoy_fishing(X))<~>(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))))))& (![X]:(room(X)=>(is_not_a_wine_connoisseur(X))))& (![X]:(room(X)=>(does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))))& (![X]:(room(X)=>(does_not_collect_antique_jewelry(X))))

room(regena)&room(jerry)&room(kina)&(![X]:(room(X)=>(X='regena'|X='jerry'|X='kina')))& has_lived_in_exactly_three_countries(regena)

% SZS status Unsatisfiable for 7800564018287975815160490 % SZS output start Proof for 7800564018287975815160490 44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0] 46. ! [X0] : (room(X0) => ~predp(X0)) [input p2] 50. ! [X0] : ((~predp(X0) | ~predb(X0) | ~predl(X0)) => ~predh(X0)) [input p6] 57. predh(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis] 133. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44] 134. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 133] 136. ! [X0] : (~predp(X0) | ~room(X0)) [ennf transformation 46] 141. ! [X0] : (~predh(X0) | (predp(X0) & predb(X0) & predl(X0))) [ennf transformation 50] 146. predh(mary) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 57] 147. predh(mary) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 146] 230. room(mary) [cnf transformation 134] 236. ~predp(X0) | ~room(X0) [cnf transformation 136] 242. ~predh(X0) | predp(X0) [cnf transformation 141] 252. predh(mary) [cnf transformation 147] 257. predp(mary) [resolution 242,252] 258. ~room(mary) [resolution 257,236] 261. $false [subsumption resolution 258,230] % SZS output end Proof for 7800564018287975815160490 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Kristen, Keith are the only persons in the room. 'Kristen hosts themed dinner parties featuring gourmet home-cooked meals' if 'everyone in the room develops open-source software projects in their free time or does not enjoy skydiving' and vice versa. Everyone in the room owns a high-end gaming PC with custom-built components. Kristen hosts themed dinner parties featuring gourmet home-cooked meals. Kristen owns an Android phone. Keith owns an Android phone. Everyone in the room does not enjoy skydiving if they either writes and illustrates their own graphic novels or enjoys stargazing but not both. Kristen enjoys skydiving.

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

entailment

room(kristen)&room(keith)&(![X]:(room(X)=>(X='kristen'|X='keith')))& ((![X]:(room(X)=>(((does_not_enjoy_skydiving(X))|(develops_open-source_software_projects_in_their_free_time(X))))))<=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(kristen)))& (![X]:(room(X)=>(owns_a_high-end_gaming_PC_with_custom-built_components(X))))& (hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(kristen))& (owns_an_Android_phone(kristen))& (owns_an_Android_phone(keith))& (![X]:(room(X)=>(((((writes_and_illustrates_their_own_graphic_novels(X))<~>(enjoys_stargazing(X))))=>(does_not_enjoy_skydiving(X))))))& (![X]:(room(X)=>(((does_not_enjoy_skydiving(X))=>(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))& (![X]:(room(X)=>(((does_not_enjoy_stargazing(X))=>(does_not_stream_on_Twitch(X))))))& (![X]:(room(X)=>(((does_not_stream_on_Twitch(X))=>(~((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))|(does_not_write_and_illustrates_their_own_graphic_novels(X))))))))& (hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(keith))& (?[X]:(room(X)&(is_a_member_of_a_local_theater_group_specializing_in_improv(X))))& (has_a_pet_dog(kristen))& (enjoys_skydiving(kristen))& (![X]:(room(X)=>(((enjoys_skydiving(X))=>(owns_an_Android_phone(X))))))& (![X]:(room(X)=>(((develops_open-source_software_projects_in_their_free_time(X))=>(((collects_action_figures(X))|(does_not_collect_first_edition_books(X))))))))& (![X]:(room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))|(owns_an_Android_phone(X))))))))& (((develops_open-source_software_projects_in_their_free_time(keith))|(owns_an_Android_phone(keith))))

room(kristen)&room(keith)&(![X]:(room(X)=>(X='kristen'|X='keith')))& develops_open-source_software_projects_in_their_free_time(kristen)

