premise
stringlengths 12
3.12k
| hypothesis
stringlengths 10
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stringclasses 3
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stringlengths 51
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| hypothesis_tptp
stringlengths 41
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sequencelengths 0
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| proof
stringlengths 767
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⌀ | rule_concentration
float64 0
0.72
|
---|---|---|---|---|---|---|---|
There is a room.
“Everyone in the room can play the guitar only if they is not an avid mountain climber who has scaled several peaks” if “everyone outside the room is not a member of a local theater group specializing in improv or can play the guitar”.
Everyone in the room who is not an avid mountain climber who has scaled several peaks collects antique jewelry.
Everyone in the room does not know morse code or does not enjoy fishing.
If someone enjoys watercolor painting then he/she plays eSports competitively.
Everyone outside the room is not a member of a local theater group specializing in improv or can play the guitar.
Not everyone outside the room who neither can play the guitar nor is an avid mountain climber who has scaled several peaks is an amateur astronomer who builds and uses custom telescopes.
Everyone in the room who is an amateur astronomer who builds and uses custom telescopes either enjoys watercolor painting or enjoys macrame but not both.
Everyone in the room who enjoys watercolor painting is a cybersecurity expert.
Everyone in the room enjoys snowboarding if they is a cybersecurity expert.
If someone is an avid mountain climber who has scaled several peaks then he/she either does not own a 3D printer or does not maintain a large, organic vegetable garden year-round but not both and vice versa.
Everyone in the room can play the guitar only if they is not an avid mountain climber who has scaled several peaks.
If someone practices and performs acrobatic dance routines then he/she enjoys fishing and vice versa.
Everyone in the room can play the guitar if they enjoys macrame. | Everyone outside the room is an amateur astronomer who builds and uses custom telescopes. | contradiction | (there_is_a_room)&
((![X]:(~room(X)=>(((can_play_the_guitar(X))|(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))))))=>(![X]:(room(X)=>(((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))<=(can_play_the_guitar(X)))))))&
(![X]:(room(X)=>(((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(collects_antique_jewelry(X))))))&
(![X]:(room(X)=>(((does_not_enjoy_fishing(X))|(does_not_know_morse_code(X))))))&
((![X]:((enjoys_watercolor_painting(X))=>(plays_eSports_competitively(X)))))&
(![X]:(~room(X)=>(((can_play_the_guitar(X))|(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))))))&
(~![X]:(~room(X)=>(((~((can_play_the_guitar(X))|(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))=>(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))&
(![X]:(room(X)=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))=>(((enjoys_watercolor_painting(X))<~>(enjoys_macrame(X))))))))&
(![X]:(room(X)=>(((enjoys_watercolor_painting(X))=>(is_a_cybersecurity_expert(X))))))&
(![X]:(room(X)=>(((is_a_cybersecurity_expert(X))=>(enjoys_snowboarding(X))))))&
((![X]:((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))<=>(((does_not_own_a_3D_printer(X))<~>(does_not_maintain_a_large,_organic_vegetable_garden_year-round(X)))))))&
(![X]:(room(X)=>(((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))<=(can_play_the_guitar(X))))))&
((![X]:((practices_and_performs_acrobatic_dance_routines(X))<=>(enjoys_fishing(X)))))&
(![X]:(room(X)=>(((enjoys_macrame(X))=>(can_play_the_guitar(X)))))) | (there_is_a_room)&
![X]:(~room(X)=>(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 3379417077651704808702086
% SZS output start Proof for 3379417077651704808702086
50. ~! [X0] : (~room(X0) => (~(predy(X0) | predz(X0)) => predc(X0))) [input p6]
58. ! [X0] : (~room(X0) => predc(X0)) & there_is_a_room [input hypothesis]
65. ! [X0] : (~room(X0) => predc(X0)) [pure predicate removal 58]
144. ? [X0] : ((~predc(X0) & (~predy(X0) & ~predz(X0))) & ~room(X0)) [ennf transformation 50]
145. ? [X0] : (~predc(X0) & ~predy(X0) & ~predz(X0) & ~room(X0)) [flattening 144]
153. ! [X0] : (predc(X0) | room(X0)) [ennf transformation 65]
158. ? [X0] : (~predc(X0) & ~predy(X0) & ~predz(X0) & ~room(X0)) => (~predc(sK1) & ~predy(sK1) & ~predz(sK1) & ~room(sK1)) [choice axiom]
159. ~predc(sK1) & ~predy(sK1) & ~predz(sK1) & ~room(sK1) [skolemisation 145,158]
246. ~room(sK1) [cnf transformation 159]
249. ~predc(sK1) [cnf transformation 159]
256. predc(X0) | room(X0) [cnf transformation 153]
276. room(sK1) [resolution 256,249]
277. $false [subsumption resolution 276,246]
% SZS output end Proof for 3379417077651704808702086
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Lee is the only person in the room.
Everyone in the room owns a smart tv if they is a client of LVMH.
Lee practices urban gardening.
Everyone in the room neither is a client of LVMH nor travels domestically frequently if they enjoys snowboarding.
Everyone anywhere travels domestically frequently if they owns a high-end gaming PC with custom-built components.
Everyone anywhere who travels domestically frequently is a client of LVMH.
Lee is a skilled home brewer experimenting with craft beer recipes.
Everyone in the room who either writes and illustrates their own graphic novels or is a Linux enthusiast but not both is a skilled home brewer experimenting with craft beer recipes.
Lee travels domestically frequently.
Everyone in the room watches fantasy movies.
Everyone in the room who writes and illustrates their own graphic novels watches fantasy movies. | Lee owns a smart tv. | entailment | room(lee)&(![X]:(room(X)=>(X='lee')))&
(![X]:(room(X)=>(((is_a_client_of_LVMH(X))=>(owns_a_smart_tv(X))))))&
(practices_urban_gardening(lee))&
(![X]:(room(X)=>(((enjoys_snowboarding(X))=>(~((is_a_client_of_LVMH(X))|(travels_domestically_frequently(X))))))))&
(![X]:(anywhere(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))=>(travels_domestically_frequently(X))))))&
(![X]:(anywhere(X)=>(((travels_domestically_frequently(X))=>(is_a_client_of_LVMH(X))))))&
(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(lee))&
(![X]:(room(X)=>(((((writes_and_illustrates_their_own_graphic_novels(X))<~>(is_a_Linux_enthusiast(X))))=>(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))))&
(travels_domestically_frequently(lee))&
(![X]:(room(X)=>(watches_fantasy_movies(X))))&
(![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))=>(watches_fantasy_movies(X)))))) | room(lee)&(![X]:(room(X)=>(X='lee')))&
owns_a_smart_tv(lee) | [
"b4",
"p0",
"p1",
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 500842191301126735120846
% SZS output start Proof for 500842191301126735120846
5. ! [X0] : anywhere(X0) [input b4]
44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
45. ! [X0] : (room(X0) => (predc(X0) => predl(X0))) [input p1]
49. ! [X0] : (anywhere(X0) => (prede(X0) => predc(X0))) [input p5]
52. prede(mary) [input p8]
55. ~(predl(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis]
134. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
135. ! [X0] : ((predl(X0) | ~predc(X0)) | ~room(X0)) [ennf transformation 45]
136. ! [X0] : (predl(X0) | ~predc(X0) | ~room(X0)) [flattening 135]
137. ! [X0] : ((predc(X0) | ~prede(X0)) | ~anywhere(X0)) [ennf transformation 49]
138. ! [X0] : (predc(X0) | ~prede(X0) | ~anywhere(X0)) [flattening 137]
139. ~predl(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 55]
141. ? [X0] : (mary != X0 & room(X0)) => (mary != sK0 & room(sK0)) [choice axiom]
142. ~predl(mary) | (mary != sK0 & room(sK0)) | ~room(mary) [skolemisation 139,141]
143. anywhere(X0) [cnf transformation 5]
224. room(mary) [cnf transformation 134]
225. ~room(X0) | mary = X0 [cnf transformation 134]
226. ~predc(X0) | predl(X0) | ~room(X0) [cnf transformation 136]
227. predc(X0) | ~prede(X0) | ~anywhere(X0) [cnf transformation 138]
228. prede(mary) [cnf transformation 52]
229. ~predl(mary) | room(sK0) | ~room(mary) [cnf transformation 142]
230. ~predl(mary) | mary != sK0 | ~room(mary) [cnf transformation 142]
231. ~prede(X0) | predc(X0) [subsumption resolution 227,143]
232. ~predl(mary) | mary != sK0 [subsumption resolution 230,224]
234. 1 <=> mary = sK0 [avatar definition]
236. mary != sK0 <- (~1) [avatar component clause 234]
238. 2 <=> predl(mary) [avatar definition]
241. ~1 | ~2 [avatar split clause 232,238,234]
242. ~predl(mary) | room(sK0) [subsumption resolution 229,224]
244. 3 <=> room(sK0) [avatar definition]
246. room(sK0) <- (3) [avatar component clause 244]
247. 3 | ~2 [avatar split clause 242,238,244]
248. predc(mary) [resolution 231,228]
250. predl(mary) | ~room(mary) [resolution 226,248]
254. predl(mary) [subsumption resolution 250,224]
255. 2 [avatar split clause 254,238]
256. mary = sK0 <- (3) [resolution 246,225]
257. $false <- (~1, 3) [subsumption resolution 256,236]
258. 1 | ~3 [avatar contradiction clause 257]
259. $false [avatar sat refutation 241,247,255,258]
% SZS output end Proof for 500842191301126735120846
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0.241808 |
Marco is the only person in the room.
If "Marco writes in-depth travel guides for off-the-beaten-path destinations" then "at least one person in the room has lived in exactly three countries".
If "Marco can play the harmonica" then "if someone has lived in exactly three countries then he/she creates bespoke furniture pieces from reclaimed wood and vice versa".
Either "Marco has lived in exactly three countries" or "Marco creates bespoke furniture pieces from reclaimed wood" but not both.
If "it is not the case that "it is not the case that "Marco designs and sews custom cosplay costumes for conventions""" then "if someone makes intricate hand-cut paper art for exhibitions then he/she enjoys stargazing and vice versa".
Marco hosts themed dinner parties featuring gourmet home-cooked meals.
It is not the case that "it is true that "Marco owns a 3D printer"".
At least one person anywhere enjoys watercolor painting.
If someone develops open-source software projects in their free time then he/she designs and sews custom cosplay costumes for conventions and vice versa.
Marco enjoys skydiving.
Marco has completed a triathlon.
Marco creates bespoke furniture pieces from reclaimed wood.
Everyone in the room who hosts regular workshops on creative writing enjoys watercolor painting.
It is not the case that "Marco owns a high-end gaming PC with custom-built components".
It is not the case that "Marco has completed a triathlon, enjoys wildlife photography and develops open-source software projects in their free time". | Marco designs and sews custom cosplay costumes for conventions. | neutral | room(marco)&(![X]:(room(X)=>(X='marco')))&
((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(marco))=>(((?[X]:(room(X)&has_lived_in_exactly_three_countries(X))))))&
((can_play_the_harmonica(marco))=>((![X]:((has_lived_in_exactly_three_countries(X))<=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))&
((has_lived_in_exactly_three_countries(marco))<~>(creates_bespoke_furniture_pieces_from_reclaimed_wood(marco)))&
((~(~(designs_and_sews_custom_cosplay_costumes_for_conventions(marco))))=>((![X]:((makes_intricate_hand-cut_paper_art_for_exhibitions(X))<=>(enjoys_stargazing(X))))))&
(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(marco))&
(~(owns_a_3D_printer(marco)))&
(((?[X]:(anywhere(X)&enjoys_watercolor_painting(X)))))&
((![X]:((develops_open-source_software_projects_in_their_free_time(X))<=>(designs_and_sews_custom_cosplay_costumes_for_conventions(X)))))&
(enjoys_skydiving(marco))&
(has_completed_a_triathlon(marco))&
(creates_bespoke_furniture_pieces_from_reclaimed_wood(marco))&
(![X]:(room(X)=>(((hosts_regular_workshops_on_creative_writing(X))=>(enjoys_watercolor_painting(X))))))&
(~(owns_a_high-end_gaming_PC_with_custom-built_components(marco)))&
(~(((has_completed_a_triathlon(marco))&(enjoys_wildlife_photography(marco))&(develops_open-source_software_projects_in_their_free_time(marco))))) | room(marco)&(![X]:(room(X)=>(X='marco')))&
designs_and_sews_custom_cosplay_costumes_for_conventions(marco) | [] | null | 0.672592 |
Genny, Tammy, Harriet, Robert, Harold are the only persons in the room. “It is not the case that “Harold is passionate about collecting and restoring classic cars”” only if “Harriet and Robert are respectively creative and humble”. If “everyone in the room has a tattoo or does not own an extensive assortment of vintage comic book memorabilia” then “no tall person is strong” otherwise “all quiet persons are humble”. Either “Leroy and Harriet like each other” or “Harold and Genny are client of Dario” but not both. If “it is not the case that “someone outside the room hates Dario”” then “everyone in the room is poorer than Leroy if they is not a old wise tall tourist”. “Everyone in the room enjoys macrame or does not enjoy trail running” if “everyone in the room is not a curious tourist or does not bake bread at home” and vice versa. Harriet owns a 3D printer. Leroy is a sibling of Tammy. Genny who is a client of Costco is not a old wise tall tourist. Everyone in the room frequently participates in hackathons and coding competitions. Everyone in the room enjoys macrame or does not enjoy trail running. Robert is not a curious brave funny strong person. Everyone in the room collects limited-edition art prints from contemporary artists if they is richer than Leroy. Everyone in the room who is hated by Dario enjoys fishing. Everyone in the room is not a coffee connoisseur or is poorer than Leroy. Robert does not own a 3D printer. Genny and Harriet are richer than Leroy. At least one person in the room is not a happy creative curious brave european. Everyone in the room is not a patient humble wise european or is quieter than Dario or both if they owns a microscope and has a curated collection of mid-century modern furniture and vice versa. All happy persons are funny. Everyone in the room owns an extensive assortment of vintage comic book memorabilia if they does not hate Leroy. All happy persons are patient. Genny and Leroy like each other. | Genny owns an extensive assortment of vintage comic book memorabilia. | entailment | room(genny)&room(tammy)&room(harriet)&room(robert)&room(harold)&(![X]:(room(X)=>(X='genny'|X='tammy'|X='harriet'|X='robert'|X='harold')))&
((~(is_passionate_about_collecting_and_restoring_classic_cars(harold)))=>((creative(harriet))&(humble(robert))))&
(((![X]:(room(X)=>(((does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))|(has_a_tattoo(X))))))=>(~?[X]:(tall(X)=>strong(X))))&((~(![X]:(room(X)=>(((does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))|(has_a_tattoo(X)))))))=>(![X]:(quiet(X)=>humble(X)))))&
(((like(leroy,harriet) & like(harriet,leroy)))<~>(client(dario,harold)&client(dario,genny)))&
((~(?[X]:(~room(X)&(hate(dario,X)))))=>(![X]:(room(X)=>(((~(old(X)&wise(X)&tall(X)&tourist(X)))=>(poorer(leroy,X)))))))&
((![X]:(room(X)=>(((does_not_bake_bread_at_home(X))|(~(curious(X)&tourist(X)))))))<=>(![X]:(room(X)=>(((does_not_enjoy_trail_running(X))|(enjoys_macrame(X)))))))&
(owns_a_3D_printer(harriet))&
(sibling(tammy,leroy))&
((is_a_client_of_Costco(genny))&(~(old(genny)&wise(genny)&tall(genny)&tourist(genny))))&
(![X]:(room(X)=>(frequently_participates_in_hackathons_and_coding_competitions(X))))&
(![X]:(room(X)=>(((does_not_enjoy_trail_running(X))|(enjoys_macrame(X))))))&
(~(curious(robert)&brave(robert)&funny(robert)&strong(robert)&person(robert)))&
(![X]:(room(X)=>(((richer(leroy,X))=>(collects_limited-edition_art_prints_from_contemporary_artists(X))))))&
(![X]:(room(X)=>(((hate(X,dario))=>(enjoys_fishing(X))))))&
(![X]:(room(X)=>(((poorer(leroy,X))|(is_not_a_coffee_connoisseur(X))))))&
(does_not_own_a_3D_printer(robert))&
(richer(leroy,genny)&richer(leroy,harriet))&
(((?[X]:(room(X)&~(happy(X)&creative(X)&curious(X)&brave(X)&european(X))))))&
(![X]:(room(X)=>(((((~(patient(X)&humble(X)&wise(X)&european(X)))|(quieter(dario,X))))<=>(((owns_a_microscope(X))&(has_a_curated_collection_of_mid-century_modern_furniture(X))))))))&
(![X]:(happy(X)=>funny(X)))&
(![X]:(room(X)=>(((~hate(leroy,X))=>(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))))&
(![X]:(happy(X)=>patient(X)))&
((like(genny,leroy) & like(leroy,genny)))&
(collects_rare_and_antique_scientific_instruments(robert)) | room(genny)&room(tammy)&room(harriet)&room(robert)&room(harold)&(![X]:(room(X)=>(X='genny'|X='tammy'|X='harriet'|X='robert'|X='harold')))&
owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(genny) | [
"b0",
"b42",
"p0",
"p20",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 142190733251252546294895
% SZS output start Proof for 142190733251252546294895
1. ! [X0,X1] : (X0 != X1 => (like(X0,X1) => ~hate(X0,X1))) [input b0]
43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42]
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]
64. ! [X0] : (room(X0) => (~hate(lucy,X0) => predk(X0))) [input p20]
66. like(lucy,mary) & like(mary,lucy) [input p22]
68. ~(predk(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]
88. ! [X0,X1] : ((~hate(X0,X1) | ~like(X0,X1)) | X0 = X1) [ennf transformation 1]
89. ! [X0,X1] : (~hate(X0,X1) | ~like(X0,X1) | X0 = X1) [flattening 88]
159. ! [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]
160. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 159]
172. ! [X0] : ((predk(X0) | hate(lucy,X0)) | ~room(X0)) [ennf transformation 64]
173. ! [X0] : (predk(X0) | hate(lucy,X0) | ~room(X0)) [flattening 172]
174. ~predk(mary) | ? [X0] : ((john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 68]
175. ~predk(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 174]
198. ? [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]
199. ~predk(mary) | (john != sK6 & alice != sK6 & fred != sK6 & paul != sK6 & mary != sK6 & room(sK6)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 175,198]
200. ~hate(X0,X1) | ~like(X0,X1) | X0 = X1 [cnf transformation 89]
276. mary != lucy [cnf transformation 43]
282. room(mary) [cnf transformation 160]
283. room(paul) [cnf transformation 160]
284. room(fred) [cnf transformation 160]
285. room(alice) [cnf transformation 160]
286. room(john) [cnf transformation 160]
287. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 160]
329. hate(lucy,X0) | predk(X0) | ~room(X0) [cnf transformation 173]
331. like(lucy,mary) [cnf transformation 66]
332. ~predk(mary) | room(sK6) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 199]
333. ~predk(mary) | mary != sK6 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 199]
334. ~predk(mary) | paul != sK6 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 199]
335. ~predk(mary) | fred != sK6 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 199]
336. ~predk(mary) | alice != sK6 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 199]
337. ~predk(mary) | john != sK6 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 199]
471. ~predk(mary) | john != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 337,286]
472. ~predk(mary) | john != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 471,285]
473. ~predk(mary) | john != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 472,284]
474. ~predk(mary) | john != sK6 | ~room(mary) [subsumption resolution 473,283]
475. ~predk(mary) | john != sK6 [subsumption resolution 474,282]
477. 30 <=> john = sK6 [avatar definition]
479. john != sK6 <- (~30) [avatar component clause 477]
481. 31 <=> predk(mary) [avatar definition]
484. ~30 | ~31 [avatar split clause 475,481,477]
485. ~predk(mary) | alice != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 336,286]
486. ~predk(mary) | alice != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 485,285]
487. ~predk(mary) | alice != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 486,284]
488. ~predk(mary) | alice != sK6 | ~room(mary) [subsumption resolution 487,283]
489. ~predk(mary) | alice != sK6 [subsumption resolution 488,282]
491. 32 <=> alice = sK6 [avatar definition]
493. alice != sK6 <- (~32) [avatar component clause 491]
494. ~32 | ~31 [avatar split clause 489,481,491]
495. ~predk(mary) | fred != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 335,286]
496. ~predk(mary) | fred != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 495,285]
497. ~predk(mary) | fred != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 496,284]
498. ~predk(mary) | fred != sK6 | ~room(mary) [subsumption resolution 497,283]
499. ~predk(mary) | fred != sK6 [subsumption resolution 498,282]
501. 33 <=> fred = sK6 [avatar definition]
503. fred != sK6 <- (~33) [avatar component clause 501]
504. ~33 | ~31 [avatar split clause 499,481,501]
505. ~predk(mary) | paul != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 334,286]
506. ~predk(mary) | paul != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 505,285]
507. ~predk(mary) | paul != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 506,284]
508. ~predk(mary) | paul != sK6 | ~room(mary) [subsumption resolution 507,283]
509. ~predk(mary) | paul != sK6 [subsumption resolution 508,282]
511. 34 <=> paul = sK6 [avatar definition]
513. paul != sK6 <- (~34) [avatar component clause 511]
514. ~34 | ~31 [avatar split clause 509,481,511]
515. ~predk(mary) | mary != sK6 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 333,286]
516. ~predk(mary) | mary != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 515,285]
517. ~predk(mary) | mary != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 516,284]
518. ~predk(mary) | mary != sK6 | ~room(mary) [subsumption resolution 517,283]
519. ~predk(mary) | mary != sK6 [subsumption resolution 518,282]
521. 35 <=> mary = sK6 [avatar definition]
523. mary != sK6 <- (~35) [avatar component clause 521]
524. ~35 | ~31 [avatar split clause 519,481,521]
525. ~predk(mary) | room(sK6) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 332,286]
526. ~predk(mary) | room(sK6) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 525,285]
527. ~predk(mary) | room(sK6) | ~room(paul) | ~room(mary) [subsumption resolution 526,284]
528. ~predk(mary) | room(sK6) | ~room(mary) [subsumption resolution 527,283]
529. ~predk(mary) | room(sK6) [subsumption resolution 528,282]
531. 36 <=> room(sK6) [avatar definition]
533. room(sK6) <- (36) [avatar component clause 531]
534. 36 | ~31 [avatar split clause 529,481,531]
604. ~like(lucy,X0) | lucy = X0 | predk(X0) | ~room(X0) [resolution 200,329]
906. mary = lucy | predk(mary) | ~room(mary) [resolution 604,331]
908. predk(mary) | ~room(mary) [subsumption resolution 906,276]
914. predk(mary) [subsumption resolution 908,282]
915. 31 [avatar split clause 914,481]
916. alice = sK6 | fred = sK6 | paul = sK6 | mary = sK6 | john = sK6 <- (36) [resolution 533,287]
925. fred = sK6 | paul = sK6 | mary = sK6 | john = sK6 <- (~32, 36) [subsumption resolution 916,493]
926. paul = sK6 | mary = sK6 | john = sK6 <- (~32, ~33, 36) [subsumption resolution 925,503]
927. mary = sK6 | john = sK6 <- (~32, ~33, ~34, 36) [subsumption resolution 926,513]
928. john = sK6 <- (~32, ~33, ~34, ~35, 36) [subsumption resolution 927,523]
929. $false <- (~30, ~32, ~33, ~34, ~35, 36) [subsumption resolution 928,479]
930. 30 | 32 | 33 | 34 | 35 | ~36 [avatar contradiction clause 929]
963. $false [avatar sat refutation 484,494,504,514,524,534,915,930]
% SZS output end Proof for 142190733251252546294895
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.039 s
% ------------------------------
% ------------------------------
| 0.117163 |
Roberto, Sheila are the only persons in the room. Only one person in the room collects historical artifacts related to ancient civilizations. If someone is right-handed then he/she enjoys writing detailed reviews of new and classic board games. Roberto dreamt that “everyone in the room is right-handed only if they is not a member of a local theater group specializing in improv”. Roberto can play the guitar. Someone in the room is right-handed. Roberto is right-handed. Sheila has a vast collection of first-edition science fiction novels. Not everyone in the room who own a television either does not enjoy writing detailed reviews of new and classic board games or cannot play the guitar but not both. Someone outside the room is not right-handed. Only one person in the room does not own a television. Not everyone in the room either practices kickboxing or own a television but not both if they practices kickboxing. | Everyone in the room does not collect historical artifacts related to ancient civilizations or practices kickboxing. | neutral | room(roberto)&room(sheila)&(![X]:(room(X)=>(X='roberto'|X='sheila')))&
(((?[X]:(room(X)&collects_historical_artifacts_related_to_ancient_civilizations(X)))&(![X,Y]:((room(X)&room(Y)&(collects_historical_artifacts_related_to_ancient_civilizations(X))&(collects_historical_artifacts_related_to_ancient_civilizations(Y)))=>(X=Y)))))&
((![X]:((is_right-handed(X))=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X)))))&
((roberto_dream=>(![X]:(room(X)=>(((is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))<=(is_right-handed(X))))))))&
(can_play_the_guitar(roberto))&
(?[X]:(room(X)&(is_right-handed(X))))&
(is_right-handed(roberto))&
(has_a_vast_collection_of_first-edition_science_fiction_novels(sheila))&
(~![X]:(room(X)=>(((own_a_television(X))=>(((does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))<~>(cannot_play_the_guitar(X))))))))&
(?[X]:(~room(X)&(is_not_right-handed(X))))&
(((?[X]:(room(X)&does_not_own_a_television(X)))&(![X,Y]:((room(X)&room(Y)&(does_not_own_a_television(X))&(does_not_own_a_television(Y)))=>(X=Y)))))&
(~![X]:(room(X)=>(((practices_kickboxing(X))=>(((practices_kickboxing(X))<~>(own_a_television(X)))))))) | room(roberto)&room(sheila)&(![X]:(room(X)=>(X='roberto'|X='sheila')))&
![X]:(room(X)=>(((practices_kickboxing(X))|(does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))))) | [] | null | 0 |
Patsy is the only person in the room.
“Everyone anywhere is an active member of a local robotics club or does not enjoy kayaking and exploring remote waterways” if “everyone outside the room collects comic books or does not write poetry” and vice versa.
“At least one person outside the room enjoys kayaking and exploring remote waterways” if “everyone in the room collects comic books or does not collect comic books”.
If “Patsy can play the piano” then “if someone collect rare sneakers then he/she does not collect comic books” otherwise “Patsy does not write poetry”.
If “someone in the room collect rare sneakers” then “Patsy either practices urban gardening or collects comic books but not both” otherwise “everyone in the room who enjoys salsa dancing can play the piano”.
If “Patsy enjoys wildlife photography” then “everyone in the room owns a smart tv or can play the piano or both if they writes poetry”.
If “everyone in the room is an avid hiker or is not an avid hiker” then “Patsy collects comic books” otherwise “everyone outside the room can play the piano or enjoys cross-country skiing or both only if they either enjoys making ceramics or practices urban gardening but not both”.
Not everyone in the room does not train for and competes in international triathlons if they practices urban gardening and owns a smartwatch.
It is true that “Patsy enjoys cross-country skiing”.
Patsy does not write poetry.
Patsy does not participate in citizen science projects related to wildlife monitoring.
Patsy does not play the drums.