% SZS status Unsatisfiable for 7387322098234198038910677 % SZS output start Proof for 7387322098234198038910677 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 45. ! [X0] : (room(X0) => (predl(X0) | ~predx(X0))) <=> predh(mary) [input p1] 47. predh(mary) [input p3] 57. predx(mary) [input p13] 62. ~(predl(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 145. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 146. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 145] 147. ! [X0] : ((predl(X0) | ~predx(X0)) | ~room(X0)) <=> predh(mary) [ennf transformation 45] 148. ! [X0] : (predl(X0) | ~predx(X0) | ~room(X0)) <=> predh(mary) [flattening 147] 155. ~predl(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 62] 156. ~predl(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 155] 158. (! [X0] : (predl(X0) | ~predx(X0) | ~room(X0)) | ~predh(mary)) & (predh(mary) | ? [X0] : (~predl(X0) & predx(X0) & room(X0))) [nnf transformation 148] 159. (! [X0] : (predl(X0) | ~predx(X0) | ~room(X0)) | ~predh(mary)) & (predh(mary) | ? [X1] : (~predl(X1) & predx(X1) & room(X1))) [rectify 158] 160. ? [X1] : (~predl(X1) & predx(X1) & room(X1)) => (~predl(sK0) & predx(sK0) & room(sK0)) [choice axiom] 161. (! [X0] : (predl(X0) | ~predx(X0) | ~room(X0)) | ~predh(mary)) & (predh(mary) | (~predl(sK0) & predx(sK0) & room(sK0))) [skolemisation 159,160] 165. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK2 & mary != sK2 & room(sK2)) [choice axiom] 166. ~predl(mary) | (paul != sK2 & mary != sK2 & room(sK2)) | ~room(paul) | ~room(mary) [skolemisation 156,165] 247. room(mary) [cnf transformation 146] 248. room(paul) [cnf transformation 146] 249. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 146] 253. predl(X0) | ~predx(X0) | ~room(X0) | ~predh(mary) [cnf transformation 161] 254. predh(mary) [cnf transformation 47] 262. predx(mary) [cnf transformation 57] 263. ~predl(mary) | room(sK2) | ~room(paul) | ~room(mary) [cnf transformation 166] 264. ~predl(mary) | mary != sK2 | ~room(paul) | ~room(mary) [cnf transformation 166] 265. ~predl(mary) | paul != sK2 | ~room(paul) | ~room(mary) [cnf transformation 166] 267. 1 <=> predh(mary) [avatar definition] 271. 2 <=> ! [X0] : (predl(X0) | ~room(X0) | ~predx(X0)) [avatar definition] 272. ~predx(X0) | ~room(X0) | predl(X0) <- (2) [avatar component clause 271] 273. ~1 | 2 [avatar split clause 253,271,267] 289. 1 [avatar split clause 254,267] 290. ~predl(mary) | paul != sK2 | ~room(mary) [subsumption resolution 265,248] 291. ~predl(mary) | paul != sK2 [subsumption resolution 290,247] 293. 6 <=> paul = sK2 [avatar definition] 295. paul != sK2 <- (~6) [avatar component clause 293] 297. 7 <=> predl(mary) [avatar definition] 300. ~6 | ~7 [avatar split clause 291,297,293] 301. ~predl(mary) | mary != sK2 | ~room(mary) [subsumption resolution 264,248] 302. ~predl(mary) | mary != sK2 [subsumption resolution 301,247] 304. 8 <=> mary = sK2 [avatar definition] 306. mary != sK2 <- (~8) [avatar component clause 304] 307. ~8 | ~7 [avatar split clause 302,297,304] 308. ~predl(mary) | room(sK2) | ~room(mary) [subsumption resolution 263,248] 309. ~predl(mary) | room(sK2) [subsumption resolution 308,247] 311. 9 <=> room(sK2) [avatar definition] 313. room(sK2) <- (9) [avatar component clause 311] 314. 9 | ~7 [avatar split clause 309,297,311] 333. ~room(mary) | predl(mary) <- (2) [resolution 272,262] 334. predl(mary) <- (2) [subsumption resolution 333,247] 337. 7 | ~2 [avatar split clause 334,271,297] 353. mary = sK2 | paul = sK2 <- (9) [resolution 249,313] 363. paul = sK2 <- (~8, 9) [subsumption resolution 353,306] 364. $false <- (~6, ~8, 9) [subsumption resolution 363,295] 365. 6 | 8 | ~9 [avatar contradiction clause 364] 366. $false [avatar sat refutation 273,289,300,307,314,337,365] % SZS output end Proof for 7387322098234198038910677 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 % ------------------------------ % ------------------------------

Roman, Mallory are the only persons in the room. If everyone in the room does not frequently participates in hackathons and coding competitions or develops open-source software projects in their free time then everyone anywhere who is allergic to anything does not enjoy virtual reality gaming otherwise if someone practices kickboxing, enjoys bird watching and hosts regular workshops on creative writing then he/she does not enjoy cross-country skiing, is allergic to anything or practices kickboxing. Everyone in the room is allergic to anything. Everyone anywhere who is allergic to anything collect rare sneakers.

Mallory collect rare sneakers.

entailment

room(roman)&room(mallory)&(![X]:(room(X)=>(X='roman'|X='mallory')))& (((![X]:(room(X)=>(((develops_open-source_software_projects_in_their_free_time(X))|(does_not_frequently_participates_in_hackathons_and_coding_competitions(X))))))=>(![X]:(anywhere(X)=>(((is_allergic_to_anything(X))=>(does_not_enjoy_virtual_reality_gaming(X)))))))&((~(![X]:(room(X)=>(((develops_open-source_software_projects_in_their_free_time(X))|(does_not_frequently_participates_in_hackathons_and_coding_competitions(X)))))))=>((![X]:((((practices_kickboxing(X))&(enjoys_bird_watching(X))&(hosts_regular_workshops_on_creative_writing(X))))=>(((does_not_enjoy_cross-country_skiing(X))|(is_allergic_to_anything(X))|(practices_kickboxing(X)))))))))& ((![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))|(does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))))))=>(~![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))<=(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X)))))))& ((![X]:(room(X)=>(((develops_open-source_software_projects_in_their_free_time(X))|(is_not_allergic_to_anything(X))))))=>(![X]:(room(X)=>(((is_not_allergic_to_anything(X))=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))<~>(enjoys_virtual_reality_gaming(X)))))))))& ((![X]:(room(X)=>(((does_not_practice_kickboxing(X))|(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))=>(![X]:(room(X)=>(((does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))<=(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X)))))))& ((![X]:(~room(X)=>(((has_a_pet_dog(X))|(cannot_play_the_guitar(X))))))=>(![X]:(room(X)=>(((cannot_play_the_guitar(X))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X)))))))& ((![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))|(does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))))))=>(![X]:(room(X)=>(((enjoys_virtual_reality_gaming(X))<=(does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X)))))))& ((![X]:(room(X)=>(((does_not_read_mystery_novels(X))|(is_not_a_client_of_LVMH(X))))))=>(![X]:(~room(X)=>(((practices_kickboxing(X))<=(does_practice_yoga(X)))))))& (![X]:(~room(X)=>(((practices_kickboxing(X))<=(does_practice_yoga(X))))))& (![X]:(room(X)=>(is_allergic_to_anything(X))))& (~![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))<=(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))& (![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))& ((![X]:((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(practices_kickboxing(X)))))& (![X]:(anywhere(X)=>(((is_allergic_to_anything(X))=>(collect_rare_sneakers(X))))))& ((![X]:((((enjoys_camping_and_organizing_outdoor_survival_workshops(X))|(enjoys_kayaking(X))))=>(owns_a_smart_tv(X)))))& ((((reads_mystery_novels(mallory))|(enjoys_bird_watching(mallory))))&(owns_a_high-end_gaming_PC_with_custom-built_components(mallory)))& (![X]:(room(X)=>(((((is_a_client_of_LVMH(X))|(reads_mystery_novels(X))|(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))=>(((enjoys_cross-country_skiing(X))&(has_a_pet_dog(X))&(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))))& (![X]:(~room(X)=>(((((enjoys_cross-country_skiing(X))&(has_a_pet_dog(X))&(owns_a_high-end_gaming_PC_with_custom-built_components(X))))=>(collect_rare_sneakers(X))))))& (~![X]:(room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))=>(collects_limited-edition_art_prints_from_contemporary_artists(X))))))& (~![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))<=>(is_a_client_of_LVMH(X))))))& (![X]:(room(X)=>(((is_a_client_of_LVMH(X))=>(can_play_the_guitar(X))))))& (![X]:(room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))|(does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))))))& (![X]:(room(X)=>(((cannot_play_the_guitar(X))<=(is_a_client_of_LVMH(X))))))& (((?[X]:(~room(X)&reads_mystery_novels(X)))))& (~![X]:(room(X)=>(((does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))=>(develops_open-source_software_projects_in_their_free_time(X))))))& (![X]:(room(X)=>(((does_not_own_a_smart_tv(X))=>(enjoys_bird_watching(X))))))