Someone in the room is an active member of a local robotics club, has a vast collection of first-edition science fiction novels or trains for and competes in international triathlons. | Patsy owns a smartwatch. | entailment | room(patsy)&(![X]:(room(X)=>(X='patsy')))&
((![X]:(~room(X)=>(((does_not_write_poetry(X))|(collects_comic_books(X))))))<=>(![X]:(anywhere(X)=>(((does_not_enjoy_kayaking_and_exploring_remote_waterways(X))|(is_an_active_member_of_a_local_robotics_club(X)))))))&
((![X]:(room(X)=>(((does_not_collect_comic_books(X))|(collects_comic_books(X))))))=>(((?[X]:(~room(X)&enjoys_kayaking_and_exploring_remote_waterways(X))))))&
(((can_play_the_piano(patsy))=>((![X]:((collect_rare_sneakers(X))=>(does_not_collect_comic_books(X))))))&((~(can_play_the_piano(patsy)))=>(does_not_write_poetry(patsy))))&
(((?[X]:(room(X)&(collect_rare_sneakers(X))))=>(((practices_urban_gardening(patsy))<~>(collects_comic_books(patsy)))))&((~(?[X]:(room(X)&(collect_rare_sneakers(X)))))=>(![X]:(room(X)=>(((enjoys_salsa_dancing(X))=>(can_play_the_piano(X))))))))&
((enjoys_wildlife_photography(patsy))=>(![X]:(room(X)=>(((writes_poetry(X))=>(((owns_a_smart_tv(X))|(can_play_the_piano(X)))))))))&
(((![X]:(room(X)=>(((is_not_an_avid_hiker(X))|(is_an_avid_hiker(X))))))=>(collects_comic_books(patsy)))&((~(![X]:(room(X)=>(((is_not_an_avid_hiker(X))|(is_an_avid_hiker(X)))))))=>(![X]:(~room(X)=>(((((enjoys_making_ceramics(X))<~>(practices_urban_gardening(X))))<=(((can_play_the_piano(X))|(enjoys_cross-country_skiing(X))))))))))&
(~![X]:(room(X)=>(((((practices_urban_gardening(X))&(owns_a_smartwatch(X))))=>(does_not_train_for_and_competes_in_international_triathlons(X))))))&
(enjoys_cross-country_skiing(patsy))&
(does_not_write_poetry(patsy))&
(does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(patsy))&
(does_not_play_the_drums(patsy))&
(?[X]:(room(X)&(((is_an_active_member_of_a_local_robotics_club(X))|(has_a_vast_collection_of_first-edition_science_fiction_novels(X))|(trains_for_and_competes_in_international_triathlons(X)))))) | room(patsy)&(![X]:(room(X)=>(X='patsy')))&
owns_a_smartwatch(patsy) | [
"p0",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 5025952680999104345503584
% SZS output start Proof for 5025952680999104345503584
44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
51. ~! [X0] : (room(X0) => ((predt(X0) & predw(X0)) => ~predr(X0))) [input p7]
57. ~(predt(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis]
65. ~! [X0] : (room(X0) => ~(predt(X0) & predw(X0))) [pure predicate removal 51]
141. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
149. ? [X0] : ((predt(X0) & predw(X0)) & room(X0)) [ennf transformation 65]
150. ? [X0] : (predt(X0) & predw(X0) & room(X0)) [flattening 149]
151. ~predt(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 57]
166. ? [X0] : (predt(X0) & predw(X0) & room(X0)) => (predt(sK5) & predw(sK5) & room(sK5)) [choice axiom]
167. predt(sK5) & predw(sK5) & room(sK5) [skolemisation 150,166]
170. ? [X0] : (mary != X0 & room(X0)) => (mary != sK7 & room(sK7)) [choice axiom]
171. ~predt(mary) | (mary != sK7 & room(sK7)) | ~room(mary) [skolemisation 151,170]
253. room(mary) [cnf transformation 141]
254. ~room(X0) | mary = X0 [cnf transformation 141]
275. room(sK5) [cnf transformation 167]
277. predt(sK5) [cnf transformation 167]
281. ~predt(mary) | room(sK7) | ~room(mary) [cnf transformation 171]
282. ~predt(mary) | mary != sK7 | ~room(mary) [cnf transformation 171]
364. ~predt(mary) | mary != sK7 [subsumption resolution 282,253]
366. 17 <=> mary = sK7 [avatar definition]
368. mary != sK7 <- (~17) [avatar component clause 366]
370. 18 <=> predt(mary) [avatar definition]
373. ~17 | ~18 [avatar split clause 364,370,366]
374. ~predt(mary) | room(sK7) [subsumption resolution 281,253]
376. 19 <=> room(sK7) [avatar definition]
378. room(sK7) <- (19) [avatar component clause 376]
379. 19 | ~18 [avatar split clause 374,370,376]
382. mary = sK5 [resolution 254,275]
386. predt(mary) [backward demodulation 277,382]
390. 18 [avatar split clause 386,370]
391. mary = sK7 <- (19) [resolution 378,254]
392. $false <- (~17, 19) [subsumption resolution 391,368]
393. 17 | ~19 [avatar contradiction clause 392]
394. $false [avatar sat refutation 373,379,390,393]
% SZS output end Proof for 5025952680999104345503584
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.11245 |
Keith, Christopher, Laureen, Willard, Charles are the only persons in the room. “Someone in the room enjoys stand-up paddleboarding” unless “Laureen frequently participates in hackathons and coding competitions”. Either “it is not the case that “Willard is right-handed or enjoys stand-up paddleboarding or both”” or “everyone in the room does not enjoy stand-up paddleboarding or enjoys logic puzzles” but not both. It is not the case that “Willard is right-handed or enjoys stand-up paddleboarding or both”. If someone creates large-scale murals for public art installations then he/she practices digital art and vice versa. Everyone anywhere who enjoys logic puzzles uses a Windows laptop. Everyone outside the room uses a Windows laptop. Keith practices digital art. Laureen is an expert in identifying and foraging wild edible plants. At least one person in the room creates large-scale murals for public art installations. Everyone in the room who uses a Windows laptop neither uses a Windows laptop nor practices digital art. Charles does not use a Windows laptop, enjoys stand-up paddleboarding or does enjoy mountain biking. Everyone outside the room uses contact lenses if they does enjoy mountain biking. Someone in the room creates large-scale murals for public art installations. Laureen enjoys stand-up paddleboarding. Everyone in the room uses contact lenses if they does enjoy mountain biking. Everyone in the room does not create large-scale murals for public art installations if they enjoys stand-up paddleboarding. Everyone in the room who is an expert in identifying and foraging wild edible plants enjoys stand-up paddleboarding. | Keith is an expert in identifying and foraging wild edible plants. | contradiction | room(keith)&room(christopher)&room(laureen)&room(willard)&room(charles)&(![X]:(room(X)=>(X='keith'|X='christopher'|X='laureen'|X='willard'|X='charles')))&
(~(frequently_participates_in_hackathons_and_coding_competitions(laureen))=>(?[X]:(room(X)&(enjoys_stand-up_paddleboarding(X)))))&
((~(((is_right-handed(willard))|(enjoys_stand-up_paddleboarding(willard)))))<~>(![X]:(room(X)=>(((enjoys_logic_puzzles(X))|(does_not_enjoy_stand-up_paddleboarding(X)))))))&
(~(((is_right-handed(willard))|(enjoys_stand-up_paddleboarding(willard)))))&
((![X]:((creates_large-scale_murals_for_public_art_installations(X))<=>(practices_digital_art(X)))))&
(![X]:(anywhere(X)=>(((enjoys_logic_puzzles(X))=>(uses_a_Windows_laptop(X))))))&
(![X]:(~room(X)=>(uses_a_Windows_laptop(X))))&
(practices_digital_art(keith))&
(is_an_expert_in_identifying_and_foraging_wild_edible_plants(laureen))&
(((?[X]:(room(X)&creates_large-scale_murals_for_public_art_installations(X)))))&
(![X]:(room(X)=>(((uses_a_Windows_laptop(X))=>(~((uses_a_Windows_laptop(X))|(practices_digital_art(X))))))))&
(((does_not_use_a_Windows_laptop(charles))|(enjoys_stand-up_paddleboarding(charles))|(does_enjoy_mountain_biking(charles))))&
(![X]:(~room(X)=>(((does_enjoy_mountain_biking(X))=>(uses_contact_lenses(X))))))&
(?[X]:(room(X)&(creates_large-scale_murals_for_public_art_installations(X))))&
(enjoys_stand-up_paddleboarding(laureen))&
(![X]:(room(X)=>(((does_enjoy_mountain_biking(X))=>(uses_contact_lenses(X))))))&
(![X]:(room(X)=>(((practices_digital_art(X))<=(enjoys_logic_puzzles(X))))))&
(![X]:(room(X)=>(((((enjoys_logic_puzzles(X))&(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))&(practices_digital_art(X))))=>(enjoys_stand-up_paddleboarding(X))))))&
(![X]:(room(X)=>(((enjoys_stand-up_paddleboarding(X))=>(does_not_create_large-scale_murals_for_public_art_installations(X))))))&
(![X]:(~room(X)=>(((does_not_create_large-scale_murals_for_public_art_installations(X))=>(practices_digital_art(X))))))&
(is_an_expert_in_identifying_and_foraging_wild_edible_plants(charles))&
(![X]:(room(X)=>(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))=>(enjoys_stand-up_paddleboarding(X))))))&
((?[X,Y]:(room(X)&room(Y)&(does_enjoy_mountain_biking(X)&does_enjoy_mountain_biking(Y))&(X!=Y))))&
(![X]:(~room(X)=>(((is_right-handed(X))|(does_not_frequently_participates_in_hackathons_and_coding_competitions(X))))))&
((creates_large-scale_murals_for_public_art_installations(christopher))&(frequently_participates_in_hackathons_and_coding_competitions(christopher))) | room(keith)&room(christopher)&room(laureen)&room(willard)&room(charles)&(![X]:(room(X)=>(X='keith'|X='christopher'|X='laureen'|X='willard'|X='charles')))&
is_an_expert_in_identifying_and_foraging_wild_edible_plants(keith) | [
"p0",
"p4",
"p7",
"p18",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7541170407089069774417889
% SZS output start Proof for 7541170407089069774417889
44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
48. ! [X0] : (predj(X0) <=> predf(X0)) [input p4]
51. predf(mary) [input p7]
62. ! [X0] : (room(X0) => (predi(X0) => ~predj(X0))) [input p18]
65. ! [X0] : (room(X0) => (predc(X0) => predi(X0))) [input p21]
69. 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]
145. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
146. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 145]
160. ! [X0] : ((~predj(X0) | ~predi(X0)) | ~room(X0)) [ennf transformation 62]
161. ! [X0] : (~predj(X0) | ~predi(X0) | ~room(X0)) [flattening 160]
164. ! [X0] : ((predi(X0) | ~predc(X0)) | ~room(X0)) [ennf transformation 65]
165. ! [X0] : (predi(X0) | ~predc(X0) | ~room(X0)) [flattening 164]
168. 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 69]
169. 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 168]
178. ! [X0] : ((predj(X0) | ~predf(X0)) & (predf(X0) | ~predj(X0))) [nnf transformation 48]
266. room(mary) [cnf transformation 146]
282. ~predf(X0) | predj(X0) [cnf transformation 178]
285. predf(mary) [cnf transformation 51]
296. ~predj(X0) | ~predi(X0) | ~room(X0) [cnf transformation 161]
299. ~predc(X0) | predi(X0) | ~room(X0) [cnf transformation 165]
312. predc(mary) [cnf transformation 169]
364. predj(mary) [resolution 282,285]
374. ~predi(mary) | ~room(mary) [resolution 296,364]
378. ~predi(mary) [subsumption resolution 374,266]
384. predi(mary) | ~room(mary) [resolution 299,312]
386. ~room(mary) [subsumption resolution 384,378]
387. $false [subsumption resolution 386,266]
% SZS output end Proof for 7541170407089069774417889
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.086428 |
Luther, Ron, Anthony are the only persons in the room.
If Ron creates YouTube content then if someone works on fridays then he/she has a tattoo and vice versa.
Either Anthony neither is an expert in identifying and foraging wild edible plants nor does enjoy trail running or Ron mentors a youth basketball team on weekends but not both.
If it is not the case that Anthony enjoys fishing then everyone in the room enjoys landscape photography only if they own a television otherwise Luther either works on fridays or enjoys fishing but not both.
If Anthony is a dedicated advocate for digital privacy and encryption then more than one person in the room owns a smartwatch.
Either Anthony works on fridays or Luther is a dedicated advocate for digital privacy and encryption but not both.
Only one person in the room streams on Twitch if Ron owns a smartwatch.
Ron creates YouTube content.
Anthony has a tattoo. | Luther is a dedicated advocate for digital privacy and encryption. | contradiction | room(luther)&room(ron)&room(anthony)&(![X]:(room(X)=>(X='luther'|X='ron'|X='anthony')))&
((creates_YouTube_content(ron))=>((![X]:((works_on_fridays(X))<=>(has_a_tattoo(X))))))&
((~((is_an_expert_in_identifying_and_foraging_wild_edible_plants(anthony))|(does_enjoy_trail_running(anthony))))<~>(mentors_a_youth_basketball_team_on_weekends(ron)))&
(((~(enjoys_fishing(anthony)))=>(![X]:(room(X)=>(((own_a_television(X))<=(enjoys_landscape_photography(X)))))))&((~(~(enjoys_fishing(anthony))))=>(((works_on_fridays(luther))<~>(enjoys_fishing(luther))))))&
((is_a_dedicated_advocate_for_digital_privacy_and_encryption(anthony))=>((?[X,Y]:(room(X)&room(Y)&(owns_a_smartwatch(X)&owns_a_smartwatch(Y))&(X!=Y)))))&
((works_on_fridays(anthony))<~>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(luther)))&
((owns_a_smartwatch(ron))=>(((?[X]:(room(X)&streams_on_Twitch(X)))&(![X,Y]:((room(X)&room(Y)&(streams_on_Twitch(X))&(streams_on_Twitch(Y)))=>(X=Y))))))&
((does_enjoy_trail_running(anthony))=>(![X]:(room(X)=>(((creates_YouTube_content(X))=>(~((enjoys_landscape_photography(X))|(has_a_tattoo(X)))))))))&
((own_a_television(ron))<=>(![X]:(room(X)=>(((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))|(collects_luxury_watches(X)))))))&
((![X]:(room(X)=>(((does_not_own_a_television(X))|(practices_graffiti_art(X))))))=>(has_a_tattoo(ron)))&
((participates_in_long-distance_cycling_events_across_the_country(luther))<~>(develops_open-source_software_projects_in_their_free_time(anthony)))&
(enjoys_fishing(luther))&
((![X]:((practices_pilates(X))<=>(practices_graffiti_art(X)))))&
(practices_pilates(ron))&
(creates_YouTube_content(ron))&
(can_play_the_harmonica(luther))&
(has_a_tattoo(anthony))&
(has_completed_a_triathlon(ron))&
((![X]:((does_enjoy_trail_running(X))<=>(develops_open-source_software_projects_in_their_free_time(X)))))&
(((is_a_drone_photographer(anthony))|(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(anthony))))&
(is_a_drone_photographer(anthony))&
((![X]:((practices_pilates(X))<=>(enjoys_landscape_photography(X)))))&
(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(luther))&
(owns_a_smartwatch(luther))&
(can_play_the_harmonica(anthony)) | room(luther)&room(ron)&room(anthony)&(![X]:(room(X)=>(X='luther'|X='ron'|X='anthony')))&
is_a_dedicated_advocate_for_digital_privacy_and_encryption(luther) | [
"p1",
"p5",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2671277489707024547556337
% SZS output start Proof for 2671277489707024547556337
45. predt(paul) => ! [X0] : (predu(X0) <=> predc(X0)) [input p1]
49. predu(fred) <~> predj(mary) [input p5]
58. predt(paul) [input p14]
60. predc(fred) [input p16]
69. predj(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis]
151. ! [X0] : (predu(X0) <=> predc(X0)) | ~predt(paul) [ennf transformation 45]
164. predj(mary) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 69]
165. predj(mary) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 164]
167. ! [X0] : ((predu(X0) | ~predc(X0)) & (predc(X0) | ~predu(X0))) | ~predt(paul) [nnf transformation 151]
173. (~predj(mary) | ~predu(fred)) & (predj(mary) | predu(fred)) [nnf transformation 49]
271. predu(X0) | ~predc(X0) | ~predt(paul) [cnf transformation 167]
284. ~predj(mary) | ~predu(fred) [cnf transformation 173]
303. predt(paul) [cnf transformation 58]
304. predc(fred) [cnf transformation 60]
314. predj(mary) [cnf transformation 165]
316. 1 <=> predt(paul) [avatar definition]
320. 2 <=> ! [X0] : (predu(X0) | ~predc(X0)) [avatar definition]
321. ~predc(X0) | predu(X0) <- (2) [avatar component clause 320]
322. ~1 | 2 [avatar split clause 271,320,316]
390. 17 <=> predu(fred) [avatar definition]
392. ~predu(fred) <- (~17) [avatar component clause 390]
394. 18 <=> predj(mary) [avatar definition]
397. ~17 | ~18 [avatar split clause 284,394,390]
478. 1 [avatar split clause 303,316]
479. 18 [avatar split clause 314,394]
484. predu(fred) <- (2) [resolution 321,304]
486. $false <- (2, ~17) [subsumption resolution 484,392]
487. ~2 | 17 [avatar contradiction clause 486]
488. $false [avatar sat refutation 322,397,478,479,487]
% SZS output end Proof for 2671277489707024547556337
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0.154994 |
Lazaro is the only person in the room.
Lazaro who is an expert in identifying and foraging wild edible plants enjoys salsa dancing.
Lazaro collects rare and antique scientific instruments and creates augmented reality experiences for mobile applications.
Only one person in the room practices urban gardening.
Everyone in the room who practices urban gardening has a saltwater aquarium. | Lazaro enjoys salsa dancing, has a saltwater aquarium and creates augmented reality experiences for mobile applications. | entailment | room(lazaro)&(![X]:(room(X)=>(X='lazaro')))&
(![X]:(room(X)=>(((enjoys_salsa_dancing(X))=>(practices_urban_gardening(X))))))&
(~![X]:(anywhere(X)=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))=>(has_lived_in_exactly_three_countries(X))))))&
(![X]:(room(X)=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))<=(enjoys_logic_puzzles(X))))))&
((![X]:((uses_a_Windows_laptop(X))=>(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X)))))&
((is_an_expert_in_identifying_and_foraging_wild_edible_plants(lazaro))&(enjoys_salsa_dancing(lazaro)))&
(((collects_rare_and_antique_scientific_instruments(lazaro))&(creates_augmented_reality_experiences_for_mobile_applications(lazaro))))&
((practices_graffiti_art(lazaro))&(enjoys_salsa_dancing(lazaro)))&
(~(enjoys_logic_puzzles(lazaro)))&
(![X]:(room(X)=>(((does_enjoy_trail_running(X))=>(is_an_avid_hiker(X))))))&
(((?[X]:(room(X)&practices_urban_gardening(X)))&(![X,Y]:((room(X)&room(Y)&(practices_urban_gardening(X))&(practices_urban_gardening(Y)))=>(X=Y)))))&
(((?[X]:(~room(X)&does_enjoy_trail_running(X)))&(![X,Y]:((~room(X)&~room(Y)&(does_enjoy_trail_running(X))&(does_enjoy_trail_running(Y)))=>(X=Y)))))&
((creates_augmented_reality_experiences_for_mobile_applications(lazaro))&(does_enjoy_mountain_biking(lazaro)))&
(does_enjoy_trail_running(lazaro))&
(is_an_expert_in_identifying_and_foraging_wild_edible_plants(lazaro))&
(![X]:(anywhere(X)=>(((has_lived_in_exactly_three_countries(X))=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))&
(![X]:(room(X)=>(((enjoys_origami(X))=>(creates_augmented_reality_experiences_for_mobile_applications(X))))))&
(![X]:(room(X)=>(((has_a_saltwater_aquarium(X))<=>(has_lived_in_exactly_three_countries(X))))))&
(((?[X]:(room(X)&uses_a_Windows_laptop(X)))&(![X,Y]:((room(X)&room(Y)&(uses_a_Windows_laptop(X))&(uses_a_Windows_laptop(Y)))=>(X=Y)))))&
(~![X]:(~room(X)=>(((is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))=>(is_right-handed(X))))))&
(((?[X]:(room(X)&((is_right-handed(X))<~>(enjoys_macrame(X)))))&(![X,Y]:((room(X)&room(Y)&(((is_right-handed(X))<~>(enjoys_macrame(X))))&(((is_right-handed(Y))<~>(enjoys_macrame(Y)))))=>(X=Y)))))&
(![X]:(room(X)=>(((practices_urban_gardening(X))=>(collects_rare_and_antique_scientific_instruments(X))))))&
(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(lazaro))<~>(has_a_saltwater_aquarium(lazaro))))&
(![X]:(room(X)=>(((practices_urban_gardening(X))=>(has_a_saltwater_aquarium(X)))))) | room(lazaro)&(![X]:(room(X)=>(X='lazaro')))&
((enjoys_salsa_dancing(lazaro))&(has_a_saltwater_aquarium(lazaro))&(creates_augmented_reality_experiences_for_mobile_applications(lazaro))) | [
"p0",
"p5",
"p6",
"p10",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 7904822959462447442967636
% SZS output start Proof for 7904822959462447442967636
44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
49. prede(mary) & predk(mary) [input p5]
50. predb(mary) & predw(mary) [input p6]
54. ! [X0,X1] : ((predg(X1) & predg(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predg(X0) & room(X0)) [input p10]
67. ! [X0] : (room(X0) => (predg(X0) => preda(X0))) [input p23]
68. ~(predb(mary) & preda(mary) & prede(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis]
69. ! [X0,X1] : ((predg(X1) & predg(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (predg(X2) & room(X2)) [rectify 54]
81. predb(mary) [pure predicate removal 50]
85. prede(mary) [pure predicate removal 49]
160. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
164. ! [X0,X1] : (X0 = X1 | (~predg(X1) | ~predg(X0) | ~room(X1) | ~room(X0))) & ? [X2] : (predg(X2) & room(X2)) [ennf transformation 69]
165. ! [X0,X1] : (X0 = X1 | ~predg(X1) | ~predg(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (predg(X2) & room(X2)) [flattening 164]
174. ! [X0] : ((preda(X0) | ~predg(X0)) | ~room(X0)) [ennf transformation 67]
175. ! [X0] : (preda(X0) | ~predg(X0) | ~room(X0)) [flattening 174]
176. ~predb(mary) | ~preda(mary) | ~prede(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 68]
180. ? [X2] : (predg(X2) & room(X2)) => (predg(sK1) & room(sK1)) [choice axiom]
181. ! [X0,X1] : (X0 = X1 | ~predg(X1) | ~predg(X0) | ~room(X1) | ~room(X0)) & (predg(sK1) & room(sK1)) [skolemisation 165,180]
194. ? [X0] : (mary != X0 & room(X0)) => (mary != sK6 & room(sK6)) [choice axiom]
195. ~predb(mary) | ~preda(mary) | ~prede(mary) | (mary != sK6 & room(sK6)) | ~room(mary) [skolemisation 176,194]
276. room(mary) [cnf transformation 160]
277. ~room(X0) | mary = X0 [cnf transformation 160]
280. prede(mary) [cnf transformation 85]
281. predb(mary) [cnf transformation 81]
283. room(sK1) [cnf transformation 181]
284. predg(sK1) [cnf transformation 181]
307. ~predg(X0) | preda(X0) | ~room(X0) [cnf transformation 175]
308. ~predb(mary) | ~preda(mary) | ~prede(mary) | room(sK6) | ~room(mary) [cnf transformation 195]
309. ~predb(mary) | ~preda(mary) | ~prede(mary) | mary != sK6 | ~room(mary) [cnf transformation 195]
325. 4 <=> preda(mary) [avatar definition]
330. ~preda(mary) | ~prede(mary) | mary != sK6 | ~room(mary) [subsumption resolution 309,281]
331. ~preda(mary) | mary != sK6 | ~room(mary) [subsumption resolution 330,280]
332. ~preda(mary) | mary != sK6 [subsumption resolution 331,276]
334. 5 <=> mary = sK6 [avatar definition]
336. mary != sK6 <- (~5) [avatar component clause 334]
337. ~5 | ~4 [avatar split clause 332,325,334]
338. ~preda(mary) | ~prede(mary) | room(sK6) | ~room(mary) [subsumption resolution 308,281]
339. ~preda(mary) | room(sK6) | ~room(mary) [subsumption resolution 338,280]
340. ~preda(mary) | room(sK6) [subsumption resolution 339,276]
342. 6 <=> room(sK6) [avatar definition]
344. room(sK6) <- (6) [avatar component clause 342]
345. 6 | ~4 [avatar split clause 340,325,342]
347. mary = sK1 [resolution 277,283]
351. predg(mary) [backward demodulation 284,347]
358. preda(mary) | ~room(mary) [resolution 307,351]
362. preda(mary) [subsumption resolution 358,276]
363. 4 [avatar split clause 362,325]
366. mary = sK6 <- (6) [resolution 344,277]
367. $false <- (~5, 6) [subsumption resolution 366,336]
368. 5 | ~6 [avatar contradiction clause 367]
369. $false [avatar sat refutation 337,345,363,368]
% SZS output end Proof for 7904822959462447442967636
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.078298 |
Jerry, Greg, Genevieve are the only persons in the room.
“Everyone in the room is not a generous person” only if “all quiet persons are calm”.
“Genevieve and Martin like each other” only if “all curious persons are kind”.
“Someone in the room does not like Felix, is not an avid hiker and is brave” only if “Jerry is the least old in the room”.
“Someone in the room uses an ios phone and is a quiet person” only if “no generous person is happy”.
Either “someone in the room enjoys windsurfing” or “no one in the room hosts regular game nights featuring complex strategy games” but not both.
Someone in the room neither is quiet nor is calm.
All quiet persons are funny.
All brave persons are happy.
Everyone in the room collects comic books or cannot play the guitar.
Someone in the room uses an ios phone and is a quiet person.
All quiet persons are old.
No old person is patient.
It is not the case that “Genevieve and Martin hate each other”. | All brave persons are funny. | entailment | room(jerry)&room(greg)&room(genevieve)&(![X]:(room(X)=>(X='jerry'|X='greg'|X='genevieve')))&
((![X]:(room(X)=>(~(generous(X)&person(X)))))=>(![X]:(quiet(X)=>calm(X))))&
(((like(genevieve,martin) & like(martin,genevieve)))=>(![X]:(curious(X)=>kind(X))))&
((?[X]:(room(X)&(((~like(felix,X))&(is_not_an_avid_hiker(X))&(brave(X))))))=>(![X]:((room(X)&(X!=jerry))=>older(jerry,X))))&
((?[X]:(room(X)&(((uses_an_ios_phone(X))&(quiet(X)&person(X))))))=>(~?[X]:(generous(X)=>happy(X))))&
((?[X]:(room(X)&(enjoys_windsurfing(X))))<~>(~?[X]:(room(X)=>(hosts_regular_game_nights_featuring_complex_strategy_games(X)))))&
(?[X]:(room(X)&(~((quiet(X))|(calm(X))))))&
(![X]:(quiet(X)=>funny(X)))&
(![X]:(brave(X)=>happy(X)))&
(![X]:(room(X)=>(((cannot_play_the_guitar(X))|(collects_comic_books(X))))))&
(?[X]:(room(X)&(((uses_an_ios_phone(X))&(quiet(X)&person(X))))))&
(![X]:(quiet(X)=>old(X)))&
(~?[X]:(old(X)=>patient(X)))&
(~((hate(genevieve,martin) & hate(martin,genevieve)))) | room(jerry)&room(greg)&room(genevieve)&(![X]:(room(X)=>(X='jerry'|X='greg'|X='genevieve')))&
![X]:(brave(X)=>funny(X)) | [
"p0",
"p4",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 5317572018989428594864861
% SZS output start Proof for 5317572018989428594864861
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
48. ? [X0] : (person(X0) & quiet(X0) & predo(X0) & room(X0)) => ~? [X0] : (generous(X0) => happy(X0)) [input p4]
52. ! [X0] : (brave(X0) => happy(X0)) [input p8]
54. ? [X0] : (person(X0) & quiet(X0) & predo(X0) & room(X0)) [input p10]
58. ~(! [X0] : (brave(X0) => funny(X0)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis]
61. ? [X0] : (person(X0) & quiet(X0) & predo(X0) & room(X0)) => ~? [X1] : (generous(X1) => happy(X1)) [rectify 48]
63. ~(! [X0] : (brave(X0) => funny(X0)) & ! [X1] : (room(X1) => (fred = X1 | paul = X1 | mary = X1)) & room(fred) & room(paul) & room(mary)) [rectify 58]
71. ? [X0] : (person(X0) & quiet(X0) & predo(X0) & room(X0)) => ~? [X1] : happy(X1) [pure predicate removal 61]
143. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
144. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 143]
146. ! [X1] : ~happy(X1) | ! [X0] : (~person(X0) | ~quiet(X0) | ~predo(X0) | ~room(X0)) [ennf transformation 71]
151. ! [X0] : (happy(X0) | ~brave(X0)) [ennf transformation 52]
154. ? [X0] : (~funny(X0) & brave(X0)) | ? [X1] : ((fred != X1 & paul != X1 & mary != X1) & room(X1)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 63]
155. ? [X0] : (~funny(X0) & brave(X0)) | ? [X1] : (fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 154]
160. ! [X0] : ~happy(X0) | ! [X1] : (~person(X1) | ~quiet(X1) | ~predo(X1) | ~room(X1)) [rectify 146]
168. ? [X0] : (person(X0) & quiet(X0) & predo(X0) & room(X0)) => (person(sK4) & quiet(sK4) & predo(sK4) & room(sK4)) [choice axiom]
169. person(sK4) & quiet(sK4) & predo(sK4) & room(sK4) [skolemisation 54,168]
170. ? [X0] : (~funny(X0) & brave(X0)) => (~funny(sK5) & brave(sK5)) [choice axiom]
171. ? [X1] : (fred != X1 & paul != X1 & mary != X1 & room(X1)) => (fred != sK6 & paul != sK6 & mary != sK6 & room(sK6)) [choice axiom]
172. (~funny(sK5) & brave(sK5)) | (fred != sK6 & paul != sK6 & mary != sK6 & room(sK6)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 155,171,170]
253. room(mary) [cnf transformation 144]
254. room(paul) [cnf transformation 144]
255. room(fred) [cnf transformation 144]
256. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 144]
259. ~happy(X0) | ~person(X1) | ~quiet(X1) | ~predo(X1) | ~room(X1) [cnf transformation 160]
269. ~brave(X0) | happy(X0) [cnf transformation 151]
270. room(sK4) [cnf transformation 169]
271. predo(sK4) [cnf transformation 169]
272. quiet(sK4) [cnf transformation 169]
273. person(sK4) [cnf transformation 169]
276. brave(sK5) | room(sK6) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 172]
277. brave(sK5) | mary != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 172]
278. brave(sK5) | paul != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 172]
279. brave(sK5) | fred != sK6 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 172]
298. 4 <=> ! [X1] : (~person(X1) | ~room(X1) | ~predo(X1) | ~quiet(X1)) [avatar definition]
299. ~predo(X1) | ~room(X1) | ~person(X1) | ~quiet(X1) <- (4) [avatar component clause 298]
301. 5 <=> ! [X0] : ~happy(X0) [avatar definition]
302. ~happy(X0) <- (5) [avatar component clause 301]
303. 4 | 5 [avatar split clause 259,301,298]
338. 13 <=> fred = sK6 [avatar definition]
340. fred != sK6 <- (~13) [avatar component clause 338]
350. 15 <=> paul = sK6 [avatar definition]
352. paul != sK6 <- (~15) [avatar component clause 350]
358. 16 <=> mary = sK6 [avatar definition]
360. mary != sK6 <- (~16) [avatar component clause 358]
366. 17 <=> room(sK6) [avatar definition]
368. room(sK6) <- (17) [avatar component clause 366]
370. brave(sK5) | fred != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 279,255]
371. brave(sK5) | fred != sK6 | ~room(mary) [subsumption resolution 370,254]
372. brave(sK5) | fred != sK6 [subsumption resolution 371,253]
374. 18 <=> brave(sK5) [avatar definition]
376. brave(sK5) <- (18) [avatar component clause 374]
377. ~13 | 18 [avatar split clause 372,374,338]
378. brave(sK5) | paul != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 278,255]
379. brave(sK5) | paul != sK6 | ~room(mary) [subsumption resolution 378,254]
380. brave(sK5) | paul != sK6 [subsumption resolution 379,253]
381. ~15 | 18 [avatar split clause 380,374,350]
382. brave(sK5) | mary != sK6 | ~room(paul) | ~room(mary) [subsumption resolution 277,255]
383. brave(sK5) | mary != sK6 | ~room(mary) [subsumption resolution 382,254]
384. brave(sK5) | mary != sK6 [subsumption resolution 383,253]
385. ~16 | 18 [avatar split clause 384,374,358]
386. brave(sK5) | room(sK6) | ~room(paul) | ~room(mary) [subsumption resolution 276,255]
387. brave(sK5) | room(sK6) | ~room(mary) [subsumption resolution 386,254]
388. brave(sK5) | room(sK6) [subsumption resolution 387,253]
389. 17 | 18 [avatar split clause 388,374,366]
393. ~room(sK4) | ~person(sK4) | ~quiet(sK4) <- (4) [resolution 299,271]
394. ~person(sK4) | ~quiet(sK4) <- (4) [subsumption resolution 393,270]
395. ~quiet(sK4) <- (4) [subsumption resolution 394,273]
396. $false <- (4) [subsumption resolution 395,272]
397. ~4 [avatar contradiction clause 396]
446. paul = sK6 | mary = sK6 | fred = sK6 <- (17) [resolution 256,368]
486. mary = sK6 | fred = sK6 <- (~15, 17) [subsumption resolution 446,352]
487. fred = sK6 <- (~15, ~16, 17) [subsumption resolution 486,360]
488. $false <- (~13, ~15, ~16, 17) [subsumption resolution 487,340]
489. 13 | 15 | 16 | ~17 [avatar contradiction clause 488]
518. happy(sK5) <- (18) [resolution 376,269]
519. $false <- (5, 18) [subsumption resolution 518,302]
520. ~5 | ~18 [avatar contradiction clause 519]
521. $false [avatar sat refutation 303,377,381,385,389,397,489,520]
% SZS output end Proof for 5317572018989428594864861
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.169376 |
Bryan, Joseph, Steven, Robert, Glenda are the only persons in the room.
“Someone in the room uses a Windows laptop” only if “Bryan dreamt that “everyone in the room is a scotch connoisseur if they has a piercing and vice versa””.
“Bryan neither maintains a large, organic vegetable garden year-round nor enjoys fishing” if “someone outside the room can play the piano” and vice versa.
If “everyone outside the room drives a hybrid car or does not maintain a personal blog focused on cybersecurity tips” then “Joseph does not use a Windows laptop”.
“Everyone anywhere does not design and sews custom cosplay costumes for conventions” if “everyone anywhere plays eSports competitively or cannot play the piano”.
If “not everyone outside the room competes in national level swimming championships and does not use a Windows laptop” then “Joseph maintains a personal blog focused on cybersecurity tips”.
If “Joseph maintains a personal blog focused on cybersecurity tips” then “everyone in the room plays eSports competitively”.
“Everyone in the room does not have a piercing or cannot play the piano” if “everyone in the room owns a 3D printer or does not watche fantasy movies” and vice versa.
Bryan maintains a personal blog focused on cybersecurity tips.
Not everyone in the room does not own an extensive assortment of vintage comic book memorabilia.
Everyone in the room either plays eSports competitively or does not practice graffiti art but not both if they has a pet dog.
Joseph enjoys windsurfing.
Joseph does not watche fantasy movies.
At least one person anywhere maintains a personal blog focused on cybersecurity tips.
Joseph competes in national level swimming championships.
Bryan writes in-depth travel guides for off-the-beaten-path destinations. | Bryan writes in-depth travel guides for off-the-beaten-path destinations. | entailment | room(bryan)&room(joseph)&room(steven)&room(robert)&room(glenda)&(![X]:(room(X)=>(X='bryan'|X='joseph'|X='steven'|X='robert'|X='glenda')))&
((?[X]:(room(X)&(uses_a_Windows_laptop(X))))=>((bryan_dream=>(![X]:(room(X)=>(((is_a_scotch_connoisseur(X))<=>(has_a_piercing(X)))))))))&
((?[X]:(~room(X)&(can_play_the_piano(X))))<=>(~((maintains_a_large,_organic_vegetable_garden_year-round(bryan))|(enjoys_fishing(bryan)))))&
((![X]:(~room(X)=>(((does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))|(drives_a_hybrid_car(X))))))=>(does_not_use_a_Windows_laptop(joseph)))&
((![X]:(anywhere(X)=>(((cannot_play_the_piano(X))|(plays_eSports_competitively(X))))))=>(![X]:(anywhere(X)=>(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X)))))&
(((~![X]:(~room(X)=>(((competes_in_national_level_swimming_championships(X))&(does_not_use_a_Windows_laptop(X))))))=>(maintains_a_personal_blog_focused_on_cybersecurity_tips(joseph)))&
((maintains_a_personal_blog_focused_on_cybersecurity_tips(joseph))=>(![X]:(room(X)=>(plays_eSports_competitively(X))))))&
((![X]:(room(X)=>(((does_not_watche_fantasy_movies(X))|(owns_a_3D_printer(X))))))<=>(![X]:(room(X)=>(((cannot_play_the_piano(X))|(does_not_have_a_piercing(X)))))))&
(maintains_a_personal_blog_focused_on_cybersecurity_tips(bryan))&
(~![X]:(room(X)=>(does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))&
(![X]:(room(X)=>(((has_a_pet_dog(X))=>(((plays_eSports_competitively(X))<~>(does_not_practice_graffiti_art(X))))))))&
(enjoys_windsurfing(joseph))&
(does_not_watche_fantasy_movies(joseph))&
(((?[X]:(anywhere(X)&maintains_a_personal_blog_focused_on_cybersecurity_tips(X)))))&
(competes_in_national_level_swimming_championships(joseph))&
(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(bryan))&
(is_a_scotch_connoisseur(joseph))&
(does_not_enjoy_fishing(joseph))&
(![X]:(room(X)=>(((owns_a_3D_printer(X))=>(~((enjoys_virtual_reality_gaming(X))|(can_play_the_piano(X))))))))&
(![X]:(room(X)=>(((~((enjoys_virtual_reality_gaming(X))|(can_play_the_piano(X))))<=>(reads_mystery_novels(X))))))&
(does_not_collect_limited-edition_art_prints_from_contemporary_artists(bryan))&
(![X]:(room(X)=>(owns_a_3D_printer(X))))&
(![X]:(room(X)=>(((enjoys_virtual_reality_gaming(X))=>(is_not_a_scotch_connoisseur(X))))))&
(does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(joseph)) | room(bryan)&room(joseph)&room(steven)&room(robert)&room(glenda)&(![X]:(room(X)=>(X='bryan'|X='joseph'|X='steven'|X='robert'|X='glenda')))&
writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(bryan) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 8370494824237711591776846
% SZS output start Proof for 8370494824237711591776846
44. ~preds(paul) & ! [X0] : (room(X0) => (predl(X0) => ~predh(X0))) & ! [X0] : (room(X0) => predv(X0)) & ~predt(mary) & ! [X0] : (room(X0) => (~(predo(X0) | predl(X0)) <=> predm(X0))) & ! [X0] : (room(X0) => (predv(X0) => ~(predo(X0) | predl(X0)))) & ~predp(paul) & predh(paul) & preds(mary) & predx(paul) & ? [X0] : (predq(X0) & anywhere(X0)) & ~predn(paul) & predj(paul) & ! [X0] : (room(X0) => (predu(X0) => (predg(X0) <~> ~predk(X0)))) & ~! [X0] : (room(X0) => ~predc(X0)) & predq(mary) & (! [X0] : (room(X0) => (predv(X0) | ~predn(X0))) <=> ! [X0] : (room(X0) => (~predb(X0) | ~predo(X0)))) & (predq(paul) => ! [X0] : (room(X0) => predg(X0))) & (~! [X0] : (~room(X0) => (~prede(X0) & predx(X0))) => predq(paul)) & (! [X0] : (anywhere(X0) => (predg(X0) | ~predo(X0))) => ! [X0] : (anywhere(X0) => ~preda(X0))) & (! [X0] : (~room(X0) => (predi(X0) | ~predq(X0))) => ~prede(paul)) & (? [X0] : (predo(X0) & ~room(X0)) <=> ~(predp(mary) | predz(mary))) & (? [X0] : (prede(X0) & room(X0)) => (mary_dream => ! [X0] : (room(X0) => (predh(X0) <=> predb(X0))))) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
45. ~(preds(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]
46. ~preds(paul) & ! [X0] : (room(X0) => (predl(X0) => ~predh(X0))) & ! [X1] : (room(X1) => predv(X1)) & ~predt(mary) & ! [X2] : (room(X2) => (~(predo(X2) | predl(X2)) <=> predm(X2))) & ! [X3] : (room(X3) => (predv(X3) => ~(predo(X3) | predl(X3)))) & ~predp(paul) & predh(paul) & preds(mary) & predx(paul) & ? [X4] : (predq(X4) & anywhere(X4)) & ~predn(paul) & predj(paul) & ! [X5] : (room(X5) => (predu(X5) => (predg(X5) <~> ~predk(X5)))) & ~! [X6] : (room(X6) => ~predc(X6)) & predq(mary) & (! [X7] : (room(X7) => (predv(X7) | ~predn(X7))) <=> ! [X8] : (room(X8) => (~predb(X8) | ~predo(X8)))) & (predq(paul) => ! [X9] : (room(X9) => predg(X9))) & (~! [X10] : (~room(X10) => (~prede(X10) & predx(X10))) => predq(paul)) & (! [X11] : (anywhere(X11) => (predg(X11) | ~predo(X11))) => ! [X12] : (anywhere(X12) => ~preda(X12))) & (! [X13] : (~room(X13) => (predi(X13) | ~predq(X13))) => ~prede(paul)) & (? [X14] : (predo(X14) & ~room(X14)) <=> ~(predp(mary) | predz(mary))) & (? [X15] : (prede(X15) & room(X15)) => (mary_dream => ! [X16] : (room(X16) => (predh(X16) <=> predb(X16))))) & ! [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. ~preds(paul) & ! [X0] : (room(X0) => (predl(X0) => ~predh(X0))) & ! [X1] : (room(X1) => predv(X1)) & ! [X2] : (room(X2) => (~(predo(X2) | predl(X2)) <=> predm(X2))) & ! [X3] : (room(X3) => (predv(X3) => ~(predo(X3) | predl(X3)))) & ~predp(paul) & predh(paul) & preds(mary) & predx(paul) & ? [X4] : (predq(X4) & anywhere(X4)) & ~predn(paul) & predj(paul) & ! [X5] : (room(X5) => (predu(X5) => (predg(X5) <~> ~predk(X5)))) & ~! [X6] : (room(X6) => ~predc(X6)) & predq(mary) & (! [X7] : (room(X7) => (predv(X7) | ~predn(X7))) <=> ! [X8] : (room(X8) => (~predb(X8) | ~predo(X8)))) & (predq(paul) => ! [X9] : (room(X9) => predg(X9))) & (~! [X10] : (~room(X10) => (~prede(X10) & predx(X10))) => predq(paul)) & (! [X11] : (anywhere(X11) => (predg(X11) | ~predo(X11))) => ! [X12] : (anywhere(X12) => ~preda(X12))) & (! [X13] : (~room(X13) => (predi(X13) | ~predq(X13))) => ~prede(paul)) & (? [X14] : (predo(X14) & ~room(X14)) <=> ~(predp(mary) | predz(mary))) & (? [X15] : (prede(X15) & room(X15)) => (mary_dream => ! [X16] : (room(X16) => (predh(X16) <=> predb(X16))))) & ! [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. ~preds(paul) & ! [X0] : (room(X0) => (predl(X0) => ~predh(X0))) & ! [X1] : (room(X1) => predv(X1)) & ! [X2] : (room(X2) => (~(predo(X2) | predl(X2)) <=> predm(X2))) & ! [X3] : (room(X3) => (predv(X3) => ~(predo(X3) | predl(X3)))) & ~predp(paul) & predh(paul) & preds(mary) & predx(paul) & ? [X4] : (predq(X4) & anywhere(X4)) & ~predn(paul) & ! [X5] : (room(X5) => (predu(X5) => (predg(X5) <~> ~predk(X5)))) & ~! [X6] : (room(X6) => ~predc(X6)) & predq(mary) & (! [X7] : (room(X7) => (predv(X7) | ~predn(X7))) <=> ! [X8] : (room(X8) => (~predb(X8) | ~predo(X8)))) & (predq(paul) => ! [X9] : (room(X9) => predg(X9))) & (~! [X10] : (~room(X10) => (~prede(X10) & predx(X10))) => predq(paul)) & (! [X11] : (anywhere(X11) => (predg(X11) | ~predo(X11))) => ! [X12] : (anywhere(X12) => ~preda(X12))) & (! [X13] : (~room(X13) => (predi(X13) | ~predq(X13))) => ~prede(paul)) & (? [X14] : (predo(X14) & ~room(X14)) <=> ~(predp(mary) | predz(mary))) & (? [X15] : (prede(X15) & room(X15)) => (mary_dream => ! [X16] : (room(X16) => (predh(X16) <=> predb(X16))))) & ! [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. ~preds(paul) & ! [X0] : (room(X0) => (predl(X0) => ~predh(X0))) & ! [X1] : (room(X1) => predv(X1)) & ! [X2] : (room(X2) => (~(predo(X2) | predl(X2)) <=> predm(X2))) & ! [X3] : (room(X3) => (predv(X3) => ~(predo(X3) | predl(X3)))) & ~predp(paul) & predh(paul) & preds(mary) & predx(paul) & ? [X4] : (predq(X4) & anywhere(X4)) & ~predn(paul) & ~! [X6] : (room(X6) => ~predc(X6)) & predq(mary) & (! [X7] : (room(X7) => (predv(X7) | ~predn(X7))) <=> ! [X8] : (room(X8) => (~predb(X8) | ~predo(X8)))) & (predq(paul) => ! [X9] : (room(X9) => predg(X9))) & (~! [X10] : (~room(X10) => (~prede(X10) & predx(X10))) => predq(paul)) & (! [X11] : (anywhere(X11) => (predg(X11) | ~predo(X11))) => ! [X12] : (anywhere(X12) => ~preda(X12))) & (! [X13] : (~room(X13) => (predi(X13) | ~predq(X13))) => ~prede(paul)) & (? [X14] : (predo(X14) & ~room(X14)) <=> ~(predp(mary) | predz(mary))) & (? [X15] : (prede(X15) & room(X15)) => (mary_dream => ! [X16] : (room(X16) => (predh(X16) <=> predb(X16))))) & ! [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. ~preds(paul) & ! [X0] : (room(X0) => (predl(X0) => ~predh(X0))) & ! [X1] : (room(X1) => predv(X1)) & ! [X2] : (room(X2) => (~(predo(X2) | predl(X2)) <=> predm(X2))) & ! [X3] : (room(X3) => (predv(X3) => ~(predo(X3) | predl(X3)))) & ~predp(paul) & predh(paul) & preds(mary) & predx(paul) & ? [X4] : (predq(X4) & anywhere(X4)) & ~predn(paul) & ~! [X6] : ~room(X6) & predq(mary) & (! [X7] : (room(X7) => (predv(X7) | ~predn(X7))) <=> ! [X8] : (room(X8) => (~predb(X8) | ~predo(X8)))) & (predq(paul) => ! [X9] : (room(X9) => predg(X9))) & (~! [X10] : (~room(X10) => (~prede(X10) & predx(X10))) => predq(paul)) & (! [X11] : (anywhere(X11) => (predg(X11) | ~predo(X11))) => ! [X12] : (anywhere(X12) => ~preda(X12))) & (! [X13] : (~room(X13) => (predi(X13) | ~predq(X13))) => ~prede(paul)) & (? [X14] : (predo(X14) & ~room(X14)) <=> ~(predp(mary) | predz(mary))) & (? [X15] : (prede(X15) & room(X15)) => (mary_dream => ! [X16] : (room(X16) => (predh(X16) <=> predb(X16))))) & ! [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. ~preds(paul) & ! [X0] : (room(X0) => (predl(X0) => ~predh(X0))) & ! [X1] : (room(X1) => predv(X1)) & ! [X2] : (room(X2) => (~(predo(X2) | predl(X2)) <=> predm(X2))) & ! [X3] : (room(X3) => (predv(X3) => ~(predo(X3) | predl(X3)))) & ~predp(paul) & predh(paul) & preds(mary) & ? [X4] : (predq(X4) & anywhere(X4)) & ~predn(paul) & ~! [X6] : ~room(X6) & predq(mary) & (! [X7] : (room(X7) => (predv(X7) | ~predn(X7))) <=> ! [X8] : (room(X8) => (~predb(X8) | ~predo(X8)))) & (predq(paul) => ! [X9] : (room(X9) => predg(X9))) & (~! [X10] : (~room(X10) => ~prede(X10)) => predq(paul)) & (! [X11] : (anywhere(X11) => (predg(X11) | ~predo(X11))) => ! [X12] : (anywhere(X12) => ~preda(X12))) & (! [X13] : (~room(X13) => (predi(X13) | ~predq(X13))) => ~prede(paul)) & (? [X14] : (predo(X14) & ~room(X14)) <=> ~(predp(mary) | predz(mary))) & (? [X15] : (prede(X15) & room(X15)) => (mary_dream => ! [X16] : (room(X16) => (predh(X16) <=> predb(X16))))) & ! [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. ~preds(paul) & ! [X0] : (room(X0) => (predl(X0) => ~predh(X0))) & ! [X1] : (room(X1) => predv(X1)) & ! [X2] : (room(X2) => (~(predo(X2) | predl(X2)) <=> predm(X2))) & ! [X3] : (room(X3) => (predv(X3) => ~(predo(X3) | predl(X3)))) & ~predp(paul) & predh(paul) & preds(mary) & ? [X4] : (predq(X4) & anywhere(X4)) & ~predn(paul) & ~! [X6] : ~room(X6) & predq(mary) & (! [X7] : (room(X7) => (predv(X7) | ~predn(X7))) <=> ! [X8] : (room(X8) => (~predb(X8) | ~predo(X8)))) & (predq(paul) => ! [X9] : (room(X9) => predg(X9))) & (~! [X10] : (~room(X10) => ~prede(X10)) => predq(paul)) & (! [X13] : (~room(X13) => (predi(X13) | ~predq(X13))) => ~prede(paul)) & (? [X14] : (predo(X14) & ~room(X14)) <=> ~(predp(mary) | predz(mary))) & (? [X15] : (prede(X15) & room(X15)) => (mary_dream => ! [X16] : (room(X16) => (predh(X16) <=> predb(X16))))) & ! [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. ~preds(paul) & ! [X0] : (room(X0) => (predl(X0) => ~predh(X0))) & ! [X1] : (room(X1) => predv(X1)) & ! [X2] : (room(X2) => (~(predo(X2) | predl(X2)) <=> predm(X2))) & ! [X3] : (room(X3) => (predv(X3) => ~(predo(X3) | predl(X3)))) & ~predp(paul) & predh(paul) & preds(mary) & ? [X4] : predq(X4) & ~predn(paul) & ~! [X6] : ~room(X6) & predq(mary) & (! [X7] : (room(X7) => (predv(X7) | ~predn(X7))) <=> ! [X8] : (room(X8) => (~predb(X8) | ~predo(X8)))) & (predq(paul) => ! [X9] : (room(X9) => predg(X9))) & (~! [X10] : (~room(X10) => ~prede(X10)) => predq(paul)) & (! [X13] : (~room(X13) => (predi(X13) | ~predq(X13))) => ~prede(paul)) & (? [X14] : (predo(X14) & ~room(X14)) <=> ~(predp(mary) | predz(mary))) & (? [X15] : (prede(X15) & room(X15)) => (mary_dream => ! [X16] : (room(X16) => (predh(X16) <=> predb(X16))))) & ! [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]
55. ~preds(paul) & ! [X0] : (room(X0) => (predl(X0) => ~predh(X0))) & ! [X1] : (room(X1) => predv(X1)) & ! [X2] : (room(X2) => (~(predo(X2) | predl(X2)) <=> predm(X2))) & ! [X3] : (room(X3) => (predv(X3) => ~(predo(X3) | predl(X3)))) & ~predp(paul) & predh(paul) & preds(mary) & ? [X4] : predq(X4) & ~predn(paul) & ~! [X6] : ~room(X6) & predq(mary) & (! [X7] : (room(X7) => (predv(X7) | ~predn(X7))) <=> ! [X8] : (room(X8) => (~predb(X8) | ~predo(X8)))) & (~! [X10] : (~room(X10) => ~prede(X10)) => predq(paul)) & (! [X13] : (~room(X13) => (predi(X13) | ~predq(X13))) => ~prede(paul)) & (? [X14] : (predo(X14) & ~room(X14)) <=> ~(predp(mary) | predz(mary))) & (? [X15] : (prede(X15) & room(X15)) => (mary_dream => ! [X16] : (room(X16) => (predh(X16) <=> predb(X16))))) & ! [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]
56. ~preds(paul) & ! [X0] : (room(X0) => (predl(X0) => ~predh(X0))) & ! [X1] : (room(X1) => predv(X1)) & ! [X2] : (room(X2) => (~(predo(X2) | predl(X2)) <=> predm(X2))) & ! [X3] : (room(X3) => (predv(X3) => ~(predo(X3) | predl(X3)))) & ~predp(paul) & predh(paul) & preds(mary) & ~predn(paul) & ~! [X6] : ~room(X6) & (! [X7] : (room(X7) => (predv(X7) | ~predn(X7))) <=> ! [X8] : (room(X8) => (~predb(X8) | ~predo(X8)))) & (! [X13] : (~room(X13) => predi(X13)) => ~prede(paul)) & (? [X14] : (predo(X14) & ~room(X14)) <=> ~(predp(mary) | predz(mary))) & (? [X15] : (prede(X15) & room(X15)) => (mary_dream => ! [X16] : (room(X16) => (predh(X16) <=> predb(X16))))) & ! [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. ~preds(paul) & ! [X0] : (room(X0) => (predl(X0) => ~predh(X0))) & ! [X1] : (room(X1) => predv(X1)) & ! [X2] : (room(X2) => (~(predo(X2) | predl(X2)) <=> predm(X2))) & ! [X3] : (room(X3) => (predv(X3) => ~(predo(X3) | predl(X3)))) & ~predp(paul) & predh(paul) & preds(mary) & ~predn(paul) & ~! [X6] : ~room(X6) & (! [X7] : (room(X7) => (predv(X7) | ~predn(X7))) <=> ! [X8] : (room(X8) => (~predb(X8) | ~predo(X8)))) & (! [X13] : ~~room(X13) => ~prede(paul)) & (? [X14] : (predo(X14) & ~room(X14)) <=> ~(predp(mary) | predz(mary))) & (? [X15] : (prede(X15) & room(X15)) => (mary_dream => ! [X16] : (room(X16) => (predh(X16) <=> predb(X16))))) & ! [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. ~preds(paul) & ! [X0] : (room(X0) => (predl(X0) => ~predh(X0))) & ! [X1] : (room(X1) => predv(X1)) & ! [X2] : (room(X2) => (~(predo(X2) | predl(X2)) <=> predm(X2))) & ! [X3] : (room(X3) => (predv(X3) => ~(predo(X3) | predl(X3)))) & ~predp(paul) & predh(paul) & preds(mary) & ~predn(paul) & ~! [X6] : ~room(X6) & (! [X7] : (room(X7) => (predv(X7) | ~predn(X7))) <=> ! [X8] : (room(X8) => (~predb(X8) | ~predo(X8)))) & (! [X13] : ~~room(X13) => ~prede(paul)) & (? [X14] : (predo(X14) & ~room(X14)) <=> ~(predp(mary) | predz(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. ~preds(paul) & ! [X0] : (room(X0) => (predl(X0) => ~predh(X0))) & ! [X1] : (room(X1) => predv(X1)) & ! [X2] : (room(X2) => (~(predo(X2) | predl(X2)) <=> predm(X2))) & ! [X3] : (room(X3) => (predv(X3) => ~(predo(X3) | predl(X3)))) & ~predp(paul) & predh(paul) & preds(mary) & ~predn(paul) & ~! [X6] : ~room(X6) & (! [X7] : (room(X7) => (predv(X7) | ~predn(X7))) <=> ! [X8] : (room(X8) => (~predb(X8) | ~predo(X8)))) & (? [X14] : (predo(X14) & ~room(X14)) <=> ~(predp(mary) | predz(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]
131. ~preds(paul) & ! [X0] : ((~predh(X0) | ~predl(X0)) | ~room(X0)) & ! [X1] : (predv(X1) | ~room(X1)) & ! [X2] : (((~predo(X2) & ~predl(X2)) <=> predm(X2)) | ~room(X2)) & ! [X3] : (((~predo(X3) & ~predl(X3)) | ~predv(X3)) | ~room(X3)) & ~predp(paul) & predh(paul) & preds(mary) & ~predn(paul) & ? [X6] : room(X6) & (! [X7] : ((predv(X7) | ~predn(X7)) | ~room(X7)) <=> ! [X8] : ((~predb(X8) | ~predo(X8)) | ~room(X8))) & (? [X14] : (predo(X14) & ~room(X14)) <=> (~predp(mary) & ~predz(mary))) & ! [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 59]
132. ~preds(paul) & ! [X0] : (~predh(X0) | ~predl(X0) | ~room(X0)) & ! [X1] : (predv(X1) | ~room(X1)) & ! [X2] : (((~predo(X2) & ~predl(X2)) <=> predm(X2)) | ~room(X2)) & ! [X3] : ((~predo(X3) & ~predl(X3)) | ~predv(X3) | ~room(X3)) & ~predp(paul) & predh(paul) & preds(mary) & ~predn(paul) & ? [X6] : room(X6) & (! [X7] : (predv(X7) | ~predn(X7) | ~room(X7)) <=> ! [X8] : (~predb(X8) | ~predo(X8) | ~room(X8))) & (? [X14] : (predo(X14) & ~room(X14)) <=> (~predp(mary) & ~predz(mary))) & ! [X17] : (john = X17 | alice = X17 | fred = X17 | paul = X17 | mary = X17 | ~room(X17)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 131]
133. ~preds(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 45]
134. ~preds(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 133]
136. ~preds(paul) & ! [X0] : (~predh(X0) | ~predl(X0) | ~room(X0)) & ! [X1] : (predv(X1) | ~room(X1)) & ! [X2] : ((((~predo(X2) & ~predl(X2)) | ~predm(X2)) & (predm(X2) | (predo(X2) | predl(X2)))) | ~room(X2)) & ! [X3] : ((~predo(X3) & ~predl(X3)) | ~predv(X3) | ~room(X3)) & ~predp(paul) & predh(paul) & preds(mary) & ~predn(paul) & ? [X6] : room(X6) & ((! [X7] : (predv(X7) | ~predn(X7) | ~room(X7)) | ? [X8] : (predb(X8) & predo(X8) & room(X8))) & (! [X8] : (~predb(X8) | ~predo(X8) | ~room(X8)) | ? [X7] : (~predv(X7) & predn(X7) & room(X7)))) & ((? [X14] : (predo(X14) & ~room(X14)) | (predp(mary) | predz(mary))) & ((~predp(mary) & ~predz(mary)) | ! [X14] : (~predo(X14) | room(X14)))) & ! [X17] : (john = X17 | alice = X17 | fred = X17 | paul = X17 | mary = X17 | ~room(X17)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [nnf transformation 132]
137. ~preds(paul) & ! [X0] : (~predh(X0) | ~predl(X0) | ~room(X0)) & ! [X1] : (predv(X1) | ~room(X1)) & ! [X2] : ((((~predo(X2) & ~predl(X2)) | ~predm(X2)) & (predm(X2) | predo(X2) | predl(X2))) | ~room(X2)) & ! [X3] : ((~predo(X3) & ~predl(X3)) | ~predv(X3) | ~room(X3)) & ~predp(paul) & predh(paul) & preds(mary) & ~predn(paul) & ? [X6] : room(X6) & (! [X7] : (predv(X7) | ~predn(X7) | ~room(X7)) | ? [X8] : (predb(X8) & predo(X8) & room(X8))) & (! [X8] : (~predb(X8) | ~predo(X8) | ~room(X8)) | ? [X7] : (~predv(X7) & predn(X7) & room(X7))) & (? [X14] : (predo(X14) & ~room(X14)) | predp(mary) | predz(mary)) & ((~predp(mary) & ~predz(mary)) | ! [X14] : (~predo(X14) | room(X14))) & ! [X17] : (john = X17 | alice = X17 | fred = X17 | paul = X17 | mary = X17 | ~room(X17)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 136]
138. ~preds(paul) & ! [X0] : (~predh(X0) | ~predl(X0) | ~room(X0)) & ! [X1] : (predv(X1) | ~room(X1)) & ! [X2] : ((((~predo(X2) & ~predl(X2)) | ~predm(X2)) & (predm(X2) | predo(X2) | predl(X2))) | ~room(X2)) & ! [X3] : ((~predo(X3) & ~predl(X3)) | ~predv(X3) | ~room(X3)) & ~predp(paul) & predh(paul) & preds(mary) & ~predn(paul) & ? [X4] : room(X4) & (! [X5] : (predv(X5) | ~predn(X5) | ~room(X5)) | ? [X6] : (predb(X6) & predo(X6) & room(X6))) & (! [X7] : (~predb(X7) | ~predo(X7) | ~room(X7)) | ? [X8] : (~predv(X8) & predn(X8) & room(X8))) & (? [X9] : (predo(X9) & ~room(X9)) | predp(mary) | predz(mary)) & ((~predp(mary) & ~predz(mary)) | ! [X10] : (~predo(X10) | room(X10))) & ! [X11] : (john = X11 | alice = X11 | fred = X11 | paul = X11 | mary = X11 | ~room(X11)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [rectify 137]
139. ? [X4] : room(X4) => room(sK0) [choice axiom]
140. ? [X6] : (predb(X6) & predo(X6) & room(X6)) => (predb(sK1) & predo(sK1) & room(sK1)) [choice axiom]
141. ? [X8] : (~predv(X8) & predn(X8) & room(X8)) => (~predv(sK2) & predn(sK2) & room(sK2)) [choice axiom]
142. ? [X9] : (predo(X9) & ~room(X9)) => (predo(sK3) & ~room(sK3)) [choice axiom]
143. ~preds(paul) & ! [X0] : (~predh(X0) | ~predl(X0) | ~room(X0)) & ! [X1] : (predv(X1) | ~room(X1)) & ! [X2] : ((((~predo(X2) & ~predl(X2)) | ~predm(X2)) & (predm(X2) | predo(X2) | predl(X2))) | ~room(X2)) & ! [X3] : ((~predo(X3) & ~predl(X3)) | ~predv(X3) | ~room(X3)) & ~predp(paul) & predh(paul) & preds(mary) & ~predn(paul) & room(sK0) & (! [X5] : (predv(X5) | ~predn(X5) | ~room(X5)) | (predb(sK1) & predo(sK1) & room(sK1))) & (! [X7] : (~predb(X7) | ~predo(X7) | ~room(X7)) | (~predv(sK2) & predn(sK2) & room(sK2))) & ((predo(sK3) & ~room(sK3)) | predp(mary) | predz(mary)) & ((~predp(mary) & ~predz(mary)) | ! [X10] : (~predo(X10) | room(X10))) & ! [X11] : (john = X11 | alice = X11 | fred = X11 | paul = X11 | mary = X11 | ~room(X11)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [skolemisation 138,142,141,140,139]
144. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK4 & alice != sK4 & fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) [choice axiom]
145. ~preds(mary) | (john != sK4 & alice != sK4 & fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 134,144]
226. room(mary) [cnf transformation 143]
227. room(paul) [cnf transformation 143]
228. room(fred) [cnf transformation 143]
229. room(alice) [cnf transformation 143]
230. room(john) [cnf transformation 143]
231. ~room(X11) | alice = X11 | fred = X11 | paul = X11 | mary = X11 | john = X11 [cnf transformation 143]
244. preds(mary) [cnf transformation 143]
255. ~preds(mary) | room(sK4) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 145]
256. ~preds(mary) | mary != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 145]
257. ~preds(mary) | paul != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 145]
258. ~preds(mary) | fred != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 145]
259. ~preds(mary) | alice != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 145]
260. ~preds(mary) | john != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 145]
288. john != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 260,244]
289. john != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 288,230]
290. john != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 289,229]
291. john != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 290,228]
292. john != sK4 | ~room(mary) [subsumption resolution 291,227]
293. john != sK4 [subsumption resolution 292,226]
294. alice != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 259,244]
295. alice != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 294,230]
296. alice != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 295,229]
297. alice != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 296,228]
298. alice != sK4 | ~room(mary) [subsumption resolution 297,227]
299. alice != sK4 [subsumption resolution 298,226]
300. fred != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 258,244]
301. fred != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 300,230]
302. fred != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 301,229]
303. fred != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 302,228]
304. fred != sK4 | ~room(mary) [subsumption resolution 303,227]
305. fred != sK4 [subsumption resolution 304,226]
306. paul != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 257,244]
307. paul != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 306,230]
308. paul != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 307,229]
309. paul != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 308,228]
310. paul != sK4 | ~room(mary) [subsumption resolution 309,227]
311. paul != sK4 [subsumption resolution 310,226]
312. mary != sK4 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 256,244]
313. mary != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 312,230]
314. mary != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 313,229]
315. mary != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 314,228]
316. mary != sK4 | ~room(mary) [subsumption resolution 315,227]
317. mary != sK4 [subsumption resolution 316,226]
318. room(sK4) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 255,244]
319. room(sK4) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 318,230]
320. room(sK4) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 319,229]
321. room(sK4) | ~room(paul) | ~room(mary) [subsumption resolution 320,228]
322. room(sK4) | ~room(mary) [subsumption resolution 321,227]
323. room(sK4) [subsumption resolution 322,226]
486. alice = sK4 | fred = sK4 | paul = sK4 | mary = sK4 | john = sK4 [resolution 231,323]
508. fred = sK4 | paul = sK4 | mary = sK4 | john = sK4 [subsumption resolution 486,299]
509. paul = sK4 | mary = sK4 | john = sK4 [subsumption resolution 508,305]
510. mary = sK4 | john = sK4 [subsumption resolution 509,311]
511. john = sK4 [subsumption resolution 510,317]
512. $false [subsumption resolution 511,293]
% SZS output end Proof for 8370494824237711591776846
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0.097011 |
Jessie is the only person in the room.