room(roman)&room(mallory)&(![X]:(room(X)=>(X='roman'|X='mallory')))& collect_rare_sneakers(mallory)

% SZS status Unsatisfiable for 7840292824570745902712625 % SZS output start Proof for 7840292824570745902712625 5. ! [X0] : anywhere(X0) [input b4] 44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0] 53. ! [X0] : (room(X0) => predz(X0)) [input p9] 57. ! [X0] : (anywhere(X0) => (predz(X0) => predp(X0))) [input p13] 70. ~(predp(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis] 167. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44] 168. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 167] 177. ! [X0] : (predz(X0) | ~room(X0)) [ennf transformation 53] 179. ! [X0] : ((predp(X0) | ~predz(X0)) | ~anywhere(X0)) [ennf transformation 57] 180. ! [X0] : (predp(X0) | ~predz(X0) | ~anywhere(X0)) [flattening 179] 194. ~predp(paul) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 70] 195. ~predp(paul) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 194] 226. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK11 & mary != sK11 & room(sK11)) [choice axiom] 227. ~predp(paul) | (paul != sK11 & mary != sK11 & room(sK11)) | ~room(paul) | ~room(mary) [skolemisation 195,226] 228. anywhere(X0) [cnf transformation 5] 309. room(mary) [cnf transformation 168] 310. room(paul) [cnf transformation 168] 311. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 168] 326. ~room(X0) | predz(X0) [cnf transformation 177] 329. predp(X0) | ~predz(X0) | ~anywhere(X0) [cnf transformation 180] 349. ~predp(paul) | room(sK11) | ~room(paul) | ~room(mary) [cnf transformation 227] 350. ~predp(paul) | mary != sK11 | ~room(paul) | ~room(mary) [cnf transformation 227] 351. ~predp(paul) | paul != sK11 | ~room(paul) | ~room(mary) [cnf transformation 227] 419. ~predz(X0) | predp(X0) [subsumption resolution 329,228] 431. ~predp(paul) | paul != sK11 | ~room(mary) [subsumption resolution 351,310] 432. ~predp(paul) | paul != sK11 [subsumption resolution 431,309] 434. 17 <=> paul = sK11 [avatar definition] 436. paul != sK11 <- (~17) [avatar component clause 434] 438. 18 <=> predp(paul) [avatar definition] 441. ~17 | ~18 [avatar split clause 432,438,434] 442. ~predp(paul) | mary != sK11 | ~room(mary) [subsumption resolution 350,310] 443. ~predp(paul) | mary != sK11 [subsumption resolution 442,309] 445. 19 <=> mary = sK11 [avatar definition] 447. mary != sK11 <- (~19) [avatar component clause 445] 448. ~19 | ~18 [avatar split clause 443,438,445] 449. ~predp(paul) | room(sK11) | ~room(mary) [subsumption resolution 349,310] 450. ~predp(paul) | room(sK11) [subsumption resolution 449,309] 452. 20 <=> room(sK11) [avatar definition] 454. room(sK11) <- (20) [avatar component clause 452] 455. 20 | ~18 [avatar split clause 450,438,452] 457. predz(paul) [resolution 326,310] 465. predp(paul) [resolution 419,457] 472. 18 [avatar split clause 465,438] 742. mary = sK11 | paul = sK11 <- (20) [resolution 311,454] 788. paul = sK11 <- (~19, 20) [subsumption resolution 742,447] 789. $false <- (~17, ~19, 20) [subsumption resolution 788,436] 790. 17 | 19 | ~20 [avatar contradiction clause 789] 791. $false [avatar sat refutation 441,448,455,472,790] % SZS output end Proof for 7840292824570745902712625 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5500 % Time elapsed: 0.037 s % ------------------------------ % ------------------------------