If “Jessie is passionate about collecting and restoring classic cars and can play the piano” then “Jessie practices kickboxing”.
Everyone in the room who is a wine connoisseur with a private cellar of vintage wines plays video games.
Everyone in the room who practices kickboxing has a piercing.
Not everyone in the room who neither can play the guitar nor creates bespoke furniture pieces from reclaimed wood drives a hybrid car.
Jessie collects vintage vinyl records, plays video games or knows morse code.
Everyone in the room who collects limited-edition art prints from contemporary artists enjoys watercolor painting.
Everyone anywhere who enjoys watercolor painting enjoys camping and organizing outdoor survival workshops.
Everyone in the room enjoys camping and organizing outdoor survival workshops only if they hosts regular game nights featuring complex strategy games.
Everyone in the room who hosts regular game nights featuring complex strategy games is a dedicated advocate for digital privacy and encryption.
Jessie enjoys watercolor painting. | Jessie hosts regular game nights featuring complex strategy games. | entailment | room(jessie)&(![X]:(room(X)=>(X='jessie')))&
((((is_passionate_about_collecting_and_restoring_classic_cars(jessie))&(can_play_the_piano(jessie))))=>(practices_kickboxing(jessie)))&
(![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(plays_video_games(X))))))&
(![X]:(room(X)=>(((practices_kickboxing(X))=>(has_a_piercing(X))))))&
(~![X]:(room(X)=>(((~((can_play_the_guitar(X))|(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))=>(drives_a_hybrid_car(X))))))&
(((collects_vintage_vinyl_records(jessie))|(plays_video_games(jessie))|(knows_morse_code(jessie))))&
(![X]:(room(X)=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))=>(enjoys_watercolor_painting(X))))))&
(![X]:(anywhere(X)=>(((enjoys_watercolor_painting(X))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))&
(![X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))<=(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))&
(![X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))&
(![X]:(room(X)=>(((is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))=>(((has_completed_a_triathlon(X))&(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))))&
(![X]:(room(X)=>(((does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))|(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))&
(~![X]:(room(X)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))=>(is_a_client_of_LVMH(X))))))&
(![X]:(room(X)=>(((is_a_client_of_LVMH(X))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))&
(![X]:(room(X)=>(((writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))=>(((has_a_tattoo(X))|(frequently_participates_in_hackathons_and_coding_competitions(X))|(has_a_saltwater_aquarium(X))))))))&
(enjoys_watercolor_painting(jessie))&
(plays_video_games(jessie))&
(![X]:(room(X)=>(((does_not_enjoy_stargazing(X))|(has_completed_a_triathlon(X))))))&
(![X]:(room(X)=>(((is_a_client_of_LVMH(X))=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))&
(![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(enjoys_coding_in_Python(X))))))&
(![X]:(room(X)=>(((enjoys_coding_in_Python(X))=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))&
(collects_limited-edition_art_prints_from_contemporary_artists(jessie)) | room(jessie)&(![X]:(room(X)=>(X='jessie')))&
hosts_regular_game_nights_featuring_complex_strategy_games(jessie) | [
"b4",
"p0",
"p7",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 596827896455217198604448
% SZS output start Proof for 596827896455217198604448
5. ! [X0] : anywhere(X0) [input b4]
44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
51. ! [X0] : (anywhere(X0) => (preda(X0) => predi(X0))) [input p7]
52. ! [X0] : (room(X0) => (predi(X0) => predp(X0))) [input p8]
59. preda(mary) [input p15]
66. ~(predp(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis]
152. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
156. ! [X0] : ((predi(X0) | ~preda(X0)) | ~anywhere(X0)) [ennf transformation 51]
157. ! [X0] : (predi(X0) | ~preda(X0) | ~anywhere(X0)) [flattening 156]
158. ! [X0] : ((predp(X0) | ~predi(X0)) | ~room(X0)) [ennf transformation 52]
159. ! [X0] : (predp(X0) | ~predi(X0) | ~room(X0)) [flattening 158]
171. ~predp(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 66]
177. ? [X0] : (mary != X0 & room(X0)) => (mary != sK2 & room(sK2)) [choice axiom]
178. ~predp(mary) | (mary != sK2 & room(sK2)) | ~room(mary) [skolemisation 171,177]
179. anywhere(X0) [cnf transformation 5]
260. room(mary) [cnf transformation 152]
261. ~room(X0) | mary = X0 [cnf transformation 152]
264. predi(X0) | ~preda(X0) | ~anywhere(X0) [cnf transformation 157]
265. ~predi(X0) | predp(X0) | ~room(X0) [cnf transformation 159]
271. preda(mary) [cnf transformation 59]
275. ~predp(mary) | room(sK2) | ~room(mary) [cnf transformation 178]
276. ~predp(mary) | mary != sK2 | ~room(mary) [cnf transformation 178]
277. ~preda(X0) | predi(X0) [subsumption resolution 264,179]
278. ~predp(mary) | mary != sK2 [subsumption resolution 276,260]
280. 1 <=> mary = sK2 [avatar definition]
282. mary != sK2 <- (~1) [avatar component clause 280]
284. 2 <=> predp(mary) [avatar definition]
287. ~1 | ~2 [avatar split clause 278,284,280]
288. ~predp(mary) | room(sK2) [subsumption resolution 275,260]
290. 3 <=> room(sK2) [avatar definition]
292. room(sK2) <- (3) [avatar component clause 290]
293. 3 | ~2 [avatar split clause 288,284,290]
294. predi(mary) [resolution 277,271]
302. predp(mary) | ~room(mary) [resolution 265,294]
306. predp(mary) [subsumption resolution 302,260]
307. 2 [avatar split clause 306,284]
308. mary = sK2 <- (3) [resolution 292,261]
309. $false <- (~1, 3) [subsumption resolution 308,282]
310. 1 | ~3 [avatar contradiction clause 309]
311. $false [avatar sat refutation 287,293,307,310]
% SZS output end Proof for 596827896455217198604448
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.152037 |
Ronnie, Lindsey, Timothy are the only persons in the room.
Everyone in the room who plays as a goalkeeper for a local amateur soccer team writes poetry, can play the guitar and knows morse code.
Everyone outside the room who collects first edition books drives a hybrid car.
Everyone in the room practices digital art if they drives a hybrid car.
Everyone in the room who either enjoys rooftop gardening or writes poetry but not both knows morse code.
Ronnie plays as a goalkeeper for a local amateur soccer team.
Everyone in the room does not play as a goalkeeper for a local amateur soccer team or knows morse code.
Everyone in the room who does not play as a goalkeeper for a local amateur soccer team knows morse code.
Everyone anywhere drives a hybrid car if they knows morse code.
Someone in the room knows morse code.
Someone in the room plays as a goalkeeper for a local amateur soccer team.
Everyone in the room who drives a hybrid car practices digital art, collects action figures and uses contact lenses.
Lindsey who collects first edition books knows morse code.
Someone in the room can play the guitar. | Everyone in the room drives a hybrid car. | entailment | room(ronnie)&room(lindsey)&room(timothy)&(![X]:(room(X)=>(X='ronnie'|X='lindsey'|X='timothy')))&
(![X]:(room(X)=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))=>(((writes_poetry(X))&(can_play_the_guitar(X))&(knows_morse_code(X))))))))&
(![X]:(~room(X)=>(((collects_first_edition_books(X))=>(drives_a_hybrid_car(X))))))&
(![X]:(room(X)=>(((drives_a_hybrid_car(X))=>(practices_digital_art(X))))))&
(![X]:(room(X)=>(((((enjoys_rooftop_gardening(X))<~>(writes_poetry(X))))=>(knows_morse_code(X))))))&
(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(ronnie))&
(![X]:(room(X)=>(((knows_morse_code(X))|(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))&
(![X]:(room(X)=>(((does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))=>(knows_morse_code(X))))))&
(![X]:(anywhere(X)=>(((knows_morse_code(X))=>(drives_a_hybrid_car(X))))))&
(?[X]:(room(X)&(knows_morse_code(X))))&
(?[X]:(room(X)&(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))&
(![X]:(room(X)=>(((drives_a_hybrid_car(X))=>(((practices_digital_art(X))&(collects_action_figures(X))&(uses_contact_lenses(X))))))))&
((collects_first_edition_books(lindsey))&(knows_morse_code(lindsey)))&
(?[X]:(room(X)&(can_play_the_guitar(X)))) | room(ronnie)&room(lindsey)&room(timothy)&(![X]:(room(X)=>(X='ronnie'|X='lindsey'|X='timothy')))&
![X]:(room(X)=>(drives_a_hybrid_car(X))) | [
"b4",
"p0",
"p1",
"p7",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 374966026258345105759462
% SZS output start Proof for 374966026258345105759462
5. ! [X0] : anywhere(X0) [input b4]
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
45. ! [X0] : (room(X0) => (preda(X0) => (predc(X0) & predh(X0) & predi(X0)))) [input p1]
51. ! [X0] : (room(X0) => (~preda(X0) => predc(X0))) [input p7]
52. ! [X0] : (anywhere(X0) => (predc(X0) => predd(X0))) [input p8]
56. predc(paul) & predb(paul) [input p12]
58. ~(! [X0] : (room(X0) => predd(X0)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis]
59. ~(! [X0] : (room(X0) => predd(X0)) & ! [X1] : (room(X1) => (fred = X1 | paul = X1 | mary = X1)) & room(fred) & room(paul) & room(mary)) [rectify 58]
65. ! [X0] : (room(X0) => (preda(X0) => (predc(X0) & predi(X0)))) [pure predicate removal 45]
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]
139. ! [X0] : (((predc(X0) & predi(X0)) | ~preda(X0)) | ~room(X0)) [ennf transformation 65]
140. ! [X0] : ((predc(X0) & predi(X0)) | ~preda(X0) | ~room(X0)) [flattening 139]
147. ! [X0] : ((predc(X0) | preda(X0)) | ~room(X0)) [ennf transformation 51]
148. ! [X0] : (predc(X0) | preda(X0) | ~room(X0)) [flattening 147]
149. ! [X0] : ((predd(X0) | ~predc(X0)) | ~anywhere(X0)) [ennf transformation 52]
150. ! [X0] : (predd(X0) | ~predc(X0) | ~anywhere(X0)) [flattening 149]
151. ? [X0] : (~predd(X0) & room(X0)) | ? [X1] : ((fred != X1 & paul != X1 & mary != X1) & room(X1)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 59]
152. ? [X0] : (~predd(X0) & room(X0)) | ? [X1] : (fred != X1 & paul != X1 & mary != X1 & room(X1)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 151]
161. ? [X0] : (~predd(X0) & room(X0)) => (~predd(sK3) & room(sK3)) [choice axiom]
162. ? [X1] : (fred != X1 & paul != X1 & mary != X1 & room(X1)) => (fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) [choice axiom]
163. (~predd(sK3) & room(sK3)) | (fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 152,162,161]
164. anywhere(X0) [cnf transformation 5]
245. room(mary) [cnf transformation 138]
246. room(paul) [cnf transformation 138]
247. room(fred) [cnf transformation 138]
248. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 138]
250. ~preda(X0) | predc(X0) | ~room(X0) [cnf transformation 140]
256. predc(X0) | preda(X0) | ~room(X0) [cnf transformation 148]
257. predd(X0) | ~predc(X0) | ~anywhere(X0) [cnf transformation 150]
263. predc(paul) [cnf transformation 56]
265. room(sK3) | room(sK4) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 163]
266. room(sK3) | mary != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 163]
267. room(sK3) | paul != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 163]
268. room(sK3) | fred != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 163]
269. ~predd(sK3) | room(sK4) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 163]
270. ~predd(sK3) | mary != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 163]
271. ~predd(sK3) | paul != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 163]
272. ~predd(sK3) | fred != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 163]
273. ~room(X0) | predc(X0) [subsumption resolution 256,250]
274. ~predc(X0) | predd(X0) [subsumption resolution 257,164]
275. ~predd(sK3) | fred != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 272,247]
276. ~predd(sK3) | fred != sK4 | ~room(mary) [subsumption resolution 275,246]
277. ~predd(sK3) | fred != sK4 [subsumption resolution 276,245]
279. 1 <=> fred = sK4 [avatar definition]
281. fred != sK4 <- (~1) [avatar component clause 279]
283. 2 <=> predd(sK3) [avatar definition]
285. ~predd(sK3) <- (~2) [avatar component clause 283]
286. ~1 | ~2 [avatar split clause 277,283,279]
287. ~predd(sK3) | paul != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 271,247]
288. ~predd(sK3) | paul != sK4 | ~room(mary) [subsumption resolution 287,246]
289. ~predd(sK3) | paul != sK4 [subsumption resolution 288,245]
291. 3 <=> paul = sK4 [avatar definition]
293. paul != sK4 <- (~3) [avatar component clause 291]
294. ~3 | ~2 [avatar split clause 289,283,291]
295. ~predd(sK3) | mary != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 270,247]
296. ~predd(sK3) | mary != sK4 | ~room(mary) [subsumption resolution 295,246]
297. ~predd(sK3) | mary != sK4 [subsumption resolution 296,245]
299. 4 <=> mary = sK4 [avatar definition]
301. mary != sK4 <- (~4) [avatar component clause 299]
302. ~4 | ~2 [avatar split clause 297,283,299]
303. ~predd(sK3) | room(sK4) | ~room(paul) | ~room(mary) [subsumption resolution 269,247]
304. ~predd(sK3) | room(sK4) | ~room(mary) [subsumption resolution 303,246]
305. ~predd(sK3) | room(sK4) [subsumption resolution 304,245]
307. 5 <=> room(sK4) [avatar definition]
309. room(sK4) <- (5) [avatar component clause 307]
310. 5 | ~2 [avatar split clause 305,283,307]
311. room(sK3) | fred != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 268,247]
312. room(sK3) | fred != sK4 | ~room(mary) [subsumption resolution 311,246]
313. room(sK3) | fred != sK4 [subsumption resolution 312,245]
315. 6 <=> room(sK3) [avatar definition]
317. room(sK3) <- (6) [avatar component clause 315]
318. ~1 | 6 [avatar split clause 313,315,279]
319. room(sK3) | paul != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 267,247]
320. room(sK3) | paul != sK4 | ~room(mary) [subsumption resolution 319,246]
321. room(sK3) | paul != sK4 [subsumption resolution 320,245]
322. ~3 | 6 [avatar split clause 321,315,291]
323. room(sK3) | mary != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 266,247]
324. room(sK3) | mary != sK4 | ~room(mary) [subsumption resolution 323,246]
325. room(sK3) | mary != sK4 [subsumption resolution 324,245]
326. ~4 | 6 [avatar split clause 325,315,299]
327. room(sK3) | room(sK4) | ~room(paul) | ~room(mary) [subsumption resolution 265,247]
328. room(sK3) | room(sK4) | ~room(mary) [subsumption resolution 327,246]
329. room(sK3) | room(sK4) [subsumption resolution 328,245]
330. 5 | 6 [avatar split clause 329,315,307]
331. predc(mary) [resolution 273,245]
333. predc(fred) [resolution 273,247]
339. predd(paul) [resolution 274,263]
340. predd(mary) [resolution 274,331]
341. predd(fred) [resolution 333,274]
396. paul = sK4 | mary = sK4 | fred = sK4 <- (5) [resolution 248,309]
436. mary = sK4 | fred = sK4 <- (~3, 5) [subsumption resolution 396,293]
437. fred = sK4 <- (~3, ~4, 5) [subsumption resolution 436,301]
438. $false <- (~1, ~3, ~4, 5) [subsumption resolution 437,281]
439. 1 | 3 | 4 | ~5 [avatar contradiction clause 438]
451. paul = sK3 | mary = sK3 | fred = sK3 <- (6) [resolution 317,248]
454. 16 <=> fred = sK3 [avatar definition]
456. fred = sK3 <- (16) [avatar component clause 454]
458. 17 <=> mary = sK3 [avatar definition]
460. mary = sK3 <- (17) [avatar component clause 458]
462. 18 <=> paul = sK3 [avatar definition]
464. paul = sK3 <- (18) [avatar component clause 462]
465. 16 | 17 | 18 | ~6 [avatar split clause 451,315,462,458,454]
468. ~predd(fred) <- (~2, 16) [backward demodulation 285,456]
469. $false <- (~2, 16) [subsumption resolution 468,341]
470. 2 | ~16 [avatar contradiction clause 469]
473. ~predd(mary) <- (~2, 17) [backward demodulation 285,460]
474. $false <- (~2, 17) [subsumption resolution 473,340]
475. 2 | ~17 [avatar contradiction clause 474]
479. ~predd(paul) <- (~2, 18) [backward demodulation 285,464]
481. $false <- (~2, 18) [subsumption resolution 479,339]
482. 2 | ~18 [avatar contradiction clause 481]
483. $false [avatar sat refutation 286,294,302,310,318,322,326,330,439,465,470,475,482]
% SZS output end Proof for 374966026258345105759462
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.041 s
% ------------------------------
% ------------------------------
| 0.266259 |
Ronnie, James, Gregory, Joshua are the only persons in the room.
“James neither is not happy nor is not humble” if “James is a kind person and is happy” and vice versa.
Either “James is not a tall person” or “Ronnie is patient, is strong or is curious” but not both.
“Gregory is a humble person” if “Ronnie is not brave”.
If “everyone in the room is strong and is not a strong tall person” then “James is kind” otherwise “Ronnie who is not a curious person, is not quiet, not generous, not humble and is not a quiet person is a patient person”.
If “Ronnie is not a kind person and is not a tall person” then “all tall persons are wise” otherwise “James is not a tall person”.
Either “Ronnie is not a happy person, is calm and is a calm person” or “Ronnie is wise” but not both.
Either “Gregory is funny” or “everyone in the room is brave” but not both.
“Ronnie is not a humble person” unless “Gregory is a happy person”.
Gregory is not a humble person.
Gregory is not a creative person.
James either is curious or is calm but not both.
James is not a generous person.
Someone who is a kind person and is not curious is richer than someone who is happy.
James is the least old in the room.
All quiet persons are curious.
All generous persons are humble.
Someone who is not generous is richer than someone who is strong, is brave and is kind.
Ronnie either is curious or is a calm person but not both.
If someone is not a patient person then he/she is kind and vice versa.
James is not creative.
Not everyone outside the room is a kind person if they is a tall person.
James is quiet.
James is funny. | James is funny. | entailment | room(ronnie)&room(james)&room(gregory)&room(joshua)&(![X]:(room(X)=>(X='ronnie'|X='james'|X='gregory'|X='joshua')))&
((((kind(james)&person(james))&(happy(james))))<=>(~((~happy(james))|(~humble(james)))))&
((~(tall(james)&person(james)))<~>(((patient(ronnie))|(strong(ronnie))|(curious(ronnie)))))&
((~brave(ronnie))=>(humble(gregory)&person(gregory)))&
(((![X]:(room(X)=>(((strong(X))&(~(strong(X)&tall(X)&person(X)))))))=>(kind(james)))&((~(![X]:(room(X)=>(((strong(X))&(~(strong(X)&tall(X)&person(X))))))))=>((((~(curious(ronnie)&person(ronnie)))&(~quiet(ronnie)&~generous(ronnie)&~humble(ronnie))&(~(quiet(ronnie)&person(ronnie)))))&(patient(ronnie)&person(ronnie)))))&
(((((~(kind(ronnie)&person(ronnie)))&(~(tall(ronnie)&person(ronnie)))))=>(![X]:(tall(X)=>wise(X))))&((~(((~(kind(ronnie)&person(ronnie)))&(~(tall(ronnie)&person(ronnie))))))=>(~(tall(james)&person(james)))))&
((((~(happy(ronnie)&person(ronnie)))&(calm(ronnie))&(calm(ronnie)&person(ronnie))))<~>(wise(ronnie)))&
((funny(gregory))<~>(![X]:(room(X)=>(brave(X)))))&
(~(happy(gregory)&person(gregory))=>(~(humble(ronnie)&person(ronnie))))&
(~(humble(gregory)&person(gregory)))&
(~(creative(gregory)&person(gregory)))&
(((curious(james))<~>(calm(james))))&
(~(generous(james)&person(james)))&
(?[X,Y]:((((kind(X)&person(X))&(~curious(X))))&(happy(Y))&(richer(X,Y))))&
(![X]:((room(X)&(X!=james))=>older(james,X)))&
(![X]:(quiet(X)=>curious(X)))&
(![X]:(generous(X)=>humble(X)))&
(?[X,Y]:((~generous(X))&(((strong(Y))&(brave(Y))&(kind(Y))))&(richer(X,Y))))&
(((curious(ronnie))<~>(calm(ronnie)&person(ronnie))))&
((![X]:((~(patient(X)&person(X)))<=>(kind(X)))))&
(~creative(james))&
(~![X]:(~room(X)=>(((tall(X)&person(X))=>(kind(X)&person(X))))))&
(quiet(james))&
(funny(james)) | room(ronnie)&room(james)&room(gregory)&room(joshua)&(![X]:(room(X)=>(X='ronnie'|X='james'|X='gregory'|X='joshua')))&
funny(james) | [
"p0",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 1160454892577843530352200
% SZS output start Proof for 1160454892577843530352200
44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
67. funny(paul) [input p23]
68. ~(funny(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis]
148. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
149. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 148]
167. ~funny(paul) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 68]
168. ~funny(paul) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 167]
196. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK8 & fred != sK8 & paul != sK8 & mary != sK8 & room(sK8)) [choice axiom]
197. ~funny(paul) | (alice != sK8 & fred != sK8 & paul != sK8 & mary != sK8 & room(sK8)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 168,196]
278. room(mary) [cnf transformation 149]
279. room(paul) [cnf transformation 149]
280. room(fred) [cnf transformation 149]
281. room(alice) [cnf transformation 149]
282. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 149]
351. funny(paul) [cnf transformation 67]
352. ~funny(paul) | room(sK8) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 197]
353. ~funny(paul) | mary != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 197]
354. ~funny(paul) | paul != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 197]
355. ~funny(paul) | fred != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 197]
356. ~funny(paul) | alice != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 197]
547. alice != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 356,351]
548. alice != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 547,281]
549. alice != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 548,280]
550. alice != sK8 | ~room(mary) [subsumption resolution 549,279]
551. alice != sK8 [subsumption resolution 550,278]
552. fred != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 355,351]
553. fred != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 552,281]
554. fred != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 553,280]
555. fred != sK8 | ~room(mary) [subsumption resolution 554,279]
556. fred != sK8 [subsumption resolution 555,278]
557. paul != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 354,351]
558. paul != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 557,281]
559. paul != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 558,280]
560. paul != sK8 | ~room(mary) [subsumption resolution 559,279]
561. paul != sK8 [subsumption resolution 560,278]
562. mary != sK8 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 353,351]
563. mary != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 562,281]
564. mary != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 563,280]
565. mary != sK8 | ~room(mary) [subsumption resolution 564,279]
566. mary != sK8 [subsumption resolution 565,278]
567. room(sK8) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 352,351]
568. room(sK8) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 567,281]
569. room(sK8) | ~room(paul) | ~room(mary) [subsumption resolution 568,280]
570. room(sK8) | ~room(mary) [subsumption resolution 569,279]
571. room(sK8) [subsumption resolution 570,278]
766. fred = sK8 | paul = sK8 | mary = sK8 | alice = sK8 [resolution 282,571]
784. paul = sK8 | mary = sK8 | alice = sK8 [subsumption resolution 766,556]
785. mary = sK8 | alice = sK8 [subsumption resolution 784,561]
786. alice = sK8 [subsumption resolution 785,566]
787. $false [subsumption resolution 786,551]
% SZS output end Proof for 1160454892577843530352200
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.042 s
% ------------------------------
% ------------------------------
| 0.639172 |
There is a room. “Everyone outside the room neither is a wise person nor is not a curious person” unless “everyone in the room is a curious person, is a funny person and is a strong person”. Everyone in the room neither is funny nor is not a humble person. Everyone in the room neither is not a quiet person nor is not a calm person. Everyone in the room is a wise person. Everyone in the room is generous and is not tall. If someone is a strong person then he/she is brave and vice versa. Everyone in the room is old and is a brave person. All creative persons are generous. | All creative persons are generous. | entailment | (there_is_a_room)&
(~(![X]:(room(X)=>(((curious(X)&person(X))&(funny(X)&person(X))&(strong(X)&person(X))))))=>(![X]:(~room(X)=>(~((wise(X)&person(X))|(~(curious(X)&person(X))))))))&
(![X]:(room(X)=>(~((funny(X))|(~(humble(X)&person(X)))))))&
(![X]:(room(X)=>(~((~(quiet(X)&person(X)))|(~(calm(X)&person(X)))))))&
(![X]:(room(X)=>(wise(X)&person(X))))&
(![X]:(room(X)=>(((generous(X))&(~tall(X))))))&
((![X]:((strong(X)&person(X))<=>(brave(X)))))&
(![X]:(room(X)=>(((old(X))&(brave(X)&person(X))))))&
(![X]:(room(X)=>(((~(old(X)&person(X)))|(generous(X)&person(X))))))&
((![X]:((~(creative(X)&person(X)))=>(humble(X)&person(X)))))&
(![X]:(room(X)=>(((~(quiet(X)&person(X)))<~>(creative(X)&person(X))))))&
(?[X,Y]:((((wise(X)&person(X))&(generous(X)&person(X))))&(~(generous(Y)&person(Y)))&(older(X,Y))))&
(![X]:(room(X)=>(~(tall(X)&person(X)))))&
(![X]:(creative(X)=>generous(X)))&
(![X]:(strong(X)=>curious(X)))&
(![X]:(room(X)=>(((curious(X)&person(X))&(funny(X)&person(X))&(strong(X)&person(X))))))&
(![X]:(patient(X)=>strong(X))) | (there_is_a_room)&
![X]:(creative(X)=>generous(X)) | [
"p0",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1750347863689035903811510
% SZS output start Proof for 1750347863689035903811510
44. there_is_a_room [input p0]
57. ! [X0] : (creative(X0) => generous(X0)) [input p13]
61. ~(! [X0] : (creative(X0) => generous(X0)) & there_is_a_room) [input hypothesis]
161. ! [X0] : (generous(X0) | ~creative(X0)) [ennf transformation 57]
163. ? [X0] : (~generous(X0) & creative(X0)) | ~there_is_a_room [ennf transformation 61]
170. ? [X0] : (~generous(X0) & creative(X0)) => (~generous(sK2) & creative(sK2)) [choice axiom]
171. (~generous(sK2) & creative(sK2)) | ~there_is_a_room [skolemisation 163,170]
252. there_is_a_room [cnf transformation 44]
287. ~creative(X0) | generous(X0) [cnf transformation 161]
292. creative(sK2) | ~there_is_a_room [cnf transformation 171]
293. ~generous(sK2) | ~there_is_a_room [cnf transformation 171]
324. ~generous(sK2) [subsumption resolution 293,252]
325. creative(sK2) [subsumption resolution 292,252]
326. generous(sK2) [resolution 287,325]
327. $false [subsumption resolution 326,324]
% SZS output end Proof for 1750347863689035903811510
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.051123 |
Irma is the only person in the room. Either “Irma practices zumba” or “Irma collects antique jewelry” but not both. Irma enjoys landscape photography. Only one person outside the room frequently participates in hackathons and coding competitions. Irma enjoys camping and organizing outdoor survival workshops. Irma who can play the piano collects first edition books or collects rare and antique scientific instruments or both. Irma is a Linux enthusiast. Someone in the room collects classic novels. Irma drives a hybrid car. Irma collects rare and antique scientific instruments. Irma is a culinary enthusiast who experiments with international cuisines, has a vast collection of first-edition science fiction novels or is a scotch connoisseur. Irma neither does not design and sews custom cosplay costumes for conventions nor collects comic books. Irma can play the piano. Irma has a vast collection of first-edition science fiction novels. At least one person in the room collects foreign coins. Irma practices zumba. Everyone in the room who designs and sews custom cosplay costumes for conventions collects rare and antique scientific instruments. Irma who designs and sews custom cosplay costumes for conventions or is a culinary enthusiast who experiments with international cuisines or both is an amateur astronomer who builds and uses custom telescopes. Irma practices calligraphy. Someone in the room does not frequently participates in hackathons and coding competitions. Irma collects foreign coins. Only one person in the room bakes bread at home or is an amateur astronomer who builds and uses custom telescopes or both. Irma is an amateur astronomer who builds and uses custom telescopes. | Irma frequently participates in hackathons and coding competitions. | contradiction | room(irma)&(![X]:(room(X)=>(X='irma')))&
((practices_zumba(irma))<~>(collects_antique_jewelry(irma)))&
(enjoys_landscape_photography(irma))&
(((?[X]:(~room(X)&frequently_participates_in_hackathons_and_coding_competitions(X)))&(![X,Y]:((~room(X)&~room(Y)&(frequently_participates_in_hackathons_and_coding_competitions(X))&(frequently_participates_in_hackathons_and_coding_competitions(Y)))=>(X=Y)))))&
(enjoys_camping_and_organizing_outdoor_survival_workshops(irma))&
((can_play_the_piano(irma))&(((collects_first_edition_books(irma))|(collects_rare_and_antique_scientific_instruments(irma)))))&
(is_a_Linux_enthusiast(irma))&
(?[X]:(room(X)&(collects_classic_novels(X))))&
(drives_a_hybrid_car(irma))&
(collects_rare_and_antique_scientific_instruments(irma))&
(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(irma))|(has_a_vast_collection_of_first-edition_science_fiction_novels(irma))|(is_a_scotch_connoisseur(irma))))&
(~((does_not_design_and_sews_custom_cosplay_costumes_for_conventions(irma))|(collects_comic_books(irma))))&
(can_play_the_piano(irma))&
(has_a_vast_collection_of_first-edition_science_fiction_novels(irma))&
(((?[X]:(room(X)&collects_foreign_coins(X)))))&
(practices_zumba(irma))&
(![X]:(room(X)=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))=>(collects_rare_and_antique_scientific_instruments(X))))))&
((((designs_and_sews_custom_cosplay_costumes_for_conventions(irma))|(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(irma))))&(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(irma)))&
(practices_calligraphy(irma))&
(?[X]:(room(X)&(does_not_frequently_participates_in_hackathons_and_coding_competitions(X))))&
(collects_foreign_coins(irma))&
(((?[X]:(room(X)&((bakes_bread_at_home(X))|(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X)))))&(![X,Y]:((room(X)&room(Y)&(((bakes_bread_at_home(X))|(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))&(((bakes_bread_at_home(Y))|(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(Y)))))=>(X=Y)))))&
(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(irma)) | room(irma)&(![X]:(room(X)=>(X='irma')))&
frequently_participates_in_hackathons_and_coding_competitions(irma) | [
"p0",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6673631699855398577701150
% SZS output start Proof for 6673631699855398577701150
44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
63. ? [X0] : (~predu(X0) & room(X0)) [input p19]
67. predu(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis]
160. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
165. predu(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 67]
174. ? [X0] : (~predu(X0) & room(X0)) => (~predu(sK3) & room(sK3)) [choice axiom]
175. ~predu(sK3) & room(sK3) [skolemisation 63,174]
259. ~room(X0) | mary = X0 [cnf transformation 160]
269. room(sK3) [cnf transformation 175]
270. ~predu(sK3) [cnf transformation 175]
280. predu(mary) [cnf transformation 165]
304. mary = sK3 [resolution 259,269]
309. ~predu(mary) [backward demodulation 270,304]
310. $false [subsumption resolution 309,280]
% SZS output end Proof for 6673631699855398577701150
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.493078 |
There is a room.
Everyone in the room is not quiet.
Everyone anywhere is a kind tall person if they is a kind person.
Everyone outside the room is a tall person.
Everyone in the room is not old, not quiet.
Everyone in the room is not old.
Everyone in the room is a quiet person.
Everyone anywhere is a kind person if they is old.
If someone either is a quiet person or is a tall person but not both then he/she is not a tall person. | Everyone in the room is a tall person. | entailment | (there_is_a_room)&
(![X]:(room(X)=>(~quiet(X))))&
(![X]:(anywhere(X)=>(((kind(X)&person(X))=>(kind(X)&tall(X)&person(X))))))&
(![X]:(~room(X)=>(tall(X)&person(X))))&
(![X]:(room(X)=>(~old(X)&~quiet(X))))&
(![X]:(room(X)=>(~old(X))))&
(![X]:(room(X)=>(quiet(X)&person(X))))&
(![X]:(anywhere(X)=>(((old(X))=>(kind(X)&person(X))))))&
((![X]:((((quiet(X)&person(X))<~>(tall(X)&person(X))))=>(~(tall(X)&person(X)))))) | (there_is_a_room)&
![X]:(room(X)=>(tall(X)&person(X))) | [
"p0",
"p1",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 5014708385952100656275798
% SZS output start Proof for 5014708385952100656275798
44. there_is_a_room [input p0]
45. ! [X0] : (room(X0) => ~quiet(X0)) [input p1]
50. ! [X0] : (room(X0) => (person(X0) & quiet(X0))) [input p6]
53. ~(! [X0] : (room(X0) => (person(X0) & tall(X0))) & there_is_a_room) [input hypothesis]
125. ! [X0] : (~quiet(X0) | ~room(X0)) [ennf transformation 45]
131. ! [X0] : ((person(X0) & quiet(X0)) | ~room(X0)) [ennf transformation 50]
136. ? [X0] : ((~person(X0) | ~tall(X0)) & room(X0)) | ~there_is_a_room [ennf transformation 53]
140. ? [X0] : ((~person(X0) | ~tall(X0)) & room(X0)) => ((~person(sK0) | ~tall(sK0)) & room(sK0)) [choice axiom]
141. ((~person(sK0) | ~tall(sK0)) & room(sK0)) | ~there_is_a_room [skolemisation 136,140]
223. there_is_a_room [cnf transformation 44]
224. ~quiet(X0) | ~room(X0) [cnf transformation 125]
233. quiet(X0) | ~room(X0) [cnf transformation 131]
241. room(sK0) | ~there_is_a_room [cnf transformation 141]
249. ~room(X0) [subsumption resolution 233,224]
254. ~there_is_a_room [subsumption resolution 241,249]
255. $false [subsumption resolution 254,223]
% SZS output end Proof for 5014708385952100656275798
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.111914 |
There is a room.
If "everyone outside the room plays as a goalkeeper for a local amateur soccer team or does not have a saltwater aquarium" then "everyone outside the room plays as a goalkeeper for a local amateur soccer team only if they is right-handed".
If "everyone in the room does not design and sews custom cosplay costumes for conventions or enjoys cross-country skiing" then "not everyone in the room is a client of Meta, is allergic to anything or is right-handed if and only if they is not a dedicated volunteer for local community service projects" otherwise "everyone in the room who does not enjoy snowboarding practices kickboxing, does not write a travel blog and owns a smart tv".
If someone is allergic to anything then he/she is a dedicated volunteer for local community service projects.
If someone does not collect antique jewelry then he/she maintains a large, organic vegetable garden year-round.
Everyone in the room collects classic novels.
Everyone in the room who either can play the piano or owns a smartwatch but not both has a saltwater aquarium.
Everyone in the room who has a saltwater aquarium collects classic novels.
Only one person outside the room owns a smartwatch.
Everyone in the room maintains a large, organic vegetable garden year-round if they can play the piano.
Everyone anywhere is a client of LVMH, owns a smartwatch or is a client of Meta if they maintains a large, organic vegetable garden year-round.
If someone collects foreign coins, is a client of LVMH or is allergic to anything then he/she is right-handed.
Everyone in the room who enjoys snowboarding cannot play the flute.
Everyone anywhere can play the piano if they cannot play the flute.
Everyone outside the room can play the piano only if they enjoys snowboarding.
Only one person in the room is right-handed, writes a travel blog or is not allergic to anything.
Everyone in the room is not right-handed, is allergic to anything or streams on Twitch if they plays as a goalkeeper for a local amateur soccer team.
Everyone in the room is not allergic to anything if they is not right-handed, is allergic to anything or streams on Twitch.
Everyone in the room is a client of Meta if they is not allergic to anything. | Everyone in the room enjoys cross-country skiing or does not enjoy cross-country skiing. | entailment | (there_is_a_room)&
((![X]:(~room(X)=>(((does_not_have_a_saltwater_aquarium(X))|(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))=>(![X]:(~room(X)=>(((is_right-handed(X))<=(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X)))))))&
(((![X]:(room(X)=>(((enjoys_cross-country_skiing(X))|(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))))))=>(~![X]:(room(X)=>(((((is_a_client_of_Meta(X))|(is_allergic_to_anything(X))|(is_right-handed(X))))<=>(is_not_a_dedicated_volunteer_for_local_community_service_projects(X)))))))&((~(![X]:(room(X)=>(((enjoys_cross-country_skiing(X))|(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X)))))))=>(![X]:(room(X)=>(((does_not_enjoy_snowboarding(X))=>(((practices_kickboxing(X))&(does_not_write_a_travel_blog(X))&(owns_a_smart_tv(X))))))))))&
((![X]:((is_allergic_to_anything(X))=>(is_a_dedicated_volunteer_for_local_community_service_projects(X)))))&
((![X]:((does_not_collect_antique_jewelry(X))=>(maintains_a_large,_organic_vegetable_garden_year-round(X)))))&
(![X]:(room(X)=>(collects_classic_novels(X))))&
(![X]:(room(X)=>(((((can_play_the_piano(X))<~>(owns_a_smartwatch(X))))=>(has_a_saltwater_aquarium(X))))))&
(![X]:(room(X)=>(((has_a_saltwater_aquarium(X))=>(collects_classic_novels(X))))))&
(((?[X]:(~room(X)&owns_a_smartwatch(X)))&(![X,Y]:((~room(X)&~room(Y)&(owns_a_smartwatch(X))&(owns_a_smartwatch(Y)))=>(X=Y)))))&
(![X]:(room(X)=>(((can_play_the_piano(X))=>(maintains_a_large,_organic_vegetable_garden_year-round(X))))))&
(![X]:(anywhere(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))=>(((is_a_client_of_LVMH(X))|(owns_a_smartwatch(X))|(is_a_client_of_Meta(X))))))))&
((![X]:((((collects_foreign_coins(X))|(is_a_client_of_LVMH(X))|(is_allergic_to_anything(X))))=>(is_right-handed(X)))))&
(![X]:(room(X)=>(((enjoys_snowboarding(X))=>(cannot_play_the_flute(X))))))&
(![X]:(anywhere(X)=>(((cannot_play_the_flute(X))=>(can_play_the_piano(X))))))&
(![X]:(~room(X)=>(((enjoys_snowboarding(X))<=(can_play_the_piano(X))))))&
(((?[X]:(room(X)&((is_right-handed(X))|(writes_a_travel_blog(X))|(is_not_allergic_to_anything(X)))))&(![X,Y]:((room(X)&room(Y)&(((is_right-handed(X))|(writes_a_travel_blog(X))|(is_not_allergic_to_anything(X))))&(((is_right-handed(Y))|(writes_a_travel_blog(Y))|(is_not_allergic_to_anything(Y)))))=>(X=Y)))))&
(![X]:(room(X)=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))=>(((is_not_right-handed(X))|(is_allergic_to_anything(X))|(streams_on_Twitch(X))))))))&
(![X]:(room(X)=>(((((is_not_right-handed(X))|(is_allergic_to_anything(X))|(streams_on_Twitch(X))))=>(is_not_allergic_to_anything(X))))))&
(![X]:(room(X)=>(((is_not_allergic_to_anything(X))=>(is_a_client_of_Meta(X)))))) | (there_is_a_room)&
![X]:(room(X)=>(((does_not_enjoy_cross-country_skiing(X))|(enjoys_cross-country_skiing(X))))) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 8522778359027579974370370
% SZS output start Proof for 8522778359027579974370370
44. there_is_a_room [input p0]
63. ~(! [X0] : (room(X0) => (predm(X0) | ~predm(X0))) & there_is_a_room) [input hypothesis]
172. ? [X0] : ((~predm(X0) & predm(X0)) & room(X0)) | ~there_is_a_room [ennf transformation 63]
173. ? [X0] : (~predm(X0) & predm(X0) & room(X0)) | ~there_is_a_room [flattening 172]
192. ? [X0] : (~predm(X0) & predm(X0) & room(X0)) => (~predm(sK6) & predm(sK6) & room(sK6)) [choice axiom]
193. (~predm(sK6) & predm(sK6) & room(sK6)) | ~there_is_a_room [skolemisation 173,192]
275. there_is_a_room [cnf transformation 44]
308. predm(sK6) | ~there_is_a_room [cnf transformation 193]
309. ~predm(sK6) | ~there_is_a_room [cnf transformation 193]
365. ~predm(sK6) [subsumption resolution 309,275]
366. ~there_is_a_room [subsumption resolution 308,365]
367. $false [subsumption resolution 366,275]
% SZS output end Proof for 8522778359027579974370370
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0.044136 |
Joseph, Jeffrey, Jose, Ashley are the only persons in the room. “Ashley is an enthusiastic bird watcher who travels for rare sightings or is a culinary enthusiast who experiments with international cuisines or both” unless “everyone anywhere does not have a specialized collection of handmade artisan pottery or plays the drums”. Everyone in the room competes in national level swimming championships, collects modern art and is an enthusiastic bird watcher who travels for rare sightings if they has completed a triathlon or is dedicated to sustainable living and zero-waste practices or both and vice versa. Joseph either is dedicated to sustainable living and zero-waste practices or collects luxury watches but not both. Joseph who either is an enthusiastic bird watcher who travels for rare sightings or is dedicated to sustainable living and zero-waste practices but not both has a specialized collection of handmade artisan pottery. | Joseph collects luxury watches. | entailment | room(joseph)&room(jeffrey)&room(jose)&room(ashley)&(![X]:(room(X)=>(X='joseph'|X='jeffrey'|X='jose'|X='ashley')))&
(~(![X]:(anywhere(X)=>(((plays_the_drums(X))|(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))))))=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(ashley))|(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(ashley)))))&
((((plays_eSports_competitively(ashley))&(competes_in_national_level_swimming_championships(ashley))&(plays_the_drums(ashley))))&(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(ashley))&(collects_luxury_watches(ashley)))))&
(((?[X]:(room(X)&((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))&(enjoys_cross-country_skiing(X))&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X)))))&(![X,Y]:((room(X)&room(Y)&(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))&(enjoys_cross-country_skiing(X))&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))&(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(Y))&(enjoys_cross-country_skiing(Y))&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(Y)))))=>(X=Y)))))&
(![X]:(room(X)=>(((~((collects_comic_books(X))|(owns_a_smart_tv(X))))<=(is_a_night_owl(X))))))&
(((has_completed_a_triathlon(jose))&(enjoys_cross-country_skiing(jose))&(owns_a_smart_tv(jose))))&
(![X]:(anywhere(X)=>(((plays_the_drums(X))|(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))))))&
(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(ashley))|(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(ashley))))&
(![X]:(room(X)=>(((((competes_in_national_level_swimming_championships(X))&(collects_modern_art(X))&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))<=>(((has_completed_a_triathlon(X))|(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))))&
(~((owns_a_smart_tv(jeffrey))|(has_a_specialized_collection_of_handmade_artisan_pottery(jeffrey))))&
((![X]:((((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))<~>(plays_the_drums(X))))<=>(enjoys_cross-country_skiing(X)))))&
(((?[X]:(anywhere(X)&is_dedicated_to_sustainable_living_and_zero-waste_practices(X)))&(![X,Y]:((anywhere(X)&anywhere(Y)&(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))&(is_dedicated_to_sustainable_living_and_zero-waste_practices(Y)))=>(X=Y)))))&
((((enjoys_macrame(jose))&(collects_classic_novels(jose))))&(owns_a_smart_tv(jose)))&
(collects_modern_art(ashley))&
(((is_dedicated_to_sustainable_living_and_zero-waste_practices(joseph))<~>(collects_luxury_watches(joseph))))&
(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(jose))<~>(collects_comic_books(jose))))&
(((is_a_certified_yoga_instructor_teaching_classes_weekly(ashley))&(practices_graffiti_art(ashley))))&
(~![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))|(does_not_play_the_drums(X))))))&
(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(ashley))<~>(enjoys_cross-country_skiing(ashley))))&
(((collects_classic_novels(jeffrey))<~>(practices_archery(jeffrey))))&
(((has_a_specialized_collection_of_handmade_artisan_pottery(jeffrey))<~>(practices_graffiti_art(jeffrey))))&
((((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(joseph))<~>(is_dedicated_to_sustainable_living_and_zero-waste_practices(joseph))))&(has_a_specialized_collection_of_handmade_artisan_pottery(joseph))) | room(joseph)&room(jeffrey)&room(jose)&room(ashley)&(![X]:(room(X)=>(X='joseph'|X='jeffrey'|X='jose'|X='ashley')))&
collects_luxury_watches(joseph) | [
"p0",
"p8",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5611784227902813696371455
% SZS output start Proof for 5611784227902813696371455
44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
52. ! [X0] : (room(X0) => ((prede(X0) & predh(X0) & predl(X0)) <=> (predv(X0) | predg(X0)))) [input p8]
58. predv(mary) <~> predk(mary) [input p14]
65. predw(mary) & (prede(mary) <~> predv(mary)) [input p21]
66. ~(predk(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis]
143. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
144. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 143]
151. ! [X0] : (((prede(X0) & predh(X0) & predl(X0)) <=> (predv(X0) | predg(X0))) | ~room(X0)) [ennf transformation 52]
157. ~predk(mary) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 66]
158. ~predk(mary) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 157]
162. ! [X0] : ((((prede(X0) & predh(X0) & predl(X0)) | (~predv(X0) & ~predg(X0))) & ((predv(X0) | predg(X0)) | (~prede(X0) | ~predh(X0) | ~predl(X0)))) | ~room(X0)) [nnf transformation 151]
163. ! [X0] : ((((prede(X0) & predh(X0) & predl(X0)) | (~predv(X0) & ~predg(X0))) & (predv(X0) | predg(X0) | ~prede(X0) | ~predh(X0) | ~predl(X0))) | ~room(X0)) [flattening 162]
167. (~predk(mary) | ~predv(mary)) & (predk(mary) | predv(mary)) [nnf transformation 58]
174. predw(mary) & ((~predv(mary) | ~prede(mary)) & (predv(mary) | prede(mary))) [nnf transformation 65]
175. predw(mary) & (~predv(mary) | ~prede(mary)) & (predv(mary) | prede(mary)) [flattening 174]
176. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) [choice axiom]
177. ~predk(mary) | (alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 158,176]
259. room(mary) [cnf transformation 144]
260. room(paul) [cnf transformation 144]
261. room(fred) [cnf transformation 144]
262. room(alice) [cnf transformation 144]
263. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 144]
285. ~predv(X0) | prede(X0) | ~room(X0) [cnf transformation 163]
298. predk(mary) | predv(mary) [cnf transformation 167]
314. ~predv(mary) | ~prede(mary) [cnf transformation 175]
316. ~predk(mary) | room(sK3) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 177]
317. ~predk(mary) | mary != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 177]
318. ~predk(mary) | paul != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 177]
319. ~predk(mary) | fred != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 177]
320. ~predk(mary) | alice != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 177]
341. 4 <=> predv(mary) [avatar definition]
342. predv(mary) <- (4) [avatar component clause 341]
345. 5 <=> predk(mary) [avatar definition]
349. 4 | 5 [avatar split clause 298,345,341]
382. 12 <=> prede(mary) [avatar definition]
384. ~prede(mary) <- (~12) [avatar component clause 382]
385. ~12 | ~4 [avatar split clause 314,341,382]
387. ~predk(mary) | alice != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 320,262]
388. ~predk(mary) | alice != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 387,261]
389. ~predk(mary) | alice != sK3 | ~room(mary) [subsumption resolution 388,260]
390. ~predk(mary) | alice != sK3 [subsumption resolution 389,259]
392. 13 <=> alice = sK3 [avatar definition]
394. alice != sK3 <- (~13) [avatar component clause 392]
395. ~13 | ~5 [avatar split clause 390,345,392]
396. ~predk(mary) | fred != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 319,262]
397. ~predk(mary) | fred != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 396,261]
398. ~predk(mary) | fred != sK3 | ~room(mary) [subsumption resolution 397,260]
399. ~predk(mary) | fred != sK3 [subsumption resolution 398,259]
401. 14 <=> fred = sK3 [avatar definition]
403. fred != sK3 <- (~14) [avatar component clause 401]
404. ~14 | ~5 [avatar split clause 399,345,401]
405. ~predk(mary) | paul != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 318,262]
406. ~predk(mary) | paul != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 405,261]
407. ~predk(mary) | paul != sK3 | ~room(mary) [subsumption resolution 406,260]
408. ~predk(mary) | paul != sK3 [subsumption resolution 407,259]
410. 15 <=> paul = sK3 [avatar definition]
412. paul != sK3 <- (~15) [avatar component clause 410]
413. ~15 | ~5 [avatar split clause 408,345,410]
414. ~predk(mary) | mary != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 317,262]
415. ~predk(mary) | mary != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 414,261]
416. ~predk(mary) | mary != sK3 | ~room(mary) [subsumption resolution 415,260]
417. ~predk(mary) | mary != sK3 [subsumption resolution 416,259]
419. 16 <=> mary = sK3 [avatar definition]
421. mary != sK3 <- (~16) [avatar component clause 419]
422. ~16 | ~5 [avatar split clause 417,345,419]
423. ~predk(mary) | room(sK3) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 316,262]
424. ~predk(mary) | room(sK3) | ~room(paul) | ~room(mary) [subsumption resolution 423,261]
425. ~predk(mary) | room(sK3) | ~room(mary) [subsumption resolution 424,260]
426. ~predk(mary) | room(sK3) [subsumption resolution 425,259]
428. 17 <=> room(sK3) [avatar definition]
430. room(sK3) <- (17) [avatar component clause 428]
431. 17 | ~5 [avatar split clause 426,345,428]
455. prede(mary) | ~room(mary) <- (4) [resolution 285,342]
456. ~room(mary) <- (4, ~12) [subsumption resolution 455,384]
457. $false <- (4, ~12) [subsumption resolution 456,259]
458. ~4 | 12 [avatar contradiction clause 457]
569. fred = sK3 | paul = sK3 | mary = sK3 | alice = sK3 <- (17) [resolution 263,430]
604. paul = sK3 | mary = sK3 | alice = sK3 <- (~14, 17) [subsumption resolution 569,403]
605. mary = sK3 | alice = sK3 <- (~14, ~15, 17) [subsumption resolution 604,412]
606. alice = sK3 <- (~14, ~15, ~16, 17) [subsumption resolution 605,421]
607. $false <- (~13, ~14, ~15, ~16, 17) [subsumption resolution 606,394]
608. 13 | 14 | 15 | 16 | ~17 [avatar contradiction clause 607]
609. $false [avatar sat refutation 349,385,395,404,413,422,431,458,608]
% SZS output end Proof for 5611784227902813696371455
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.029 s
% ------------------------------
% ------------------------------
| 0.390755 |
Teddy is the only person in the room. Teddy works as a freelance web developer specializing in e-commerce sites. Teddy collects luxury watches. Teddy either enjoys rooftop gardening or collects modern art but not both. If someone collects luxury watches then he/she enjoys fishing and vice versa. Teddy enjoys origami, enjoys rooftop gardening and enjoys snowboarding. Teddy enjoys fishing, enjoys camping and organizing outdoor survival workshops and enjoys snowboarding. Everyone outside the room who does not build model airplanes does not work as a freelance web developer specializing in e-commerce sites. | Teddy enjoys snowboarding. | entailment | room(teddy)&(![X]:(room(X)=>(X='teddy')))&
(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(teddy))&
(collects_luxury_watches(teddy))&
(((enjoys_rooftop_gardening(teddy))<~>(collects_modern_art(teddy))))&
((![X]:((collects_luxury_watches(X))<=>(enjoys_fishing(X)))))&
(((enjoys_origami(teddy))&(enjoys_rooftop_gardening(teddy))&(enjoys_snowboarding(teddy))))&
(((enjoys_fishing(teddy))&(enjoys_camping_and_organizing_outdoor_survival_workshops(teddy))&(enjoys_snowboarding(teddy))))&
(![X]:(~room(X)=>(((does_not_build_model_airplanes(X))=>(does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))))))&
(does_not_create_large-scale_murals_for_public_art_installations(teddy))&
((enjoys_kayaking(teddy))&(does_not_build_model_airplanes(teddy)))&
(?[X]:(room(X)&(((enjoys_making_ceramics(X))<~>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))&
((![X]:((enjoys_fishing(X))<=>(is_an_active_member_of_a_local_robotics_club(X)))))&
(does_not_enjoy_making_ceramics(teddy))&
(is_an_active_member_of_a_local_robotics_club(teddy))&
((![X]:((enjoys_rooftop_gardening(X))<=>(hosts_regular_workshops_on_creative_writing(X)))))&
((enjoys_kayaking(teddy))&(enjoys_camping_and_organizing_outdoor_survival_workshops(teddy)))&
(is_not_a_Linux_enthusiast(teddy))&
(enjoys_camping_and_organizing_outdoor_survival_workshops(teddy))&
(enjoys_fishing(teddy))&
(((?[X]:(~room(X)&collects_modern_art(X)))&(![X,Y]:((~room(X)&~room(Y)&(collects_modern_art(X))&(collects_modern_art(Y)))=>(X=Y)))))&
(does_not_build_model_airplanes(teddy)) | room(teddy)&(![X]:(room(X)=>(X='teddy')))&
enjoys_snowboarding(teddy) | [
"p0",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 5737111638080703493344670
% SZS output start Proof for 5737111638080703493344670
44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
49. predf(mary) & predm(mary) & predh(mary) [input p5]
65. ~(predf(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis]
79. predf(mary) & predm(mary) [pure predicate removal 49]
152. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
157. ~predf(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 65]
167. ? [X0] : (mary != X0 & room(X0)) => (mary != sK2 & room(sK2)) [choice axiom]
168. ~predf(mary) | (mary != sK2 & room(sK2)) | ~room(mary) [skolemisation 157,167]
249. room(mary) [cnf transformation 152]
250. ~room(X0) | mary = X0 [cnf transformation 152]
255. predf(mary) [cnf transformation 79]
272. ~predf(mary) | room(sK2) | ~room(mary) [cnf transformation 168]
273. ~predf(mary) | mary != sK2 | ~room(mary) [cnf transformation 168]
295. mary != sK2 | ~room(mary) [subsumption resolution 273,255]
296. mary != sK2 [subsumption resolution 295,249]
297. room(sK2) | ~room(mary) [subsumption resolution 272,255]
298. room(sK2) [subsumption resolution 297,249]
303. mary = sK2 [resolution 250,298]
307. $false [subsumption resolution 303,296]
% SZS output end Proof for 5737111638080703493344670
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0.132997 |
Betty is the only person in the room.
Everyone in the room neither does not collect historical artifacts related to ancient civilizations nor does not stream on Twitch.
Everyone in the room either creates bespoke furniture pieces from reclaimed wood or has completed a triathlon but not both.
Betty owns a significant collection of rare gemstones and minerals.
Betty who develops open-source software projects in their free time and owns an Android phone is an expert in identifying and foraging wild edible plants.
Betty either is an amateur astronomer who builds and uses custom telescopes or does not collect luxury watches but not both.
Betty is allergic to anything.
Everyone in the room who is a professional photographer specializing in portrait photography does not collect luxury watches.
Everyone in the room is a client of LVMH if they does not collect luxury watches.
Betty who owns an Android phone and is a professional photographer specializing in portrait photography neither is not an avid mountain climber who has scaled several peaks nor has a tattoo.
Everyone in the room either writes poetry or owns an Android phone but not both if they plays eSports competitively.
Betty collects modern art.
Betty who either enjoys origami or has a tattoo but not both is an active member of a local robotics club.
Everyone in the room writes poetry if they enjoys origami and is not allergic to anything.
Betty does not practice urban gardening and owns an Android phone.
Betty develops open-source software projects in their free time, streams on Twitch and enjoys macrame.
Everyone outside the room develops open-source software projects in their free time if they creates bespoke furniture pieces from reclaimed wood.
Everyone in the room owns a significant collection of rare gemstones and minerals.
If someone composes and performs experimental electronic music and plays eSports competitively then he/she is not an amateur astronomer who builds and uses custom telescopes and vice versa. | Betty is a professional photographer specializing in portrait photography, enjoys macrame and composes and performs experimental electronic music. | entailment | room(betty)&(![X]:(room(X)=>(X='betty')))&
(![X]:(room(X)=>(~((does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))|(does_not_stream_on_Twitch(X))))))&
(![X]:(room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))<~>(has_completed_a_triathlon(X))))))&
(owns_a_significant_collection_of_rare_gemstones_and_minerals(betty))&
((((develops_open-source_software_projects_in_their_free_time(betty))&(owns_an_Android_phone(betty))))&(is_an_expert_in_identifying_and_foraging_wild_edible_plants(betty)))&
(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(betty))<~>(does_not_collect_luxury_watches(betty))))&
(is_allergic_to_anything(betty))&
(![X]:(room(X)=>(((is_a_professional_photographer_specializing_in_portrait_photography(X))=>(does_not_collect_luxury_watches(X))))))&
(![X]:(room(X)=>(((does_not_collect_luxury_watches(X))=>(is_a_client_of_LVMH(X))))))&
((((owns_an_Android_phone(betty))&(is_a_professional_photographer_specializing_in_portrait_photography(betty))))&(~((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(betty))|(has_a_tattoo(betty)))))&
(![X]:(room(X)=>(((plays_eSports_competitively(X))=>(((writes_poetry(X))<~>(owns_an_Android_phone(X))))))))&
(collects_modern_art(betty))&
((((enjoys_origami(betty))<~>(has_a_tattoo(betty))))&(is_an_active_member_of_a_local_robotics_club(betty)))&
(![X]:(room(X)=>(((((enjoys_origami(X))&(is_not_allergic_to_anything(X))))=>(writes_poetry(X))))))&
(((does_not_practice_urban_gardening(betty))&(owns_an_Android_phone(betty))))&
(((develops_open-source_software_projects_in_their_free_time(betty))&(streams_on_Twitch(betty))&(enjoys_macrame(betty))))&
(![X]:(~room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))=>(develops_open-source_software_projects_in_their_free_time(X))))))&
(![X]:(room(X)=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))&
((![X]:((((composes_and_performs_experimental_electronic_music(X))&(plays_eSports_competitively(X))))<=>(is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))) | room(betty)&(![X]:(room(X)=>(X='betty')))&
((is_a_professional_photographer_specializing_in_portrait_photography(betty))&(enjoys_macrame(betty))&(composes_and_performs_experimental_electronic_music(betty))) | [
"p0",
"p5",
"p7",
"p9",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6440649362429592801958468
% SZS output start Proof for 6440649362429592801958468
44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
49. predd(mary) <~> ~predm(mary) [input p5]
51. ! [X0] : (room(X0) => (prede(X0) => ~predm(X0))) [input p7]
53. ~(predq(mary) | ~predi(mary)) & prede(mary) & predv(mary) [input p9]
59. preda(mary) & predu(mary) & predl(mary) [input p15]
62. ! [X0] : ((predc(X0) & predb(X0)) <=> ~predd(X0)) [input p18]
63. ~(predb(mary) & preda(mary) & prede(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis]
67. ~predq(mary) & prede(mary) & predv(mary) [pure predicate removal 53]
72. preda(mary) & predu(mary) [pure predicate removal 59]
77. preda(mary) [pure predicate removal 72]
152. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
154. ! [X0] : ((~predm(X0) | ~prede(X0)) | ~room(X0)) [ennf transformation 51]
155. ! [X0] : (~predm(X0) | ~prede(X0) | ~room(X0)) [flattening 154]
156. ~predq(mary) & prede(mary) & predv(mary) [ennf transformation 67]
159. ~predb(mary) | ~preda(mary) | ~prede(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 63]
162. (predm(mary) | ~predd(mary)) & (~predm(mary) | predd(mary)) [nnf transformation 49]
165. ! [X0] : (((predc(X0) & predb(X0)) | predd(X0)) & (~predd(X0) | (~predc(X0) | ~predb(X0)))) [nnf transformation 62]
166. ! [X0] : (((predc(X0) & predb(X0)) | predd(X0)) & (~predd(X0) | ~predc(X0) | ~predb(X0))) [flattening 165]
167. ? [X0] : (mary != X0 & room(X0)) => (mary != sK0 & room(sK0)) [choice axiom]
168. ~predb(mary) | ~preda(mary) | ~prede(mary) | (mary != sK0 & room(sK0)) | ~room(mary) [skolemisation 159,167]
249. room(mary) [cnf transformation 152]
250. ~room(X0) | mary = X0 [cnf transformation 152]
255. predm(mary) | ~predd(mary) [cnf transformation 162]
256. ~prede(X0) | ~predm(X0) | ~room(X0) [cnf transformation 155]
258. prede(mary) [cnf transformation 156]
265. preda(mary) [cnf transformation 77]
267. predb(X0) | predd(X0) [cnf transformation 166]
269. ~predb(mary) | ~preda(mary) | ~prede(mary) | room(sK0) | ~room(mary) [cnf transformation 168]
270. ~predb(mary) | ~preda(mary) | ~prede(mary) | mary != sK0 | ~room(mary) [cnf transformation 168]
272. 1 <=> predd(mary) [avatar definition]
274. ~predd(mary) <- (~1) [avatar component clause 272]
276. 2 <=> predm(mary) [avatar definition]
278. predm(mary) <- (2) [avatar component clause 276]
279. ~1 | 2 [avatar split clause 255,276,272]
282. ~predb(mary) | ~prede(mary) | mary != sK0 | ~room(mary) [subsumption resolution 270,265]
283. ~predb(mary) | mary != sK0 | ~room(mary) [subsumption resolution 282,258]
284. ~predb(mary) | mary != sK0 [subsumption resolution 283,249]
286. 3 <=> mary = sK0 [avatar definition]
290. 4 <=> predb(mary) [avatar definition]
292. ~predb(mary) <- (~4) [avatar component clause 290]
293. ~3 | ~4 [avatar split clause 284,290,286]
294. ~predb(mary) | ~prede(mary) | room(sK0) | ~room(mary) [subsumption resolution 269,265]
295. ~predb(mary) | room(sK0) | ~room(mary) [subsumption resolution 294,258]
296. ~predb(mary) | room(sK0) [subsumption resolution 295,249]
298. 5 <=> room(sK0) [avatar definition]
300. room(sK0) <- (5) [avatar component clause 298]
301. 5 | ~4 [avatar split clause 296,290,298]
302. predd(mary) <- (~4) [resolution 267,292]
303. $false <- (~1, ~4) [subsumption resolution 302,274]
304. 1 | 4 [avatar contradiction clause 303]
306. mary = sK0 <- (5) [resolution 250,300]
309. 3 | ~5 [avatar split clause 306,298,286]
325. ~predm(mary) | ~room(mary) [resolution 256,258]
326. ~room(mary) <- (2) [subsumption resolution 325,278]
327. $false <- (2) [subsumption resolution 326,249]
328. ~2 [avatar contradiction clause 327]
329. $false [avatar sat refutation 279,293,301,304,309,328]
% SZS output end Proof for 6440649362429592801958468
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.440614 |
Antione is the only person in the room.