Sonya, Sandy, David, Donna are the only persons in the room. 'Sonya own a television' only if 'David owns a 3D printer'. If 'Donna bakes bread at home' then 'everyone outside the room who enjoys kayaking bakes bread at home'.

Donna bakes bread at home.

neutral

room(sonya)&room(sandy)&room(david)&room(donna)&(![X]:(room(X)=>(X='sonya'|X='sandy'|X='david'|X='donna')))& ((own_a_television(sonya))=>(owns_a_3D_printer(david)))& ((bakes_bread_at_home(donna))=>(![X]:(~room(X)=>(((enjoys_kayaking(X))=>(bakes_bread_at_home(X)))))))& ((enjoys_kayaking(donna))<~>(![X]:(room(X)=>(((does_not_own_a_television(X))|(bakes_bread_at_home(X)))))))& ((own_a_television(sonya))=>(~?[X]:(room(X)=>(((bakes_bread_at_home(X))=>(enjoys_kayaking(X)))))))& ((![X]:(room(X)=>(((enjoys_kayaking(X))|(does_not_own_a_3D_printer(X))))))=>(![X]:(room(X)=>(((does_not_own_a_3D_printer(X))=>(own_a_television(X)))))))& (owns_a_3D_printer(sandy))& (~(own_a_television(donna)))& (![X]:(room(X)=>(((owns_a_3D_printer(X))|(does_not_volunteer_for_local_environmental_conservation_projects(X))))))& (![X]:(anywhere(X)=>(((does_not_volunteer_for_local_environmental_conservation_projects(X))=>(bakes_bread_at_home(X))))))& (![X]:(room(X)=>(((does_not_enjoy_kayaking(X))|(enjoys_kayaking(X))))))& (![X]:(room(X)=>(((owns_a_3D_printer(X))|(does_not_own_a_3D_printer(X))))))& (![X]:(room(X)=>(((does_not_own_a_3D_printer(X))=>(own_a_television(X))))))

room(sonya)&room(sandy)&room(david)&room(donna)&(![X]:(room(X)=>(X='sonya'|X='sandy'|X='david'|X='donna')))& bakes_bread_at_home(donna)

Mindy, Mariann, Nikki, Pam, Bradford are the only persons in the room. If “everyone in the room owns an Android phone or does not own a 3D printer” then “everyone in the room writes in-depth travel guides for off-the-beaten-path destinations if they maintains a large, organic vegetable garden year-round and vice versa”. “Everyone in the room has a tattoo” only if “only one person in the room can play the harmonica and owns an Android phone”. If “everyone in the room enjoys rooftop gardening or does not create YouTube content” then “someone anywhere does not play as a goalkeeper for a local amateur soccer team and owns a microscope”. If “everyone in the room can play the harmonica or does not have a tattoo” then “no one in the room owns a microscope”. “Everyone in the room does not practice urban gardening or does not travel domestically frequently” only if “someone in the room does not enjoy logic puzzles”. Everyone in the room can play the guitar if they does not practice urban gardening. If someone collects comic books then he/she owns a smart tv. Everyone in the room does not own a smartwatch if they owns a smartwatch and does not own a smartwatch. Everyone in the room does not own a smartwatch if they collect rare sneakers and vice versa. Not everyone outside the room collects rare minerals or works as a freelance web developer specializing in e-commerce sites or both if they collect rare sneakers. Everyone in the room who collects rare minerals or works as a freelance web developer specializing in e-commerce sites or both does not play as a goalkeeper for a local amateur soccer team or enjoys macrame or both. Everyone in the room travels domestically frequently. Everyone in the room collects rare minerals if they travels domestically frequently. Everyone in the room plays as a goalkeeper for a local amateur soccer team.