Antione is passionate about collecting and restoring classic cars.
Antione is a client of Meta.
Antione uses contact lenses and enjoys making ceramics.
Antione creates large-scale murals for public art installations.
Antione neither develops open-source software projects in their free time nor collects vintage vinyl records.
Only one person in the room uses contact lenses.
Antione enjoys virtual reality gaming. | Antione collects vintage vinyl records. | contradiction | room(antione)&(![X]:(room(X)=>(X='antione')))&
(is_passionate_about_collecting_and_restoring_classic_cars(antione))&
(is_a_client_of_Meta(antione))&
(((uses_contact_lenses(antione))&(enjoys_making_ceramics(antione))))&
(creates_large-scale_murals_for_public_art_installations(antione))&
(~((develops_open-source_software_projects_in_their_free_time(antione))|(collects_vintage_vinyl_records(antione))))&
(((?[X]:(room(X)&uses_contact_lenses(X)))&(![X,Y]:((room(X)&room(Y)&(uses_contact_lenses(X))&(uses_contact_lenses(Y)))=>(X=Y)))))&
(enjoys_virtual_reality_gaming(antione))&
(knows_morse_code(antione))&
((![X]:((plays_the_violin(X))<=>(develops_open-source_software_projects_in_their_free_time(X)))))&
(collects_historical_artifacts_related_to_ancient_civilizations(antione))&
(?[X]:(room(X)&(knows_morse_code(X))))&
((antione_dream=>(does_practice_yoga(antione))))&
(practices_and_performs_acrobatic_dance_routines(antione))&
(does_not_play_video_games(antione))&
(works_on_fridays(antione))&
(?[X]:(~room(X)&(enjoys_spelunking(X))))&
(is_dedicated_to_sustainable_living_and_zero-waste_practices(antione))&
(is_a_professional_photographer_specializing_in_portrait_photography(antione))&
(~(develops_open-source_software_projects_in_their_free_time(antione))) | room(antione)&(![X]:(room(X)=>(X='antione')))&
collects_vintage_vinyl_records(antione) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 3841572734030108158473858
% SZS output start Proof for 3841572734030108158473858
49. ~(predm(mary) | prede(mary)) [input p5]
64. predm(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis]
66. ~predm(mary) [pure predicate removal 49]
156. ~predm(mary) [ennf transformation 66]
159. predm(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 64]
250. ~predm(mary) [cnf transformation 156]
258. predm(mary) [cnf transformation 159]
259. $false [subsumption resolution 258,250]
% SZS output end Proof for 3841572734030108158473858
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.350223 |
Larry, Donna are the only persons in the room.
“Everyone in the room does not own a high-end gaming PC with custom-built components or participates in citizen science projects related to wildlife monitoring” if “not everyone in the room has a curated collection of mid-century modern furniture or does not enjoy kayaking and exploring remote waterways” and vice versa.
If “everyone in the room does not have a curated collection of mid-century modern furniture or owns a high-end gaming PC with custom-built components” then “if someone enjoys kayaking and exploring remote waterways then he/she participates in citizen science projects related to wildlife monitoring and vice versa”.
“Everyone in the room who does not enjoy kayaking and exploring remote waterways participates in citizen science projects related to wildlife monitoring” if “everyone in the room does not enjoy kayaking and exploring remote waterways or enjoys kayaking and exploring remote waterways”.
If “not everyone outside the room does not participate in citizen science projects related to wildlife monitoring or owns a high-end gaming PC with custom-built components” then “everyone in the room enjoys kayaking and exploring remote waterways only if they either participates in citizen science projects related to wildlife monitoring or has a curated collection of mid-century modern furniture but not both”.
Everyone in the room who enjoys kayaking and exploring remote waterways participates in citizen science projects related to wildlife monitoring.
Everyone outside the room either enjoys kayaking and exploring remote waterways or has a curated collection of mid-century modern furniture but not both if they has a curated collection of mid-century modern furniture.
Everyone anywhere enjoys kayaking and exploring remote waterways if they either enjoys kayaking and exploring remote waterways or owns a high-end gaming PC with custom-built components but not both.
Everyone in the room enjoys kayaking and exploring remote waterways.
Everyone in the room owns a high-end gaming PC with custom-built components. | Larry owns a high-end gaming PC with custom-built components. | entailment | room(larry)&room(donna)&(![X]:(room(X)=>(X='larry'|X='donna')))&
((~![X]:(room(X)=>(((does_not_enjoy_kayaking_and_exploring_remote_waterways(X))|(has_a_curated_collection_of_mid-century_modern_furniture(X))))))<=>(![X]:(room(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(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))|(does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))))))=>((![X]:((enjoys_kayaking_and_exploring_remote_waterways(X))<=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))&
((![X]:(room(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))|(does_not_enjoy_kayaking_and_exploring_remote_waterways(X))))))=>(![X]:(room(X)=>(((does_not_enjoy_kayaking_and_exploring_remote_waterways(X))=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X)))))))&
((~![X]:(~room(X)=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))|(does_not_participate_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))=>(![X]:(room(X)=>(((((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))<~>(has_a_curated_collection_of_mid-century_modern_furniture(X))))<=(enjoys_kayaking_and_exploring_remote_waterways(X)))))))&
(![X]:(room(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))&
(![X]:(~room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(((enjoys_kayaking_and_exploring_remote_waterways(X))<~>(has_a_curated_collection_of_mid-century_modern_furniture(X))))))))&
(![X]:(anywhere(X)=>(((((enjoys_kayaking_and_exploring_remote_waterways(X))<~>(owns_a_high-end_gaming_PC_with_custom-built_components(X))))=>(enjoys_kayaking_and_exploring_remote_waterways(X))))))&
(![X]:(room(X)=>(enjoys_kayaking_and_exploring_remote_waterways(X))))&
(![X]:(room(X)=>(owns_a_high-end_gaming_PC_with_custom-built_components(X)))) | room(larry)&room(donna)&(![X]:(room(X)=>(X='larry'|X='donna')))&
owns_a_high-end_gaming_PC_with_custom-built_components(larry) | [
"p0",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 128646867551331859036299
% SZS output start Proof for 128646867551331859036299
44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0]
53. ! [X0] : (room(X0) => predb(X0)) [input p9]
54. ~(predb(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis]
130. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44]
131. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 130]
147. ! [X0] : (predb(X0) | ~room(X0)) [ennf transformation 53]
148. ~predb(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 54]
149. ~predb(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 148]
172. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK5 & mary != sK5 & room(sK5)) [choice axiom]
173. ~predb(mary) | (paul != sK5 & mary != sK5 & room(sK5)) | ~room(paul) | ~room(mary) [skolemisation 149,172]
255. room(mary) [cnf transformation 131]
256. room(paul) [cnf transformation 131]
257. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 131]
283. ~room(X0) | predb(X0) [cnf transformation 147]
284. ~predb(mary) | room(sK5) | ~room(paul) | ~room(mary) [cnf transformation 173]
285. ~predb(mary) | mary != sK5 | ~room(paul) | ~room(mary) [cnf transformation 173]
286. ~predb(mary) | paul != sK5 | ~room(paul) | ~room(mary) [cnf transformation 173]
381. ~predb(mary) | paul != sK5 | ~room(mary) [subsumption resolution 286,256]
382. ~predb(mary) | paul != sK5 [subsumption resolution 381,255]
384. 21 <=> paul = sK5 [avatar definition]
386. paul != sK5 <- (~21) [avatar component clause 384]
388. 22 <=> predb(mary) [avatar definition]
391. ~21 | ~22 [avatar split clause 382,388,384]
392. ~predb(mary) | mary != sK5 | ~room(mary) [subsumption resolution 285,256]
393. ~predb(mary) | mary != sK5 [subsumption resolution 392,255]
395. 23 <=> mary = sK5 [avatar definition]
397. mary != sK5 <- (~23) [avatar component clause 395]
398. ~23 | ~22 [avatar split clause 393,388,395]
399. ~predb(mary) | room(sK5) | ~room(mary) [subsumption resolution 284,256]
400. ~predb(mary) | room(sK5) [subsumption resolution 399,255]
402. 24 <=> room(sK5) [avatar definition]
404. room(sK5) <- (24) [avatar component clause 402]
405. 24 | ~22 [avatar split clause 400,388,402]
412. predb(mary) [resolution 283,255]
420. 22 [avatar split clause 412,388]
450. mary = sK5 | paul = sK5 <- (24) [resolution 257,404]
460. paul = sK5 <- (~23, 24) [subsumption resolution 450,397]
461. $false <- (~21, ~23, 24) [subsumption resolution 460,386]
462. 21 | 23 | ~24 [avatar contradiction clause 461]
463. $false [avatar sat refutation 391,398,405,420,462]
% SZS output end Proof for 128646867551331859036299
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Harry is the only person in the room.
If "not everyone in the room is a coffee connoisseur or does not host regular game nights featuring complex strategy games" then "if someone frequently participates in hackathons and coding competitions then he/she hosts regular game nights featuring complex strategy games, is a coffee connoisseur or hosts a YouTube channel dedicated to art tutorials and vice versa".
If "everyone in the room is not a coffee connoisseur or does not enjoy camping and organizing outdoor survival workshops" then "Harry does not enjoy camping and organizing outdoor survival workshops or does not host regular game nights featuring complex strategy games or both" otherwise "everyone in the room who does not host regular game nights featuring complex strategy games and does not enjoy camping and organizing outdoor survival workshops hosts regular game nights featuring complex strategy games".
Everyone in the room who hosts regular game nights featuring complex strategy games frequently participates in hackathons and coding competitions.
Everyone in the room is a coffee connoisseur if they frequently participates in hackathons and coding competitions.
Everyone in the room frequently participates in hackathons and coding competitions if they is a coffee connoisseur.
Harry hosts regular game nights featuring complex strategy games.
Harry frequently participates in hackathons and coding competitions.
Everyone in the room who frequently participates in hackathons and coding competitions creates bespoke furniture pieces from reclaimed wood.
Everyone in the room who creates bespoke furniture pieces from reclaimed wood hosts regular game nights featuring complex strategy games.
Everyone in the room who does not host regular game nights featuring complex strategy games and does not enjoy camping and organizing outdoor survival workshops hosts regular game nights featuring complex strategy games.
Everyone in the room enjoys camping and organizing outdoor survival workshops if they creates bespoke furniture pieces from reclaimed wood.
Everyone in the room creates bespoke furniture pieces from reclaimed wood if they is a coffee connoisseur.
Everyone in the room does not host regular game nights featuring complex strategy games and does not enjoy camping and organizing outdoor survival workshops if they does not host a YouTube channel dedicated to art tutorials.
More than one person outside the room is a coffee connoisseur.
Harry hosts a YouTube channel dedicated to art tutorials.
Harry enjoys camping and organizing outdoor survival workshops. | Not everyone in the room is a coffee connoisseur. | contradiction | room(harry)&(![X]:(room(X)=>(X='harry')))&
((~![X]:(room(X)=>(((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))|(is_a_coffee_connoisseur(X))))))=>((![X]:((frequently_participates_in_hackathons_and_coding_competitions(X))<=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))|(is_a_coffee_connoisseur(X))|(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))))&
(((![X]:(room(X)=>(((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))|(is_not_a_coffee_connoisseur(X))))))=>(((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(harry))|(does_not_host_regular_game_nights_featuring_complex_strategy_games(harry)))))&((~(![X]:(room(X)=>(((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))|(is_not_a_coffee_connoisseur(X)))))))=>(![X]:(room(X)=>(((((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))&(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))))&
(![X]:(room(X)=>(((hosts_regular_game_nights_featuring_complex_strategy_games(X))=>(frequently_participates_in_hackathons_and_coding_competitions(X))))))&
(![X]:(room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))=>(is_a_coffee_connoisseur(X))))))&
(![X]:(room(X)=>(((is_a_coffee_connoisseur(X))=>(frequently_participates_in_hackathons_and_coding_competitions(X))))))&
(hosts_regular_game_nights_featuring_complex_strategy_games(harry))&
(frequently_participates_in_hackathons_and_coding_competitions(harry))&
(![X]:(room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))&
(![X]:(room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))&
(![X]:(room(X)=>(((((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))&(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))&
(![X]:(room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X))))))&
(![X]:(room(X)=>(((is_a_coffee_connoisseur(X))=>(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))&
(![X]:(room(X)=>(((does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))=>(((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))&(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))))))))&
((?[X,Y]:(~room(X)&~room(Y)&(is_a_coffee_connoisseur(X)&is_a_coffee_connoisseur(Y))&(X!=Y))))&
(hosts_a_YouTube_channel_dedicated_to_art_tutorials(harry))&
(enjoys_camping_and_organizing_outdoor_survival_workshops(harry)) | room(harry)&(![X]:(room(X)=>(X='harry')))&
~![X]:(room(X)=>(is_a_coffee_connoisseur(X))) | [
"p0",
"p2",
"p6",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5705792394881450115827285
% SZS output start Proof for 5705792394881450115827285
44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
46. (~! [X0] : (room(X0) => (~predd(X0) | ~predf(X0))) => ! [X0] : (room(X0) => ((~predf(X0) & ~predb(X0)) => predb(X0)))) & (! [X0] : (room(X0) => (~predd(X0) | ~predf(X0))) => (~predb(mary) | ~predf(mary))) [input p2]
50. predb(mary) [input p6]
60. predf(mary) [input p16]
61. ~! [X0] : (room(X0) => predd(X0)) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis]
63. (~! [X0] : (room(X0) => (~predd(X0) | ~predf(X0))) => ! [X1] : (room(X1) => ((~predf(X1) & ~predb(X1)) => predb(X1)))) & (! [X2] : (room(X2) => (~predd(X2) | ~predf(X2))) => (~predb(mary) | ~predf(mary))) [rectify 46]
64. ~! [X0] : (room(X0) => predd(X0)) & ! [X1] : (room(X1) => mary = X1) & room(mary) [rectify 61]
137. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
140. (! [X1] : ((predb(X1) | (predf(X1) | predb(X1))) | ~room(X1)) | ! [X0] : ((~predd(X0) | ~predf(X0)) | ~room(X0))) & ((~predb(mary) | ~predf(mary)) | ? [X2] : ((predd(X2) & predf(X2)) & room(X2))) [ennf transformation 63]
141. (! [X1] : (predb(X1) | predf(X1) | predb(X1) | ~room(X1)) | ! [X0] : (~predd(X0) | ~predf(X0) | ~room(X0))) & (~predb(mary) | ~predf(mary) | ? [X2] : (predd(X2) & predf(X2) & room(X2))) [flattening 140]
160. ? [X0] : (~predd(X0) & room(X0)) & ! [X1] : (mary = X1 | ~room(X1)) & room(mary) [ennf transformation 64]
165. (! [X0] : (predb(X0) | predf(X0) | predb(X0) | ~room(X0)) | ! [X1] : (~predd(X1) | ~predf(X1) | ~room(X1))) & (~predb(mary) | ~predf(mary) | ? [X2] : (predd(X2) & predf(X2) & room(X2))) [rectify 141]
166. ? [X2] : (predd(X2) & predf(X2) & room(X2)) => (predd(sK0) & predf(sK0) & room(sK0)) [choice axiom]
167. (! [X0] : (predb(X0) | predf(X0) | predb(X0) | ~room(X0)) | ! [X1] : (~predd(X1) | ~predf(X1) | ~room(X1))) & (~predb(mary) | ~predf(mary) | (predd(sK0) & predf(sK0) & room(sK0))) [skolemisation 165,166]
170. ? [X0] : (~predd(X0) & room(X0)) => (~predd(sK3) & room(sK3)) [choice axiom]
171. (~predd(sK3) & room(sK3)) & ! [X1] : (mary = X1 | ~room(X1)) & room(mary) [skolemisation 160,170]
253. ~room(X0) | mary = X0 [cnf transformation 137]
258. ~predb(mary) | ~predf(mary) | room(sK0) [cnf transformation 167]
260. ~predb(mary) | ~predf(mary) | predd(sK0) [cnf transformation 167]
265. predb(mary) [cnf transformation 50]
280. predf(mary) [cnf transformation 60]
283. room(sK3) [cnf transformation 171]
284. ~predd(sK3) [cnf transformation 171]
314. 8 <=> predd(sK0) [avatar definition]
316. predd(sK0) <- (8) [avatar component clause 314]
318. 9 <=> predf(mary) [avatar definition]
322. 10 <=> predb(mary) [avatar definition]
325. 8 | ~9 | ~10 [avatar split clause 260,322,318,314]
332. 12 <=> room(sK0) [avatar definition]
334. room(sK0) <- (12) [avatar component clause 332]
335. 12 | ~9 | ~10 [avatar split clause 258,322,318,332]
336. 10 [avatar split clause 265,322]
338. 9 [avatar split clause 280,318]
345. mary = sK3 [resolution 253,283]
346. mary = sK0 <- (12) [resolution 253,334]
348. ~predd(mary) [backward demodulation 284,345]
350. predd(mary) <- (8, 12) [backward demodulation 316,346]
353. $false <- (8, 12) [subsumption resolution 350,348]
354. ~8 | ~12 [avatar contradiction clause 353]
355. $false [avatar sat refutation 325,335,336,338,354]
% SZS output end Proof for 5705792394881450115827285
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0.076975 |
Mark is the only person in the room. Mark practices pilates. Mark plays as a goalkeeper for a local amateur soccer team. Someone in the room uses a Windows laptop. Mark dreamt that everyone in the room makes homemade pastries only if they plays as a goalkeeper for a local amateur soccer team. Mark owns a significant collection of rare gemstones and minerals. Mark enjoys writing detailed reviews of new and classic board games. At least one person in the room drives a hybrid car. | It is not the case that Mark makes homemade pastries. | neutral | room(mark)&(![X]:(room(X)=>(X='mark')))&
(practices_pilates(mark))&
(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(mark))&
(?[X]:(room(X)&(uses_a_Windows_laptop(X))))&
((mark_dream=>(![X]:(room(X)=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))<=(makes_homemade_pastries(X))))))))&
(owns_a_significant_collection_of_rare_gemstones_and_minerals(mark))&
(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(mark))&
(((?[X]:(room(X)&drives_a_hybrid_car(X))))) | room(mark)&(![X]:(room(X)=>(X='mark')))&
~(makes_homemade_pastries(mark)) | [] | null | 0.129903 |
Joseph, Elizabeth, Thomas, Dianne are the only persons in the room.
It is not the case that “Elizabeth is a old person”.
All quiet persons are old.
Joseph is a old person.
Only one person outside the room is old.
Thomas is old.
Dianne is a quiet old person.
Everyone in the room is not old if they is not quiet.
Everyone in the room is old if they is a quiet person.
If someone is quiet then he/she is old and vice versa.
Thomas is quiet.
All old persons are quiet. | Elizabeth is quiet. | neutral | room(joseph)&room(elizabeth)&room(thomas)&room(dianne)&(![X]:(room(X)=>(X='joseph'|X='elizabeth'|X='thomas'|X='dianne')))&
(~(old(elizabeth)&person(elizabeth)))&
(![X]:(quiet(X)=>old(X)))&
(old(joseph)&person(joseph))&
(((?[X]:(~room(X)&old(X)))&(![X,Y]:((~room(X)&~room(Y)&(old(X))&(old(Y)))=>(X=Y)))))&
(old(thomas))&
(quiet(dianne)&old(dianne)&person(dianne))&
(![X]:(room(X)=>(((~quiet(X))=>(~old(X))))))&
(![X]:(room(X)=>(((quiet(X)&person(X))=>(old(X))))))&
((![X]:((quiet(X))<=>(old(X)))))&
(quiet(thomas))&
(![X]:(old(X)=>quiet(X))) | room(joseph)&room(elizabeth)&room(thomas)&room(dianne)&(![X]:(room(X)=>(X='joseph'|X='elizabeth'|X='thomas'|X='dianne')))&
quiet(elizabeth) | [] | null | 0.323039 |
There is a room.
Only one person in the room designs and sews custom cosplay costumes for conventions.
Everyone in the room neither plays as a goalkeeper for a local amateur soccer team nor collects first edition books if they neither does not collect action figures nor collects action figures and vice versa.
Everyone in the room enjoys watercolor painting or does not collect action figures. | Everyone in the room enjoys watercolor painting. | neutral | (there_is_a_room)&
(((?[X]:(room(X)&designs_and_sews_custom_cosplay_costumes_for_conventions(X)))&(![X,Y]:((room(X)&room(Y)&(designs_and_sews_custom_cosplay_costumes_for_conventions(X))&(designs_and_sews_custom_cosplay_costumes_for_conventions(Y)))=>(X=Y)))))&
(![X]:(room(X)=>(((~((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))|(collects_first_edition_books(X))))<=>(~((does_not_collect_action_figures(X))|(collects_action_figures(X))))))))&
(![X]:(room(X)=>(((does_not_collect_action_figures(X))|(enjoys_watercolor_painting(X))))))&
(![X]:(room(X)=>(collects_first_edition_books(X)))) | (there_is_a_room)&
![X]:(room(X)=>(enjoys_watercolor_painting(X))) | [] | null | 0.05084 |
Richard, Jolynn, Vanessa, Ellen are the only persons in the room.
If Jolynn frequently participates in hackathons and coding competitions and is a chess master who participates in national tournaments then everyone in the room either is a chess master who participates in national tournaments or does not practice kickboxing but not both only if they practices zumba.
If everyone in the room frequently participates in hackathons and coding competitions or is not a culinary enthusiast who experiments with international cuisines then everyone anywhere does not practice kickboxing or is a Linux enthusiast.
Not everyone in the room is a Linux enthusiast or is not a Linux enthusiast only if Richard mentors a youth basketball team on weekends.
Jolynn is a Linux enthusiast and collects first edition books if Richard collects first edition books.
If it is not the case that Jolynn mentors a youth basketball team on weekends then if someone practices kickboxing, cannot play the harmonica or mentors a youth basketball team on weekends then he/she mentors a youth basketball team on weekends and vice versa otherwise everyone in the room frequently participates in hackathons and coding competitions.
Everyone in the room is a culinary enthusiast who experiments with international cuisines if they neither mentors a youth basketball team on weekends nor frequently participates in hackathons and coding competitions.
Only one person in the room neither mentors a youth basketball team on weekends nor frequently participates in hackathons and coding competitions.
Everyone in the room does not frequently participates in hackathons and coding competitions or is a culinary enthusiast who experiments with international cuisines. | It is true that Jolynn is a culinary enthusiast who experiments with international cuisines. | entailment | room(richard)&room(jolynn)&room(vanessa)&room(ellen)&(![X]:(room(X)=>(X='richard'|X='jolynn'|X='vanessa'|X='ellen')))&
((((frequently_participates_in_hackathons_and_coding_competitions(jolynn))&(is_a_chess_master_who_participates_in_national_tournaments(jolynn))))=>(![X]:(room(X)=>(((practices_zumba(X))<=(((is_a_chess_master_who_participates_in_national_tournaments(X))<~>(does_not_practice_kickboxing(X)))))))))&
((![X]:(room(X)=>(((is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(frequently_participates_in_hackathons_and_coding_competitions(X))))))=>(![X]:(anywhere(X)=>(((is_a_Linux_enthusiast(X))|(does_not_practice_kickboxing(X)))))))&
((~![X]:(room(X)=>(((is_not_a_Linux_enthusiast(X))|(is_a_Linux_enthusiast(X))))))=>(mentors_a_youth_basketball_team_on_weekends(richard)))&
((collects_first_edition_books(richard))=>(((is_a_Linux_enthusiast(jolynn))&(collects_first_edition_books(jolynn)))))&
((((is_a_chess_master_who_participates_in_national_tournaments(richard))&(collects_first_edition_books(richard))))<~>(mentors_a_youth_basketball_team_on_weekends(richard)))&
(((~(mentors_a_youth_basketball_team_on_weekends(jolynn)))=>((![X]:((((practices_kickboxing(X))|(cannot_play_the_harmonica(X))|(mentors_a_youth_basketball_team_on_weekends(X))))<=>(mentors_a_youth_basketball_team_on_weekends(X))))))&((~(~(mentors_a_youth_basketball_team_on_weekends(jolynn))))=>(![X]:(room(X)=>(frequently_participates_in_hackathons_and_coding_competitions(X))))))&
((![X]:(room(X)=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(does_not_frequently_participates_in_hackathons_and_coding_competitions(X))))))=>(collects_first_edition_books(jolynn)))&
((![X]:(room(X)=>(((is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(is_a_scotch_connoisseur(X))))))<~>(((collects_first_edition_books(vanessa))|(practices_zumba(vanessa)))))&
(can_play_the_harmonica(richard))&
(![X]:(room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))<=(does_not_collect_first_edition_books(X))))))&
(practices_kickboxing(vanessa))&
(collects_first_edition_books(vanessa))&
(![X]:(room(X)=>(((~((mentors_a_youth_basketball_team_on_weekends(X))|(frequently_participates_in_hackathons_and_coding_competitions(X))))=>(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))&
(collects_first_edition_books(richard))&
(((?[X]:(room(X)&~((mentors_a_youth_basketball_team_on_weekends(X))|(frequently_participates_in_hackathons_and_coding_competitions(X)))))&(![X,Y]:((room(X)&room(Y)&(~((mentors_a_youth_basketball_team_on_weekends(X))|(frequently_participates_in_hackathons_and_coding_competitions(X))))&(~((mentors_a_youth_basketball_team_on_weekends(Y))|(frequently_participates_in_hackathons_and_coding_competitions(Y)))))=>(X=Y)))))&
((![X]:((does_enjoy_mountain_biking(X))<=>(frequently_participates_in_hackathons_and_coding_competitions(X)))))&
(![X]:(room(X)=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(does_not_frequently_participates_in_hackathons_and_coding_competitions(X)))))) | room(richard)&room(jolynn)&room(vanessa)&room(ellen)&(![X]:(room(X)=>(X='richard'|X='jolynn'|X='vanessa'|X='ellen')))&
is_a_culinary_enthusiast_who_experiments_with_international_cuisines(jolynn) | [
"p0",
"p6",
"p13",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3806182193575308069689065
% SZS output start Proof for 3806182193575308069689065
44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
50. (predi(paul) => ! [X0] : (room(X0) => predb(X0))) & (~predi(paul) => ! [X0] : ((predi(X0) | ~predk(X0) | prede(X0)) <=> predi(X0))) [input p6]
57. ! [X0] : (room(X0) => (~(predb(X0) | predi(X0)) => predd(X0))) [input p13]
59. ! [X0,X1] : ((~(predb(X1) | predi(X1)) & ~(predb(X0) | predi(X0)) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (~(predb(X0) | predi(X0)) & room(X0)) [input p15]
61. ! [X0] : (room(X0) => (~predb(X0) | predd(X0))) [input p17]
62. ~(predd(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis]
64. (predi(paul) => ! [X0] : (room(X0) => predb(X0))) & (~predi(paul) => ! [X1] : ((predi(X1) | ~predk(X1) | prede(X1)) <=> predi(X1))) [rectify 50]
65. ! [X0,X1] : ((~(predb(X1) | predi(X1)) & ~(predb(X0) | predi(X0)) & room(X1) & room(X0)) => X0 = X1) & ? [X2] : (~(predb(X2) | predi(X2)) & room(X2)) [rectify 59]
137. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
138. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 137]
146. (! [X0] : (predb(X0) | ~room(X0)) | ~predi(paul)) & (! [X1] : ((predi(X1) | ~predk(X1) | prede(X1)) <=> predi(X1)) | predi(paul)) [ennf transformation 64]
153. ! [X0] : ((predd(X0) | (predb(X0) | predi(X0))) | ~room(X0)) [ennf transformation 57]
154. ! [X0] : (predd(X0) | predb(X0) | predi(X0) | ~room(X0)) [flattening 153]
155. ! [X0,X1] : (X0 = X1 | ((predb(X1) | predi(X1)) | (predb(X0) | predi(X0)) | ~room(X1) | ~room(X0))) & ? [X2] : ((~predb(X2) & ~predi(X2)) & room(X2)) [ennf transformation 65]
156. ! [X0,X1] : (X0 = X1 | predb(X1) | predi(X1) | predb(X0) | predi(X0) | ~room(X1) | ~room(X0)) & ? [X2] : (~predb(X2) & ~predi(X2) & room(X2)) [flattening 155]
157. ! [X0] : ((~predb(X0) | predd(X0)) | ~room(X0)) [ennf transformation 61]
158. ! [X0] : (~predb(X0) | predd(X0) | ~room(X0)) [flattening 157]
159. ~predd(paul) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 62]
160. ~predd(paul) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 159]
168. (! [X0] : (predb(X0) | ~room(X0)) | ~predi(paul)) & (! [X1] : (((predi(X1) | ~predk(X1) | prede(X1)) | ~predi(X1)) & (predi(X1) | (~predi(X1) & predk(X1) & ~prede(X1)))) | predi(paul)) [nnf transformation 146]
169. (! [X0] : (predb(X0) | ~room(X0)) | ~predi(paul)) & (! [X1] : ((predi(X1) | ~predk(X1) | prede(X1) | ~predi(X1)) & (predi(X1) | (~predi(X1) & predk(X1) & ~prede(X1)))) | predi(paul)) [flattening 168]
177. ? [X2] : (~predb(X2) & ~predi(X2) & room(X2)) => (~predb(sK3) & ~predi(sK3) & room(sK3)) [choice axiom]
178. ! [X0,X1] : (X0 = X1 | predb(X1) | predi(X1) | predb(X0) | predi(X0) | ~room(X1) | ~room(X0)) & (~predb(sK3) & ~predi(sK3) & room(sK3)) [skolemisation 156,177]
179. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK4 & fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) [choice axiom]
180. ~predd(paul) | (alice != sK4 & fred != sK4 & paul != sK4 & mary != sK4 & room(sK4)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 160,179]
262. room(mary) [cnf transformation 138]
263. room(paul) [cnf transformation 138]
264. room(fred) [cnf transformation 138]
265. room(alice) [cnf transformation 138]
266. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 138]
282. predb(X0) | ~room(X0) | ~predi(paul) [cnf transformation 169]
297. ~room(X0) | predb(X0) | predi(X0) | predd(X0) [cnf transformation 154]
299. room(sK3) [cnf transformation 178]
301. ~predb(sK3) [cnf transformation 178]
303. ~predb(X0) | predd(X0) | ~room(X0) [cnf transformation 158]
304. ~predd(paul) | room(sK4) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 180]
305. ~predd(paul) | mary != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 180]
306. ~predd(paul) | paul != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 180]
307. ~predd(paul) | fred != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 180]
308. ~predd(paul) | alice != sK4 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 180]
310. 1 <=> predb(paul) [avatar definition]
311. predb(paul) <- (1) [avatar component clause 310]
372. 14 <=> predi(paul) [avatar definition]
374. ~predi(paul) <- (~14) [avatar component clause 372]
376. 15 <=> ! [X0] : (predb(X0) | ~room(X0)) [avatar definition]
377. ~room(X0) | predb(X0) <- (15) [avatar component clause 376]
378. ~14 | 15 [avatar split clause 282,376,372]
434. ~predd(paul) | alice != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 308,265]
435. ~predd(paul) | alice != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 434,264]
436. ~predd(paul) | alice != sK4 | ~room(mary) [subsumption resolution 435,263]
437. ~predd(paul) | alice != sK4 [subsumption resolution 436,262]
439. 27 <=> alice = sK4 [avatar definition]
441. alice != sK4 <- (~27) [avatar component clause 439]
443. 28 <=> predd(paul) [avatar definition]
446. ~27 | ~28 [avatar split clause 437,443,439]
447. ~predd(paul) | fred != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 307,265]
448. ~predd(paul) | fred != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 447,264]
449. ~predd(paul) | fred != sK4 | ~room(mary) [subsumption resolution 448,263]
450. ~predd(paul) | fred != sK4 [subsumption resolution 449,262]
452. 29 <=> fred = sK4 [avatar definition]
454. fred != sK4 <- (~29) [avatar component clause 452]
455. ~29 | ~28 [avatar split clause 450,443,452]
456. ~predd(paul) | paul != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 306,265]
457. ~predd(paul) | paul != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 456,264]
458. ~predd(paul) | paul != sK4 | ~room(mary) [subsumption resolution 457,263]
459. ~predd(paul) | paul != sK4 [subsumption resolution 458,262]
461. 30 <=> paul = sK4 [avatar definition]
463. paul != sK4 <- (~30) [avatar component clause 461]
464. ~30 | ~28 [avatar split clause 459,443,461]
465. ~predd(paul) | mary != sK4 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 305,265]
466. ~predd(paul) | mary != sK4 | ~room(paul) | ~room(mary) [subsumption resolution 465,264]
467. ~predd(paul) | mary != sK4 | ~room(mary) [subsumption resolution 466,263]
468. ~predd(paul) | mary != sK4 [subsumption resolution 467,262]
470. 31 <=> mary = sK4 [avatar definition]
472. mary != sK4 <- (~31) [avatar component clause 470]
473. ~31 | ~28 [avatar split clause 468,443,470]
474. ~predd(paul) | room(sK4) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 304,265]
475. ~predd(paul) | room(sK4) | ~room(paul) | ~room(mary) [subsumption resolution 474,264]
476. ~predd(paul) | room(sK4) | ~room(mary) [subsumption resolution 475,263]
477. ~predd(paul) | room(sK4) [subsumption resolution 476,262]
479. 32 <=> room(sK4) [avatar definition]
481. room(sK4) <- (32) [avatar component clause 479]
482. 32 | ~28 [avatar split clause 477,443,479]
489. predb(sK3) <- (15) [resolution 377,299]
492. $false <- (15) [subsumption resolution 489,301]
493. ~15 [avatar contradiction clause 492]
524. predb(paul) | predi(paul) | predd(paul) [resolution 297,263]
567. predb(paul) | predd(paul) <- (~14) [subsumption resolution 524,374]
568. 28 | 1 | 14 [avatar split clause 567,372,310,443]
569. predd(paul) | ~room(paul) <- (1) [resolution 311,303]
573. predd(paul) <- (1) [subsumption resolution 569,263]
574. 28 | ~1 [avatar split clause 573,310,443]
628. fred = sK4 | paul = sK4 | mary = sK4 | alice = sK4 <- (32) [resolution 266,481]
663. paul = sK4 | mary = sK4 | alice = sK4 <- (~29, 32) [subsumption resolution 628,454]
664. mary = sK4 | alice = sK4 <- (~29, ~30, 32) [subsumption resolution 663,463]
665. alice = sK4 <- (~29, ~30, ~31, 32) [subsumption resolution 664,472]
666. $false <- (~27, ~29, ~30, ~31, 32) [subsumption resolution 665,441]
667. 27 | 29 | 30 | 31 | ~32 [avatar contradiction clause 666]
668. $false [avatar sat refutation 378,446,455,464,473,482,493,568,574,667]
% SZS output end Proof for 3806182193575308069689065
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Joseph, Sylvia, Warren, Laura are the only persons in the room.