Mindy enjoys macrame.

entailment

room(mindy)&room(mariann)&room(nikki)&room(pam)&room(bradford)&(![X]:(room(X)=>(X='mindy'|X='mariann'|X='nikki'|X='pam'|X='bradford')))& ((![X]:(room(X)=>(((does_not_own_a_3D_printer(X))|(owns_an_Android_phone(X))))))=>(![X]:(room(X)=>(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))<=>(maintains_a_large,_organic_vegetable_garden_year-round(X)))))))& ((![X]:(room(X)=>(has_a_tattoo(X))))=>(((?[X]:(room(X)&((can_play_the_harmonica(X))&(owns_an_Android_phone(X)))))&(![X,Y]:((room(X)&room(Y)&(((can_play_the_harmonica(X))&(owns_an_Android_phone(X))))&(((can_play_the_harmonica(Y))&(owns_an_Android_phone(Y)))))=>(X=Y))))))& ((![X]:(room(X)=>(((does_not_create_YouTube_content(X))|(enjoys_rooftop_gardening(X))))))=>(?[X]:(anywhere(X)&(((does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))&(owns_a_microscope(X)))))))& ((![X]:(room(X)=>(((does_not_have_a_tattoo(X))|(can_play_the_harmonica(X))))))=>(~?[X]:(room(X)=>(owns_a_microscope(X)))))& ((![X]:(room(X)=>(((does_not_travel_domestically_frequently(X))|(does_not_practice_urban_gardening(X))))))=>(?[X]:(room(X)&(does_not_enjoy_logic_puzzles(X)))))& (![X]:(room(X)=>(((does_not_practice_urban_gardening(X))=>(can_play_the_guitar(X))))))& ((![X]:((collects_comic_books(X))=>(owns_a_smart_tv(X)))))& (![X]:(room(X)=>(((((owns_a_smartwatch(X))&(does_not_own_a_smartwatch(X))))=>(does_not_own_a_smartwatch(X))))))& (![X]:(room(X)=>(((does_not_own_a_smartwatch(X))<=>(collect_rare_sneakers(X))))))& (~![X]:(~room(X)=>(((collect_rare_sneakers(X))=>(((collects_rare_minerals(X))|(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))))& (![X]:(room(X)=>(((((collects_rare_minerals(X))|(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))=>(((does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))|(enjoys_macrame(X))))))))& (![X]:(anywhere(X)=>(((((does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))|(enjoys_macrame(X))))=>(((does_not_own_a_smart_tv(X))|(collects_comic_books(X))))))))& (![X]:(room(X)=>(creates_YouTube_content(X))))& (![X]:(~room(X)=>(does_not_travel_domestically_frequently(X))))& (~![X]:(room(X)=>(((owns_a_smart_tv(X))=>(((can_play_the_harmonica(X))&(enjoys_logic_puzzles(X))))))))& (![X]:(room(X)=>(travels_domestically_frequently(X))))& (~![X]:(room(X)=>(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))& (![X]:(room(X)=>(((travels_domestically_frequently(X))=>(collects_rare_minerals(X))))))& ((![X]:((((can_play_the_guitar(X))|(owns_an_Android_phone(X))))=>(travels_domestically_frequently(X)))))& (?[X]:(room(X)&(does_not_enjoy_logic_puzzles(X))))& ((?[X,Y]:(room(X)&room(Y)&(has_a_tattoo(X)&has_a_tattoo(Y))&(X!=Y))))& (![X]:(room(X)=>(((streams_on_Twitch(X))=>(does_not_enjoy_logic_puzzles(X))))))& (![X]:(room(X)=>(((owns_a_smartwatch(X))=>(owns_an_Android_phone(X))))))& (![X]:(room(X)=>(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))<=>(maintains_a_large,_organic_vegetable_garden_year-round(X))))))& (![X]:(room(X)=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))

room(mindy)&room(mariann)&room(nikki)&room(pam)&room(bradford)&(![X]:(room(X)=>(X='mindy'|X='mariann'|X='nikki'|X='pam'|X='bradford')))& enjoys_macrame(mindy)

% SZS status Unsatisfiable for 3003197669531580850321461 % SZS output start Proof for 3003197669531580850321461 44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0] 55. ! [X0] : (room(X0) => ((predf(X0) | predk(X0)) => (predc(X0) | ~predv(X0)))) [input p11] 60. ! [X0] : (room(X0) => predh(X0)) [input p16] 62. ! [X0] : (room(X0) => (predh(X0) => predk(X0))) [input p18] 69. ! [X0] : (room(X0) => predv(X0)) [input p25] 70. ~(predc(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] 78. ! [X0] : (room(X0) => (predk(X0) => (predc(X0) | ~predv(X0)))) [pure predicate removal 55] 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] 175. ! [X0] : (((predc(X0) | ~predv(X0)) | ~predk(X0)) | ~room(X0)) [ennf transformation 78] 176. ! [X0] : (predc(X0) | ~predv(X0) | ~predk(X0) | ~room(X0)) [flattening 175] 181. ! [X0] : (predh(X0) | ~room(X0)) [ennf transformation 60] 183. ! [X0] : ((predk(X0) | ~predh(X0)) | ~room(X0)) [ennf transformation 62] 184. ! [X0] : (predk(X0) | ~predh(X0) | ~room(X0)) [flattening 183] 189. ! [X0] : (predv(X0) | ~room(X0)) [ennf transformation 69] 190. ~predc(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 70] 191. ~predc(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 190] 224. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK14 & alice != sK14 & fred != sK14 & paul != sK14 & mary != sK14 & room(sK14)) [choice axiom] 225. ~predc(mary) | (john != sK14 & alice != sK14 & fred != sK14 & paul != sK14 & mary != sK14 & room(sK14)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 191,224] 307. room(mary) [cnf transformation 161] 308. room(paul) [cnf transformation 161] 309. room(fred) [cnf transformation 161] 310. room(alice) [cnf transformation 161] 311. room(john) [cnf transformation 161] 312. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 161] 343. ~predk(X0) | ~predv(X0) | predc(X0) | ~room(X0) [cnf transformation 176] 349. ~room(X0) | predh(X0) [cnf transformation 181] 352. predk(X0) | ~predh(X0) | ~room(X0) [cnf transformation 184] 363. ~room(X0) | predv(X0) [cnf transformation 189] 364. ~predc(mary) | room(sK14) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 225] 365. ~predc(mary) | mary != sK14 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 225] 366. ~predc(mary) | paul != sK14 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 225] 367. ~predc(mary) | fred != sK14 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 225] 368. ~predc(mary) | alice != sK14 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 225] 369. ~predc(mary) | john != sK14 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 225] 474. ~room(X0) | predk(X0) [subsumption resolution 352,349] 477. ~predc(mary) | john != sK14 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 369,311] 478. ~predc(mary) | john != sK14 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 477,310] 479. ~predc(mary) | john != sK14 | ~room(paul) | ~room(mary) [subsumption resolution 478,309] 480. ~predc(mary) | john != sK14 | ~room(mary) [subsumption resolution 479,308] 481. ~predc(mary) | john != sK14 [subsumption resolution 480,307] 483. 22 <=> john = sK14 [avatar definition] 485. john != sK14 <- (~22) [avatar component clause 483] 487. 23 <=> predc(mary) [avatar definition] 490. ~22 | ~23 [avatar split clause 481,487,483] 491. ~predc(mary) | alice != sK14 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 368,311] 492. ~predc(mary) | alice != sK14 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 491,310] 493. ~predc(mary) | alice != sK14 | ~room(paul) | ~room(mary) [subsumption resolution 492,309] 494. ~predc(mary) | alice != sK14 | ~room(mary) [subsumption resolution 493,308] 495. ~predc(mary) | alice != sK14 [subsumption resolution 494,307] 497. 