If "everyone in the room does not own a smart tv or bakes bread at home" then "everyone in the room collect rare sneakers, enjoys cross-country skiing or practices and performs acrobatic dance routines if they does not own a smart tv".
Joseph owns a smart tv.
Sylvia owns a smart tv.
Everyone in the room who is not a wine connoisseur with a private cellar of vintage wines does not own a smart tv.
Everyone in the room who is a wine connoisseur with a private cellar of vintage wines is not an avid hiker.
Everyone outside the room who is a tea enthusiast owns a smart tv.
Everyone in the room who owns a smart tv bakes bread at home.
Everyone in the room who bakes bread at home collect rare sneakers.
Joseph practices and performs acrobatic dance routines.
Everyone in the room enjoys making ceramics.
Someone in the room is a tea enthusiast.
Everyone in the room collect rare sneakers, enjoys cross-country skiing or practices and performs acrobatic dance routines if they does not own a smart tv. | Joseph is an avid hiker. | contradiction | room(joseph)&room(sylvia)&room(warren)&room(laura)&(![X]:(room(X)=>(X='joseph'|X='sylvia'|X='warren'|X='laura')))&
((![X]:(room(X)=>(((bakes_bread_at_home(X))|(does_not_own_a_smart_tv(X))))))=>(![X]:(room(X)=>(((does_not_own_a_smart_tv(X))=>(((collect_rare_sneakers(X))|(enjoys_cross-country_skiing(X))|(practices_and_performs_acrobatic_dance_routines(X)))))))))&
(owns_a_smart_tv(joseph))&
(owns_a_smart_tv(sylvia))&
(![X]:(room(X)=>(((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(does_not_own_a_smart_tv(X))))))&
(![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))=>(is_not_an_avid_hiker(X))))))&
(![X]:(~room(X)=>(((is_a_tea_enthusiast(X))=>(owns_a_smart_tv(X))))))&
(![X]:(room(X)=>(((owns_a_smart_tv(X))=>(bakes_bread_at_home(X))))))&
(![X]:(room(X)=>(((bakes_bread_at_home(X))=>(collect_rare_sneakers(X))))))&
(practices_and_performs_acrobatic_dance_routines(joseph))&
(![X]:(room(X)=>(enjoys_making_ceramics(X))))&
(?[X]:(room(X)&(is_a_tea_enthusiast(X))))&
(![X]:(room(X)=>(((does_not_own_a_smart_tv(X))=>(((collect_rare_sneakers(X))|(enjoys_cross-country_skiing(X))|(practices_and_performs_acrobatic_dance_routines(X)))))))) | room(joseph)&room(sylvia)&room(warren)&room(laura)&(![X]:(room(X)=>(X='joseph'|X='sylvia'|X='warren'|X='laura')))&
is_an_avid_hiker(joseph) | [
"p0",
"p2",
"p4",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 859937439451580383924940
% SZS output start Proof for 859937439451580383924940
44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
46. predg(mary) [input p2]
48. ! [X0] : (room(X0) => (~predd(X0) => ~predg(X0))) [input p4]
49. ! [X0] : (room(X0) => (predd(X0) => ~predi(X0))) [input p5]
57. predi(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis]
137. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
138. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 137]
139. ! [X0] : ((~predg(X0) | predd(X0)) | ~room(X0)) [ennf transformation 48]
140. ! [X0] : (~predg(X0) | predd(X0) | ~room(X0)) [flattening 139]
141. ! [X0] : ((~predi(X0) | ~predd(X0)) | ~room(X0)) [ennf transformation 49]
142. ! [X0] : (~predi(X0) | ~predd(X0) | ~room(X0)) [flattening 141]
145. predi(mary) & ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 57]
146. predi(mary) & ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 145]
230. room(mary) [cnf transformation 138]
235. predg(mary) [cnf transformation 46]
237. ~predg(X0) | predd(X0) | ~room(X0) [cnf transformation 140]
238. ~predi(X0) | ~predd(X0) | ~room(X0) [cnf transformation 142]
247. predi(mary) [cnf transformation 146]
248. predd(mary) | ~room(mary) [resolution 237,235]
250. predd(mary) [subsumption resolution 248,230]
252. ~predd(mary) | ~room(mary) [resolution 238,247]
253. ~room(mary) [subsumption resolution 252,250]
254. $false [subsumption resolution 253,230]
% SZS output end Proof for 859937439451580383924940
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0.009397 |
Jane, Jin are the only persons in the room.
If everyone in the room is passionate about collecting and restoring classic cars or does not enjoy snowboarding then everyone in the room who can play the flute is passionate about collecting and restoring classic cars otherwise everyone outside the room plays as a goalkeeper for a local amateur soccer team if they is passionate about collecting and restoring classic cars.
Everyone in the room is not a member of a local theater group specializing in improv or is not a culinary enthusiast who experiments with international cuisines if everyone in the room does not play as a goalkeeper for a local amateur soccer team or enjoys stand-up paddleboarding and vice versa.
Everyone outside the room is not a member of a local theater group specializing in improv if they does not bake bread at home and vice versa.
Everyone in the room who enjoys stand-up paddleboarding has lived in exactly three countries.
Jin enjoys stand-up paddleboarding.
Jane drives a hybrid car.
Everyone in the room enjoys stand-up paddleboarding only if they cannot play the flute.
Jane is a certified scuba diver with advanced underwater photography skills.
Everyone outside the room practices and performs acrobatic dance routines.
Jane does not enjoy snowboarding.
Not everyone in the room who can play the flute or is not a member of a local theater group specializing in improv or both does not have a tattoo.
Everyone in the room has a tattoo if they has a piercing.
Not everyone in the room drives a hybrid car if they has a tattoo.
Someone in the room enjoys snowboarding.
Everyone in the room bakes bread at home if they does not drive a hybrid car and vice versa.
Everyone in the room does not drive a hybrid car only if they is a culinary enthusiast who experiments with international cuisines. | Only one person in the room is a certified scuba diver with advanced underwater photography skills. | neutral | room(jane)&room(jin)&(![X]:(room(X)=>(X='jane'|X='jin')))&
(((![X]:(room(X)=>(((does_not_enjoy_snowboarding(X))|(is_passionate_about_collecting_and_restoring_classic_cars(X))))))=>(![X]:(room(X)=>(((can_play_the_flute(X))=>(is_passionate_about_collecting_and_restoring_classic_cars(X)))))))&((~(![X]:(room(X)=>(((does_not_enjoy_snowboarding(X))|(is_passionate_about_collecting_and_restoring_classic_cars(X)))))))=>(![X]:(~room(X)=>(((is_passionate_about_collecting_and_restoring_classic_cars(X))=>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))))&
((![X]:(room(X)=>(((enjoys_stand-up_paddleboarding(X))|(does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))<=>(![X]:(room(X)=>(((is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X)))))))&
(![X]:(~room(X)=>(((is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))<=>(does_not_bake_bread_at_home(X))))))&
(![X]:(room(X)=>(((enjoys_stand-up_paddleboarding(X))=>(has_lived_in_exactly_three_countries(X))))))&
(enjoys_stand-up_paddleboarding(jin))&
(drives_a_hybrid_car(jane))&
(![X]:(room(X)=>(((cannot_play_the_flute(X))<=(enjoys_stand-up_paddleboarding(X))))))&
(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(jane))&
(![X]:(~room(X)=>(practices_and_performs_acrobatic_dance_routines(X))))&
(does_not_enjoy_snowboarding(jane))&
(~![X]:(room(X)=>(((((can_play_the_flute(X))|(is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))))=>(does_not_have_a_tattoo(X))))))&
(![X]:(room(X)=>(((has_a_piercing(X))=>(has_a_tattoo(X))))))&
(~![X]:(room(X)=>(((has_a_tattoo(X))=>(drives_a_hybrid_car(X))))))&
(?[X]:(room(X)&(enjoys_snowboarding(X))))&
(![X]:(room(X)=>(((bakes_bread_at_home(X))<=>(does_not_drive_a_hybrid_car(X))))))&
(![X]:(room(X)=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))<=(does_not_drive_a_hybrid_car(X)))))) | room(jane)&room(jin)&(![X]:(room(X)=>(X='jane'|X='jin')))&
((?[X]:(room(X)&is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))&(![X,Y]:((room(X)&room(Y)&(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))&(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(Y)))=>(X=Y)))) | [] | null | 0.283478 |
There is a room. If “no one in the room does not enjoy rooftop gardening or enjoys rooftop gardening” then “everyone in the room is not a coffee connoisseur or is an active member of a local robotics club”. If “everyone in the room is not a coffee connoisseur or is an active member of a local robotics club” then “everyone outside the room who enjoys rooftop gardening is an active member of a local robotics club”. If “everyone anywhere does not practice zumba or owns a microscope” then “everyone in the room does not collect rare and antique scientific instruments or is not a dedicated advocate for digital privacy and encryption”. | Everyone in the room is a dedicated advocate for digital privacy and encryption. | contradiction | (there_is_a_room)&
(((~?[X]:(room(X)=>(((enjoys_rooftop_gardening(X))|(does_not_enjoy_rooftop_gardening(X))))))=>(![X]:(room(X)=>(((is_an_active_member_of_a_local_robotics_club(X))|(is_not_a_coffee_connoisseur(X)))))))&
((![X]:(room(X)=>(((is_an_active_member_of_a_local_robotics_club(X))|(is_not_a_coffee_connoisseur(X))))))=>(![X]:(~room(X)=>(((enjoys_rooftop_gardening(X))=>(is_an_active_member_of_a_local_robotics_club(X))))))))&
(((![X]:(anywhere(X)=>(((owns_a_microscope(X))|(does_not_practice_zumba(X))))))=>(![X]:(room(X)=>(((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(does_not_collect_rare_and_antique_scientific_instruments(X)))))))&
((![X]:(room(X)=>(((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(does_not_collect_rare_and_antique_scientific_instruments(X))))))=>(![X]:(anywhere(X)=>(((does_not_enjoy_logic_puzzles(X))<=(does_not_collect_rare_and_antique_scientific_instruments(X))))))))&
((~![X]:(~room(X)=>(((competes_in_national_level_swimming_championships(X))|(does_not_collect_comic_books(X))))))=>(![X]:(room(X)=>(((does_not_collect_comic_books(X))=>(((enjoys_rooftop_gardening(X))&(competes_in_national_level_swimming_championships(X)))))))))&
(((![X]:(~room(X)=>(((does_not_enjoy_rooftop_gardening(X))<~>(does_not_host_regular_workshops_on_creative_writing(X))))))=>(~![X]:(room(X)=>(((((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))&(collects_comic_books(X))))<=(((does_not_enjoy_rooftop_gardening(X))<~>(does_not_own_a_smart_tv(X)))))))))&((~(![X]:(~room(X)=>(((does_not_enjoy_rooftop_gardening(X))<~>(does_not_host_regular_workshops_on_creative_writing(X)))))))=>(?[X]:(room(X)&(is_a_Linux_enthusiast(X))))))&
((![X]:(room(X)=>(((does_enjoy_mountain_biking(X))|(is_not_a_Linux_enthusiast(X))))))=>(?[X]:(room(X)&(is_not_a_scotch_connoisseur(X)))))&
((![X]:(anywhere(X)=>(regularly_contributes_to_tech_forums_and_online_communities(X))))=>(![X]:(room(X)=>(((is_a_client_of_Meta(X))<=>(plays_eSports_competitively(X)))))))&
((![X]:(room(X)=>(((watches_fantasy_movies(X))|(is_not_a_Linux_enthusiast(X))))))=>(~![X]:(room(X)=>(((is_not_a_Linux_enthusiast(X))=>(is_not_a_client_of_Meta(X)))))))&
(![X]:(~room(X)=>(((is_not_a_client_of_Meta(X))=>(((does_enjoy_mountain_biking(X))<~>(owns_a_smart_tv(X))))))))&
(![X]:(room(X)=>(((regularly_contributes_to_tech_forums_and_online_communities(X))&(is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))))))&
(((?[X]:(anywhere(X)&plays_eSports_competitively(X)))&(![X,Y]:((anywhere(X)&anywhere(Y)&(plays_eSports_competitively(X))&(plays_eSports_competitively(Y)))=>(X=Y)))))&
(![X]:(room(X)=>(((does_not_have_a_piercing(X))=>(is_a_Linux_enthusiast(X))))))&
(![X]:(room(X)=>(((is_not_a_coffee_connoisseur(X))<=(is_a_Linux_enthusiast(X))))))&
(![X]:(room(X)=>(((is_a_client_of_Meta(X))|(does_not_practice_zumba(X))))))&
(![X]:(room(X)=>(((does_not_practice_zumba(X))=>(enjoys_logic_puzzles(X))))))&
(![X]:(room(X)=>(((enjoys_logic_puzzles(X))=>(does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))))))&
(((?[X]:(room(X)&((practices_zumba(X))&(collects_comic_books(X)))))&(![X,Y]:((room(X)&room(Y)&(((practices_zumba(X))&(collects_comic_books(X))))&(((practices_zumba(Y))&(collects_comic_books(Y)))))=>(X=Y)))))&
(![X]:(room(X)=>(((practices_zumba(X))|(does_not_enjoy_mountain_biking(X))|(is_not_a_Linux_enthusiast(X))))))&
(~![X]:(room(X)=>(((is_not_a_Linux_enthusiast(X))=>(is_not_a_client_of_Meta(X))))))&
(![X]:(room(X)=>(((is_not_a_scotch_connoisseur(X))=>(is_an_active_member_of_a_local_robotics_club(X))))))&
(![X]:(room(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(((practices_zumba(X))<~>(does_not_collect_comic_books(X))))))))&
(~![X]:(room(X)=>(((((practices_zumba(X))<~>(does_not_collect_comic_books(X))))=>(enjoys_logic_puzzles(X))))))&
(![X]:(~room(X)=>(((enjoys_logic_puzzles(X))=>(collects_rare_and_antique_scientific_instruments(X)))))) | (there_is_a_room)&
![X]:(room(X)=>(is_a_dedicated_advocate_for_digital_privacy_and_encryption(X))) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 6721980247881708955525176
% SZS output start Proof for 6721980247881708955525176
44. ! [X0] : (~room(X0) => (prede(X0) => predu(X0))) & ~! [X0] : (room(X0) => ((predm(X0) <~> ~predn(X0)) => prede(X0))) & ! [X0] : (room(X0) => (predv(X0) => (predm(X0) <~> ~predn(X0)))) & ! [X0] : (room(X0) => (~predr(X0) => predq(X0))) & ~! [X0] : (room(X0) => (~predz(X0) => ~preda(X0))) & ! [X0] : (room(X0) => (~predz(X0) | ~predt(X0) | predm(X0))) & ! [X0,X1] : ((predn(X1) & predm(X1) & predn(X0) & predm(X0) & room(X1) & room(X0)) => X0 = X1) & ? [X0] : (predn(X0) & predm(X0) & room(X0)) & ! [X0] : (room(X0) => (prede(X0) => ~predk(X0))) & ! [X0] : (room(X0) => (~predm(X0) => prede(X0))) & ! [X0] : (room(X0) => (~predm(X0) | preda(X0))) & ! [X0] : (room(X0) => (predz(X0) => ~predg(X0))) & ! [X0] : (room(X0) => (~predf(X0) => predz(X0))) & ! [X0,X1] : ((predy(X1) & predy(X0) & anywhere(X1) & anywhere(X0)) => X0 = X1) & ? [X0] : (predy(X0) & anywhere(X0)) & ! [X0] : (room(X0) => (~predc(X0) & predw(X0))) & ! [X0] : (~room(X0) => (~preda(X0) => (predt(X0) <~> predb(X0)))) & (! [X0] : (room(X0) => (~predz(X0) | predp(X0))) => ~! [X0] : (room(X0) => (~predz(X0) => ~preda(X0)))) & (! [X0] : (anywhere(X0) => predw(X0)) => ! [X0] : (room(X0) => (preda(X0) <=> predy(X0)))) & (! [X0] : (room(X0) => (~predz(X0) | predt(X0))) => ? [X0] : (~predr(X0) & room(X0))) & (~! [X0] : (~room(X0) => (~predl(X0) <~> ~predh(X0))) => ? [X0] : (predz(X0) & room(X0))) & (! [X0] : (~room(X0) => (~predl(X0) <~> ~predh(X0))) => ~! [X0] : (room(X0) => ((~predl(X0) <~> ~predb(X0)) => (predn(X0) & predi(X0))))) & (~! [X0] : (~room(X0) => (~predn(X0) | predd(X0))) => ! [X0] : (room(X0) => (~predn(X0) => (predd(X0) & predl(X0))))) & (! [X0] : (room(X0) => (~predu(X0) | ~predc(X0))) => ! [X0] : (anywhere(X0) => (~predu(X0) => ~prede(X0)))) & (! [X0] : (anywhere(X0) => (~predm(X0) | predo(X0))) => ! [X0] : (room(X0) => (~predu(X0) | ~predc(X0)))) & (! [X0] : (room(X0) => (~predg(X0) | predq(X0))) => ! [X0] : (~room(X0) => (predl(X0) => predq(X0)))) & (~? [X0] : (room(X0) => (~predl(X0) | predl(X0))) => ! [X0] : (room(X0) => (~predg(X0) | predq(X0)))) & there_is_a_room [input p0]
45. ! [X0] : (room(X0) => predc(X0)) & there_is_a_room [input hypothesis]
46. ! [X0] : (~room(X0) => (prede(X0) => predu(X0))) & ~! [X1] : (room(X1) => ((predm(X1) <~> ~predn(X1)) => prede(X1))) & ! [X2] : (room(X2) => (predv(X2) => (predm(X2) <~> ~predn(X2)))) & ! [X3] : (room(X3) => (~predr(X3) => predq(X3))) & ~! [X4] : (room(X4) => (~predz(X4) => ~preda(X4))) & ! [X5] : (room(X5) => (~predz(X5) | ~predt(X5) | predm(X5))) & ! [X6,X7] : ((predn(X7) & predm(X7) & predn(X6) & predm(X6) & room(X7) & room(X6)) => X6 = X7) & ? [X8] : (predn(X8) & predm(X8) & room(X8)) & ! [X9] : (room(X9) => (prede(X9) => ~predk(X9))) & ! [X10] : (room(X10) => (~predm(X10) => prede(X10))) & ! [X11] : (room(X11) => (~predm(X11) | preda(X11))) & ! [X12] : (room(X12) => (predz(X12) => ~predg(X12))) & ! [X13] : (room(X13) => (~predf(X13) => predz(X13))) & ! [X14,X15] : ((predy(X15) & predy(X14) & anywhere(X15) & anywhere(X14)) => X14 = X15) & ? [X16] : (predy(X16) & anywhere(X16)) & ! [X17] : (room(X17) => (~predc(X17) & predw(X17))) & ! [X18] : (~room(X18) => (~preda(X18) => (predt(X18) <~> predb(X18)))) & (! [X19] : (room(X19) => (~predz(X19) | predp(X19))) => ~! [X20] : (room(X20) => (~predz(X20) => ~preda(X20)))) & (! [X21] : (anywhere(X21) => predw(X21)) => ! [X22] : (room(X22) => (preda(X22) <=> predy(X22)))) & (! [X23] : (room(X23) => (~predz(X23) | predt(X23))) => ? [X24] : (~predr(X24) & room(X24))) & (~! [X25] : (~room(X25) => (~predl(X25) <~> ~predh(X25))) => ? [X26] : (predz(X26) & room(X26))) & (! [X27] : (~room(X27) => (~predl(X27) <~> ~predh(X27))) => ~! [X28] : (room(X28) => ((~predl(X28) <~> ~predb(X28)) => (predn(X28) & predi(X28))))) & (~! [X29] : (~room(X29) => (~predn(X29) | predd(X29))) => ! [X30] : (room(X30) => (~predn(X30) => (predd(X30) & predl(X30))))) & (! [X31] : (room(X31) => (~predu(X31) | ~predc(X31))) => ! [X32] : (anywhere(X32) => (~predu(X32) => ~prede(X32)))) & (! [X33] : (anywhere(X33) => (~predm(X33) | predo(X33))) => ! [X34] : (room(X34) => (~predu(X34) | ~predc(X34)))) & (! [X35] : (room(X35) => (~predg(X35) | predq(X35))) => ! [X36] : (~room(X36) => (predl(X36) => predq(X36)))) & (~? [X37] : (room(X37) => (~predl(X37) | predl(X37))) => ! [X38] : (room(X38) => (~predg(X38) | predq(X38)))) & there_is_a_room [rectify 44]
47. ! [X0] : (~room(X0) => (prede(X0) => predu(X0))) & ~! [X1] : (room(X1) => ((predm(X1) <~> ~predn(X1)) => prede(X1))) & ! [X3] : (room(X3) => (~predr(X3) => predq(X3))) & ~! [X4] : (room(X4) => (~predz(X4) => ~preda(X4))) & ! [X5] : (room(X5) => (~predz(X5) | ~predt(X5) | predm(X5))) & ! [X6,X7] : ((predn(X7) & predm(X7) & predn(X6) & predm(X6) & room(X7) & room(X6)) => X6 = X7) & ? [X8] : (predn(X8) & predm(X8) & room(X8)) & ! [X9] : (room(X9) => (prede(X9) => ~predk(X9))) & ! [X10] : (room(X10) => (~predm(X10) => prede(X10))) & ! [X11] : (room(X11) => (~predm(X11) | preda(X11))) & ! [X12] : (room(X12) => (predz(X12) => ~predg(X12))) & ! [X13] : (room(X13) => (~predf(X13) => predz(X13))) & ! [X14,X15] : ((predy(X15) & predy(X14) & anywhere(X15) & anywhere(X14)) => X14 = X15) & ? [X16] : (predy(X16) & anywhere(X16)) & ! [X17] : (room(X17) => (~predc(X17) & predw(X17))) & ! [X18] : (~room(X18) => (~preda(X18) => (predt(X18) <~> predb(X18)))) & (! [X19] : (room(X19) => (~predz(X19) | predp(X19))) => ~! [X20] : (room(X20) => (~predz(X20) => ~preda(X20)))) & (! [X21] : (anywhere(X21) => predw(X21)) => ! [X22] : (room(X22) => (preda(X22) <=> predy(X22)))) & (! [X23] : (room(X23) => (~predz(X23) | predt(X23))) => ? [X24] : (~predr(X24) & room(X24))) & (~! [X25] : (~room(X25) => (~predl(X25) <~> ~predh(X25))) => ? [X26] : (predz(X26) & room(X26))) & (! [X27] : (~room(X27) => (~predl(X27) <~> ~predh(X27))) => ~! [X28] : (room(X28) => ((~predl(X28) <~> ~predb(X28)) => (predn(X28) & predi(X28))))) & (~! [X29] : (~room(X29) => (~predn(X29) | predd(X29))) => ! [X30] : (room(X30) => (~predn(X30) => (predd(X30) & predl(X30))))) & (! [X31] : (room(X31) => (~predu(X31) | ~predc(X31))) => ! [X32] : (anywhere(X32) => (~predu(X32) => ~prede(X32)))) & (! [X33] : (anywhere(X33) => (~predm(X33) | predo(X33))) => ! [X34] : (room(X34) => (~predu(X34) | ~predc(X34)))) & (! [X35] : (room(X35) => (~predg(X35) | predq(X35))) => ! [X36] : (~room(X36) => (predl(X36) => predq(X36)))) & (~? [X37] : (room(X37) => (~predl(X37) | predl(X37))) => ! [X38] : (room(X38) => (~predg(X38) | predq(X38)))) & there_is_a_room [pure predicate removal 46]
48. ! [X0] : (~room(X0) => (prede(X0) => predu(X0))) & ~! [X1] : (room(X1) => ((predm(X1) <~> ~predn(X1)) => prede(X1))) & ! [X3] : (room(X3) => (~predr(X3) => predq(X3))) & ~! [X4] : (room(X4) => (~predz(X4) => ~preda(X4))) & ! [X5] : (room(X5) => (~predz(X5) | ~predt(X5) | predm(X5))) & ! [X6,X7] : ((predn(X7) & predm(X7) & predn(X6) & predm(X6) & room(X7) & room(X6)) => X6 = X7) & ? [X8] : (predn(X8) & predm(X8) & room(X8)) & ! [X10] : (room(X10) => (~predm(X10) => prede(X10))) & ! [X11] : (room(X11) => (~predm(X11) | preda(X11))) & ! [X12] : (room(X12) => (predz(X12) => ~predg(X12))) & ! [X13] : (room(X13) => (~predf(X13) => predz(X13))) & ! [X14,X15] : ((predy(X15) & predy(X14) & anywhere(X15) & anywhere(X14)) => X14 = X15) & ? [X16] : (predy(X16) & anywhere(X16)) & ! [X17] : (room(X17) => (~predc(X17) & predw(X17))) & ! [X18] : (~room(X18) => (~preda(X18) => (predt(X18) <~> predb(X18)))) & (! [X19] : (room(X19) => (~predz(X19) | predp(X19))) => ~! [X20] : (room(X20) => (~predz(X20) => ~preda(X20)))) & (! [X21] : (anywhere(X21) => predw(X21)) => ! [X22] : (room(X22) => (preda(X22) <=> predy(X22)))) & (! [X23] : (room(X23) => (~predz(X23) | predt(X23))) => ? [X24] : (~predr(X24) & room(X24))) & (~! [X25] : (~room(X25) => (~predl(X25) <~> ~predh(X25))) => ? [X26] : (predz(X26) & room(X26))) & (! [X27] : (~room(X27) => (~predl(X27) <~> ~predh(X27))) => ~! [X28] : (room(X28) => ((~predl(X28) <~> ~predb(X28)) => (predn(X28) & predi(X28))))) & (~! [X29] : (~room(X29) => (~predn(X29) | predd(X29))) => ! [X30] : (room(X30) => (~predn(X30) => (predd(X30) & predl(X30))))) & (! [X31] : (room(X31) => (~predu(X31) | ~predc(X31))) => ! [X32] : (anywhere(X32) => (~predu(X32) => ~prede(X32)))) & (! [X33] : (anywhere(X33) => (~predm(X33) | predo(X33))) => ! [X34] : (room(X34) => (~predu(X34) | ~predc(X34)))) & (! [X35] : (room(X35) => (~predg(X35) | predq(X35))) => ! [X36] : (~room(X36) => (predl(X36) => predq(X36)))) & (~? [X37] : (room(X37) => (~predl(X37) | predl(X37))) => ! [X38] : (room(X38) => (~predg(X38) | predq(X38)))) & there_is_a_room [pure predicate removal 47]