24 <=> alice = sK14 [avatar definition] 499. alice != sK14 <- (~24) [avatar component clause 497] 500. ~24 | ~23 [avatar split clause 495,487,497] 501. ~predc(mary) | fred != sK14 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 367,311] 502. ~predc(mary) | fred != sK14 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 501,310] 503. ~predc(mary) | fred != sK14 | ~room(paul) | ~room(mary) [subsumption resolution 502,309] 504. ~predc(mary) | fred != sK14 | ~room(mary) [subsumption resolution 503,308] 505. ~predc(mary) | fred != sK14 [subsumption resolution 504,307] 507. 25 <=> fred = sK14 [avatar definition] 509. fred != sK14 <- (~25) [avatar component clause 507] 510. ~25 | ~23 [avatar split clause 505,487,507] 511. ~predc(mary) | paul != sK14 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 366,311] 512. ~predc(mary) | paul != sK14 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 511,310] 513. ~predc(mary) | paul != sK14 | ~room(paul) | ~room(mary) [subsumption resolution 512,309] 514. ~predc(mary) | paul != sK14 | ~room(mary) [subsumption resolution 513,308] 515. ~predc(mary) | paul != sK14 [subsumption resolution 514,307] 517. 26 <=> paul = sK14 [avatar definition] 519. paul != sK14 <- (~26) [avatar component clause 517] 520. ~26 | ~23 [avatar split clause 515,487,517] 521. ~predc(mary) | mary != sK14 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 365,311] 522. ~predc(mary) | mary != sK14 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 521,310] 523. ~predc(mary) | mary != sK14 | ~room(paul) | ~room(mary) [subsumption resolution 522,309] 524. ~predc(mary) | mary != sK14 | ~room(mary) [subsumption resolution 523,308] 525. ~predc(mary) | mary != sK14 [subsumption resolution 524,307] 527. 27 <=> mary = sK14 [avatar definition] 529. mary != sK14 <- (~27) [avatar component clause 527] 530. ~27 | ~23 [avatar split clause 525,487,527] 531. ~predc(mary) | room(sK14) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 364,311] 532. ~predc(mary) | room(sK14) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 531,310] 533. ~predc(mary) | room(sK14) | ~room(paul) | ~room(mary) [subsumption resolution 532,309] 534. ~predc(mary) | room(sK14) | ~room(mary) [subsumption resolution 533,308] 535. ~predc(mary) | room(sK14) [subsumption resolution 534,307] 537. 28 <=> room(sK14) [avatar definition] 539. room(sK14) <- (28) [avatar component clause 537] 540. 28 | ~23 [avatar split clause 535,487,537] 557. predv(mary) [resolution 363,307] 572. predk(mary) [resolution 474,307] 796. ~predv(mary) | predc(mary) | ~room(mary) [resolution 572,343] 797. predc(mary) | ~room(mary) [subsumption resolution 796,557] 801. predc(mary) [subsumption resolution 797,307] 802. 23 [avatar split clause 801,487] 925. alice = sK14 | fred = sK14 | paul = sK14 | mary = sK14 | john = sK14 <- (28) [resolution 312,539] 1115. fred = sK14 | paul = sK14 | mary = sK14 | john = sK14 <- (~24, 28) [subsumption resolution 925,499] 1116. paul = sK14 | mary = sK14 | john = sK14 <- (~24, ~25, 28) [subsumption resolution 1115,509] 1117. mary = sK14 | john = sK14 <- (~24, ~25, ~26, 28) [subsumption resolution 1116,519] 1118. john = sK14 <- (~24, ~25, ~26, ~27, 28) [subsumption resolution 1117,529] 1119. $false <- (~22, ~24, ~25, ~26, ~27, 28) [subsumption resolution 1118,485] 1120. 22 | 24 | 25 | 26 | 27 | ~28 [avatar contradiction clause 1119] 1121. $false [avatar sat refutation 490,500,510,520,530,540,802,1120] % SZS output end Proof for 3003197669531580850321461 % ------------------------------ % Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000) % Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44 % Termination reason: Refutation % Memory used [KB]: 5628 % Time elapsed: 0.041 s % ------------------------------ % ------------------------------