49. ! [X0] : (~room(X0) => (prede(X0) => predu(X0))) & ~! [X1] : (room(X1) => ((predm(X1) <~> ~predn(X1)) => prede(X1))) & ! [X3] : (room(X3) => (~predr(X3) => predq(X3))) & ~! [X4] : (room(X4) => (~predz(X4) => ~preda(X4))) & ! [X5] : (room(X5) => (~predz(X5) | ~predt(X5) | predm(X5))) & ! [X6,X7] : ((predn(X7) & predm(X7) & predn(X6) & predm(X6) & room(X7) & room(X6)) => X6 = X7) & ? [X8] : (predn(X8) & predm(X8) & room(X8)) & ! [X10] : (room(X10) => (~predm(X10) => prede(X10))) & ! [X11] : (room(X11) => (~predm(X11) | preda(X11))) & ! [X12] : (room(X12) => (predz(X12) => ~predg(X12))) & ! [X14,X15] : ((predy(X15) & predy(X14) & anywhere(X15) & anywhere(X14)) => X14 = X15) & ? [X16] : (predy(X16) & anywhere(X16)) & ! [X17] : (room(X17) => (~predc(X17) & predw(X17))) & ! [X18] : (~room(X18) => (~preda(X18) => (predt(X18) <~> predb(X18)))) & (! [X19] : (room(X19) => (~predz(X19) | predp(X19))) => ~! [X20] : (room(X20) => (~predz(X20) => ~preda(X20)))) & (! [X21] : (anywhere(X21) => predw(X21)) => ! [X22] : (room(X22) => (preda(X22) <=> predy(X22)))) & (! [X23] : (room(X23) => (~predz(X23) | predt(X23))) => ? [X24] : (~predr(X24) & room(X24))) & (~! [X25] : (~room(X25) => (~predl(X25) <~> ~predh(X25))) => ? [X26] : (predz(X26) & room(X26))) & (! [X27] : (~room(X27) => (~predl(X27) <~> ~predh(X27))) => ~! [X28] : (room(X28) => ((~predl(X28) <~> ~predb(X28)) => (predn(X28) & predi(X28))))) & (~! [X29] : (~room(X29) => (~predn(X29) | predd(X29))) => ! [X30] : (room(X30) => (~predn(X30) => (predd(X30) & predl(X30))))) & (! [X31] : (room(X31) => (~predu(X31) | ~predc(X31))) => ! [X32] : (anywhere(X32) => (~predu(X32) => ~prede(X32)))) & (! [X33] : (anywhere(X33) => (~predm(X33) | predo(X33))) => ! [X34] : (room(X34) => (~predu(X34) | ~predc(X34)))) & (! [X35] : (room(X35) => (~predg(X35) | predq(X35))) => ! [X36] : (~room(X36) => (predl(X36) => predq(X36)))) & (~? [X37] : (room(X37) => (~predl(X37) | predl(X37))) => ! [X38] : (room(X38) => (~predg(X38) | predq(X38)))) & there_is_a_room [pure predicate removal 48]
50. ! [X0] : (~room(X0) => (prede(X0) => predu(X0))) & ~! [X1] : (room(X1) => ((predm(X1) <~> ~predn(X1)) => prede(X1))) & ! [X3] : (room(X3) => (~predr(X3) => predq(X3))) & ~! [X4] : (room(X4) => (~predz(X4) => ~preda(X4))) & ! [X5] : (room(X5) => (~predz(X5) | ~predt(X5) | predm(X5))) & ! [X6,X7] : ((predn(X7) & predm(X7) & predn(X6) & predm(X6) & room(X7) & room(X6)) => X6 = X7) & ? [X8] : (predn(X8) & predm(X8) & room(X8)) & ! [X10] : (room(X10) => (~predm(X10) => prede(X10))) & ! [X11] : (room(X11) => (~predm(X11) | preda(X11))) & ! [X12] : (room(X12) => (predz(X12) => ~predg(X12))) & ! [X14,X15] : ((predy(X15) & predy(X14) & anywhere(X15) & anywhere(X14)) => X14 = X15) & ? [X16] : (predy(X16) & anywhere(X16)) & ! [X17] : (room(X17) => (~predc(X17) & predw(X17))) & ! [X18] : (~room(X18) => (~preda(X18) => (predt(X18) <~> predb(X18)))) & (! [X19] : (room(X19) => ~predz(X19)) => ~! [X20] : (room(X20) => (~predz(X20) => ~preda(X20)))) & (! [X21] : (anywhere(X21) => predw(X21)) => ! [X22] : (room(X22) => (preda(X22) <=> predy(X22)))) & (! [X23] : (room(X23) => (~predz(X23) | predt(X23))) => ? [X24] : (~predr(X24) & room(X24))) & (~! [X25] : (~room(X25) => (~predl(X25) <~> ~predh(X25))) => ? [X26] : (predz(X26) & room(X26))) & (! [X27] : (~room(X27) => (~predl(X27) <~> ~predh(X27))) => ~! [X28] : (room(X28) => ((~predl(X28) <~> ~predb(X28)) => (predn(X28) & predi(X28))))) & (~! [X29] : (~room(X29) => (~predn(X29) | predd(X29))) => ! [X30] : (room(X30) => (~predn(X30) => (predd(X30) & predl(X30))))) & (! [X31] : (room(X31) => (~predu(X31) | ~predc(X31))) => ! [X32] : (anywhere(X32) => (~predu(X32) => ~prede(X32)))) & (! [X33] : (anywhere(X33) => (~predm(X33) | predo(X33))) => ! [X34] : (room(X34) => (~predu(X34) | ~predc(X34)))) & (! [X35] : (room(X35) => (~predg(X35) | predq(X35))) => ! [X36] : (~room(X36) => (predl(X36) => predq(X36)))) & (~? [X37] : (room(X37) => (~predl(X37) | predl(X37))) => ! [X38] : (room(X38) => (~predg(X38) | predq(X38)))) & there_is_a_room [pure predicate removal 49]
51. ! [X0] : (~room(X0) => (prede(X0) => predu(X0))) & ~! [X1] : (room(X1) => ((predm(X1) <~> ~predn(X1)) => prede(X1))) & ! [X3] : (room(X3) => (~predr(X3) => predq(X3))) & ~! [X4] : (room(X4) => (~predz(X4) => ~preda(X4))) & ! [X5] : (room(X5) => (~predz(X5) | ~predt(X5) | predm(X5))) & ! [X6,X7] : ((predn(X7) & predm(X7) & predn(X6) & predm(X6) & room(X7) & room(X6)) => X6 = X7) & ? [X8] : (predn(X8) & predm(X8) & room(X8)) & ! [X10] : (room(X10) => (~predm(X10) => prede(X10))) & ! [X11] : (room(X11) => (~predm(X11) | preda(X11))) & ! [X12] : (room(X12) => (predz(X12) => ~predg(X12))) & ! [X14,X15] : ((predy(X15) & predy(X14) & anywhere(X15) & anywhere(X14)) => X14 = X15) & ? [X16] : (predy(X16) & anywhere(X16)) & ! [X17] : (room(X17) => (~predc(X17) & predw(X17))) & ! [X18] : (~room(X18) => (~preda(X18) => (predt(X18) <~> predb(X18)))) & (! [X19] : (room(X19) => ~predz(X19)) => ~! [X20] : (room(X20) => (~predz(X20) => ~preda(X20)))) & (! [X21] : (anywhere(X21) => predw(X21)) => ! [X22] : (room(X22) => (preda(X22) <=> predy(X22)))) & (! [X23] : (room(X23) => (~predz(X23) | predt(X23))) => ? [X24] : (~predr(X24) & room(X24))) & (~! [X25] : (~room(X25) => (~predl(X25) <~> ~predh(X25))) => ? [X26] : (predz(X26) & room(X26))) & (! [X27] : (~room(X27) => (~predl(X27) <~> ~predh(X27))) => ~! [X28] : (room(X28) => ~(~predl(X28) <~> ~predb(X28)))) & (~! [X29] : (~room(X29) => (~predn(X29) | predd(X29))) => ! [X30] : (room(X30) => (~predn(X30) => (predd(X30) & predl(X30))))) & (! [X31] : (room(X31) => (~predu(X31) | ~predc(X31))) => ! [X32] : (anywhere(X32) => (~predu(X32) => ~prede(X32)))) & (! [X33] : (anywhere(X33) => (~predm(X33) | predo(X33))) => ! [X34] : (room(X34) => (~predu(X34) | ~predc(X34)))) & (! [X35] : (room(X35) => (~predg(X35) | predq(X35))) => ! [X36] : (~room(X36) => (predl(X36) => predq(X36)))) & (~? [X37] : (room(X37) => (~predl(X37) | predl(X37))) => ! [X38] : (room(X38) => (~predg(X38) | predq(X38)))) & there_is_a_room [pure predicate removal 50]
52. ! [X0] : (~room(X0) => (prede(X0) => predu(X0))) & ~! [X1] : (room(X1) => ((predm(X1) <~> ~predn(X1)) => prede(X1))) & ! [X3] : (room(X3) => (~predr(X3) => predq(X3))) & ~! [X4] : (room(X4) => (~predz(X4) => ~preda(X4))) & ! [X5] : (room(X5) => (~predz(X5) | ~predt(X5) | predm(X5))) & ! [X6,X7] : ((predn(X7) & predm(X7) & predn(X6) & predm(X6) & room(X7) & room(X6)) => X6 = X7) & ? [X8] : (predn(X8) & predm(X8) & room(X8)) & ! [X10] : (room(X10) => (~predm(X10) => prede(X10))) & ! [X11] : (room(X11) => (~predm(X11) | preda(X11))) & ! [X12] : (room(X12) => (predz(X12) => ~predg(X12))) & ! [X14,X15] : ((predy(X15) & predy(X14) & anywhere(X15) & anywhere(X14)) => X14 = X15) & ? [X16] : (predy(X16) & anywhere(X16)) & ! [X17] : (room(X17) => (~predc(X17) & predw(X17))) & ! [X18] : (~room(X18) => (~preda(X18) => (predt(X18) <~> predb(X18)))) & (! [X19] : (room(X19) => ~predz(X19)) => ~! [X20] : (room(X20) => (~predz(X20) => ~preda(X20)))) & (! [X21] : (anywhere(X21) => predw(X21)) => ! [X22] : (room(X22) => (preda(X22) <=> predy(X22)))) & (! [X23] : (room(X23) => (~predz(X23) | predt(X23))) => ? [X24] : (~predr(X24) & room(X24))) & (~! [X25] : (~room(X25) => (~predl(X25) <~> ~predh(X25))) => ? [X26] : (predz(X26) & room(X26))) & (! [X27] : (~room(X27) => (~predl(X27) <~> ~predh(X27))) => ~! [X28] : (room(X28) => ~(~predl(X28) <~> ~predb(X28)))) & (! [X31] : (room(X31) => (~predu(X31) | ~predc(X31))) => ! [X32] : (anywhere(X32) => (~predu(X32) => ~prede(X32)))) & (! [X33] : (anywhere(X33) => (~predm(X33) | predo(X33))) => ! [X34] : (room(X34) => (~predu(X34) | ~predc(X34)))) & (! [X35] : (room(X35) => (~predg(X35) | predq(X35))) => ! [X36] : (~room(X36) => (predl(X36) => predq(X36)))) & (~? [X37] : (room(X37) => (~predl(X37) | predl(X37))) => ! [X38] : (room(X38) => (~predg(X38) | predq(X38)))) & there_is_a_room [pure predicate removal 51]
53. ! [X0] : (~room(X0) => (prede(X0) => predu(X0))) & ~! [X1] : (room(X1) => ((predm(X1) <~> ~predn(X1)) => prede(X1))) & ! [X3] : (room(X3) => (~predr(X3) => predq(X3))) & ~! [X4] : (room(X4) => (~predz(X4) => ~preda(X4))) & ! [X5] : (room(X5) => (~predz(X5) | ~predt(X5) | predm(X5))) & ! [X6,X7] : ((predn(X7) & predm(X7) & predn(X6) & predm(X6) & room(X7) & room(X6)) => X6 = X7) & ? [X8] : (predn(X8) & predm(X8) & room(X8)) & ! [X10] : (room(X10) => (~predm(X10) => prede(X10))) & ! [X11] : (room(X11) => (~predm(X11) | preda(X11))) & ! [X12] : (room(X12) => (predz(X12) => ~predg(X12))) & ! [X14,X15] : ((predy(X15) & predy(X14) & anywhere(X15) & anywhere(X14)) => X14 = X15) & ? [X16] : (predy(X16) & anywhere(X16)) & ! [X17] : (room(X17) => (~predc(X17) & predw(X17))) & ! [X18] : (~room(X18) => (~preda(X18) => (predt(X18) <~> predb(X18)))) & (! [X19] : (room(X19) => ~predz(X19)) => ~! [X20] : (room(X20) => (~predz(X20) => ~preda(X20)))) & (! [X21] : (anywhere(X21) => predw(X21)) => ! [X22] : (room(X22) => (preda(X22) <=> predy(X22)))) & (! [X23] : (room(X23) => (~predz(X23) | predt(X23))) => ? [X24] : (~predr(X24) & room(X24))) & (~! [X25] : (~room(X25) => (~predl(X25) <~> ~predh(X25))) => ? [X26] : (predz(X26) & room(X26))) & (! [X27] : (~room(X27) => (~predl(X27) <~> ~predh(X27))) => ~! [X28] : (room(X28) => ~(~predl(X28) <~> ~predb(X28)))) & (! [X31] : (room(X31) => (~predu(X31) | ~predc(X31))) => ! [X32] : (anywhere(X32) => (~predu(X32) => ~prede(X32)))) & (! [X33] : (anywhere(X33) => ~predm(X33)) => ! [X34] : (room(X34) => (~predu(X34) | ~predc(X34)))) & (! [X35] : (room(X35) => (~predg(X35) | predq(X35))) => ! [X36] : (~room(X36) => (predl(X36) => predq(X36)))) & (~? [X37] : (room(X37) => (~predl(X37) | predl(X37))) => ! [X38] : (room(X38) => (~predg(X38) | predq(X38)))) & there_is_a_room [pure predicate removal 52]
54. ! [X0] : (room(X0) => predc(X0)) [pure predicate removal 45]
55. ! [X0] : (~room(X0) => (prede(X0) => predu(X0))) & ~! [X1] : (room(X1) => ((predm(X1) <~> ~predn(X1)) => prede(X1))) & ! [X3] : (room(X3) => (~predr(X3) => predq(X3))) & ~! [X4] : (room(X4) => (~predz(X4) => ~preda(X4))) & ! [X5] : (room(X5) => (~predz(X5) | ~predt(X5) | predm(X5))) & ! [X6,X7] : ((predn(X7) & predm(X7) & predn(X6) & predm(X6) & room(X7) & room(X6)) => X6 = X7) & ? [X8] : (predn(X8) & predm(X8) & room(X8)) & ! [X10] : (room(X10) => (~predm(X10) => prede(X10))) & ! [X11] : (room(X11) => (~predm(X11) | preda(X11))) & ! [X12] : (room(X12) => (predz(X12) => ~predg(X12))) & ! [X14,X15] : ((predy(X15) & predy(X14) & anywhere(X15) & anywhere(X14)) => X14 = X15) & ? [X16] : (predy(X16) & anywhere(X16)) & ! [X17] : (room(X17) => (~predc(X17) & predw(X17))) & ! [X18] : (~room(X18) => (~preda(X18) => (predt(X18) <~> predb(X18)))) & (! [X19] : (room(X19) => ~predz(X19)) => ~! [X20] : (room(X20) => (~predz(X20) => ~preda(X20)))) & (! [X21] : (anywhere(X21) => predw(X21)) => ! [X22] : (room(X22) => (preda(X22) <=> predy(X22)))) & (! [X23] : (room(X23) => (~predz(X23) | predt(X23))) => ? [X24] : (~predr(X24) & room(X24))) & (~! [X25] : (~room(X25) => (~predl(X25) <~> ~predh(X25))) => ? [X26] : (predz(X26) & room(X26))) & (! [X27] : (~room(X27) => (~predl(X27) <~> ~predh(X27))) => ~! [X28] : (room(X28) => ~(~predl(X28) <~> ~predb(X28)))) & (! [X31] : (room(X31) => (~predu(X31) | ~predc(X31))) => ! [X32] : (anywhere(X32) => (~predu(X32) => ~prede(X32)))) & (! [X33] : (anywhere(X33) => ~predm(X33)) => ! [X34] : (room(X34) => (~predu(X34) | ~predc(X34)))) & (! [X35] : (room(X35) => (~predg(X35) | predq(X35))) => ! [X36] : (~room(X36) => (predl(X36) => predq(X36)))) & (~? [X37] : (room(X37) => (~predl(X37) | predl(X37))) => ! [X38] : (room(X38) => (~predg(X38) | predq(X38)))) [pure predicate removal 53]
127. ! [X0] : ((predu(X0) | ~prede(X0)) | room(X0)) & ? [X1] : ((~prede(X1) & (predm(X1) <~> ~predn(X1))) & room(X1)) & ! [X3] : ((predq(X3) | predr(X3)) | ~room(X3)) & ? [X4] : ((preda(X4) & ~predz(X4)) & room(X4)) & ! [X5] : ((~predz(X5) | ~predt(X5) | predm(X5)) | ~room(X5)) & ! [X6,X7] : (X6 = X7 | (~predn(X7) | ~predm(X7) | ~predn(X6) | ~predm(X6) | ~room(X7) | ~room(X6))) & ? [X8] : (predn(X8) & predm(X8) & room(X8)) & ! [X10] : ((prede(X10) | predm(X10)) | ~room(X10)) & ! [X11] : ((~predm(X11) | preda(X11)) | ~room(X11)) & ! [X12] : ((~predg(X12) | ~predz(X12)) | ~room(X12)) & ! [X14,X15] : (X14 = X15 | (~predy(X15) | ~predy(X14) | ~anywhere(X15) | ~anywhere(X14))) & ? [X16] : (predy(X16) & anywhere(X16)) & ! [X17] : ((~predc(X17) & predw(X17)) | ~room(X17)) & ! [X18] : (((predt(X18) <~> predb(X18)) | preda(X18)) | room(X18)) & (? [X20] : ((preda(X20) & ~predz(X20)) & room(X20)) | ? [X19] : (predz(X19) & room(X19))) & (! [X22] : ((preda(X22) <=> predy(X22)) | ~room(X22)) | ? [X21] : (~predw(X21) & anywhere(X21))) & (? [X24] : (~predr(X24) & room(X24)) | ? [X23] : ((predz(X23) & ~predt(X23)) & room(X23))) & (? [X26] : (predz(X26) & room(X26)) | ! [X25] : ((~predl(X25) <~> ~predh(X25)) | room(X25))) & (? [X28] : ((~predl(X28) <~> ~predb(X28)) & room(X28)) | ? [X27] : ((~predl(X27) <=> ~predh(X27)) & ~room(X27))) & (! [X32] : ((~prede(X32) | predu(X32)) | ~anywhere(X32)) | ? [X31] : ((predu(X31) & predc(X31)) & room(X31))) & (! [X34] : ((~predu(X34) | ~predc(X34)) | ~room(X34)) | ? [X33] : (predm(X33) & anywhere(X33))) & (! [X36] : ((predq(X36) | ~predl(X36)) | room(X36)) | ? [X35] : ((predg(X35) & ~predq(X35)) & room(X35))) & (! [X38] : ((~predg(X38) | predq(X38)) | ~room(X38)) | ? [X37] : ((~predl(X37) | predl(X37)) | ~room(X37))) [ennf transformation 55]
128. ! [X0] : (predu(X0) | ~prede(X0) | room(X0)) & ? [X1] : (~prede(X1) & (predm(X1) <~> ~predn(X1)) & room(X1)) & ! [X3] : (predq(X3) | predr(X3) | ~room(X3)) & ? [X4] : (preda(X4) & ~predz(X4) & room(X4)) & ! [X5] : (~predz(X5) | ~predt(X5) | predm(X5) | ~room(X5)) & ! [X6,X7] : (X6 = X7 | ~predn(X7) | ~predm(X7) | ~predn(X6) | ~predm(X6) | ~room(X7) | ~room(X6)) & ? [X8] : (predn(X8) & predm(X8) & room(X8)) & ! [X10] : (prede(X10) | predm(X10) | ~room(X10)) & ! [X11] : (~predm(X11) | preda(X11) | ~room(X11)) & ! [X12] : (~predg(X12) | ~predz(X12) | ~room(X12)) & ! [X14,X15] : (X14 = X15 | ~predy(X15) | ~predy(X14) | ~anywhere(X15) | ~anywhere(X14)) & ? [X16] : (predy(X16) & anywhere(X16)) & ! [X17] : ((~predc(X17) & predw(X17)) | ~room(X17)) & ! [X18] : ((predt(X18) <~> predb(X18)) | preda(X18) | room(X18)) & (? [X20] : (preda(X20) & ~predz(X20) & room(X20)) | ? [X19] : (predz(X19) & room(X19))) & (! [X22] : ((preda(X22) <=> predy(X22)) | ~room(X22)) | ? [X21] : (~predw(X21) & anywhere(X21))) & (? [X24] : (~predr(X24) & room(X24)) | ? [X23] : (predz(X23) & ~predt(X23) & room(X23))) & (? [X26] : (predz(X26) & room(X26)) | ! [X25] : ((~predl(X25) <~> ~predh(X25)) | room(X25))) & (? [X28] : ((~predl(X28) <~> ~predb(X28)) & room(X28)) | ? [X27] : ((~predl(X27) <=> ~predh(X27)) & ~room(X27))) & (! [X32] : (~prede(X32) | predu(X32) | ~anywhere(X32)) | ? [X31] : (predu(X31) & predc(X31) & room(X31))) & (! [X34] : (~predu(X34) | ~predc(X34) | ~room(X34)) | ? [X33] : (predm(X33) & anywhere(X33))) & (! [X36] : (predq(X36) | ~predl(X36) | room(X36)) | ? [X35] : (predg(X35) & ~predq(X35) & room(X35))) & (! [X38] : (~predg(X38) | predq(X38) | ~room(X38)) | ? [X37] : (~predl(X37) | predl(X37) | ~room(X37))) [flattening 127]
129. ! [X0] : (predc(X0) | ~room(X0)) [ennf transformation 54]
130. ? [X27] : ((~predl(X27) <=> ~predh(X27)) & ~room(X27)) | ~sP0 [predicate definition introduction]
131. ! [X0] : (predu(X0) | ~prede(X0) | room(X0)) & ? [X1] : (~prede(X1) & (predm(X1) <~> ~predn(X1)) & room(X1)) & ! [X3] : (predq(X3) | predr(X3) | ~room(X3)) & ? [X4] : (preda(X4) & ~predz(X4) & room(X4)) & ! [X5] : (~predz(X5) | ~predt(X5) | predm(X5) | ~room(X5)) & ! [X6,X7] : (X6 = X7 | ~predn(X7) | ~predm(X7) | ~predn(X6) | ~predm(X6) | ~room(X7) | ~room(X6)) & ? [X8] : (predn(X8) & predm(X8) & room(X8)) & ! [X10] : (prede(X10) | predm(X10) | ~room(X10)) & ! [X11] : (~predm(X11) | preda(X11) | ~room(X11)) & ! [X12] : (~predg(X12) | ~predz(X12) | ~room(X12)) & ! [X14,X15] : (X14 = X15 | ~predy(X15) | ~predy(X14) | ~anywhere(X15) | ~anywhere(X14)) & ? [X16] : (predy(X16) & anywhere(X16)) & ! [X17] : ((~predc(X17) & predw(X17)) | ~room(X17)) & ! [X18] : ((predt(X18) <~> predb(X18)) | preda(X18) | room(X18)) & (? [X20] : (preda(X20) & ~predz(X20) & room(X20)) | ? [X19] : (predz(X19) & room(X19))) & (! [X22] : ((preda(X22) <=> predy(X22)) | ~room(X22)) | ? [X21] : (~predw(X21) & anywhere(X21))) & (? [X24] : (~predr(X24) & room(X24)) | ? [X23] : (predz(X23) & ~predt(X23) & room(X23))) & (? [X26] : (predz(X26) & room(X26)) | ! [X25] : ((~predl(X25) <~> ~predh(X25)) | room(X25))) & (? [X28] : ((~predl(X28) <~> ~predb(X28)) & room(X28)) | sP0) & (! [X32] : (~prede(X32) | predu(X32) | ~anywhere(X32)) | ? [X31] : (predu(X31) & predc(X31) & room(X31))) & (! [X34] : (~predu(X34) | ~predc(X34) | ~room(X34)) | ? [X33] : (predm(X33) & anywhere(X33))) & (! [X36] : (predq(X36) | ~predl(X36) | room(X36)) | ? [X35] : (predg(X35) & ~predq(X35) & room(X35))) & (! [X38] : (~predg(X38) | predq(X38) | ~room(X38)) | ? [X37] : (~predl(X37) | predl(X37) | ~room(X37))) [definition folding 128,130]
138. ! [X0] : (predu(X0) | ~prede(X0) | room(X0)) & ? [X1] : (~prede(X1) & ((predn(X1) | ~predm(X1)) & (~predn(X1) | predm(X1))) & room(X1)) & ! [X3] : (predq(X3) | predr(X3) | ~room(X3)) & ? [X4] : (preda(X4) & ~predz(X4) & room(X4)) & ! [X5] : (~predz(X5) | ~predt(X5) | predm(X5) | ~room(X5)) & ! [X6,X7] : (X6 = X7 | ~predn(X7) | ~predm(X7) | ~predn(X6) | ~predm(X6) | ~room(X7) | ~room(X6)) & ? [X8] : (predn(X8) & predm(X8) & room(X8)) & ! [X10] : (prede(X10) | predm(X10) | ~room(X10)) & ! [X11] : (~predm(X11) | preda(X11) | ~room(X11)) & ! [X12] : (~predg(X12) | ~predz(X12) | ~room(X12)) & ! [X14,X15] : (X14 = X15 | ~predy(X15) | ~predy(X14) | ~anywhere(X15) | ~anywhere(X14)) & ? [X16] : (predy(X16) & anywhere(X16)) & ! [X17] : ((~predc(X17) & predw(X17)) | ~room(X17)) & ! [X18] : (((~predb(X18) | ~predt(X18)) & (predb(X18) | predt(X18))) | preda(X18) | room(X18)) & (? [X20] : (preda(X20) & ~predz(X20) & room(X20)) | ? [X19] : (predz(X19) & room(X19))) & (! [X22] : (((preda(X22) | ~predy(X22)) & (predy(X22) | ~preda(X22))) | ~room(X22)) | ? [X21] : (~predw(X21) & anywhere(X21))) & (? [X24] : (~predr(X24) & room(X24)) | ? [X23] : (predz(X23) & ~predt(X23) & room(X23))) & (? [X26] : (predz(X26) & room(X26)) | ! [X25] : (((predh(X25) | predl(X25)) & (~predh(X25) | ~predl(X25))) | room(X25))) & (? [X28] : (((predb(X28) | predl(X28)) & (~predb(X28) | ~predl(X28))) & room(X28)) | sP0) & (! [X32] : (~prede(X32) | predu(X32) | ~anywhere(X32)) | ? [X31] : (predu(X31) & predc(X31) & room(X31))) & (! [X34] : (~predu(X34) | ~predc(X34) | ~room(X34)) | ? [X33] : (predm(X33) & anywhere(X33))) & (! [X36] : (predq(X36) | ~predl(X36) | room(X36)) | ? [X35] : (predg(X35) & ~predq(X35) & room(X35))) & (! [X38] : (~predg(X38) | predq(X38) | ~room(X38)) | ? [X37] : (~predl(X37) | predl(X37) | ~room(X37))) [nnf transformation 131]
139. ! [X0] : (predu(X0) | ~prede(X0) | room(X0)) & ? [X1] : (~prede(X1) & (predn(X1) | ~predm(X1)) & (~predn(X1) | predm(X1)) & room(X1)) & ! [X3] : (predq(X3) | predr(X3) | ~room(X3)) & ? [X4] : (preda(X4) & ~predz(X4) & room(X4)) & ! [X5] : (~predz(X5) | ~predt(X5) | predm(X5) | ~room(X5)) & ! [X6,X7] : (X6 = X7 | ~predn(X7) | ~predm(X7) | ~predn(X6) | ~predm(X6) | ~room(X7) | ~room(X6)) & ? [X8] : (predn(X8) & predm(X8) & room(X8)) & ! [X10] : (prede(X10) | predm(X10) | ~room(X10)) & ! [X11] : (~predm(X11) | preda(X11) | ~room(X11)) & ! [X12] : (~predg(X12) | ~predz(X12) | ~room(X12)) & ! [X14,X15] : (X14 = X15 | ~predy(X15) | ~predy(X14) | ~anywhere(X15) | ~anywhere(X14)) & ? [X16] : (predy(X16) & anywhere(X16)) & ! [X17] : ((~predc(X17) & predw(X17)) | ~room(X17)) & ! [X18] : (((~predb(X18) | ~predt(X18)) & (predb(X18) | predt(X18))) | preda(X18) | room(X18)) & (? [X20] : (preda(X20) & ~predz(X20) & room(X20)) | ? [X19] : (predz(X19) & room(X19))) & (! [X22] : (((preda(X22) | ~predy(X22)) & (predy(X22) | ~preda(X22))) | ~room(X22)) | ? [X21] : (~predw(X21) & anywhere(X21))) & (? [X24] : (~predr(X24) & room(X24)) | ? [X23] : (predz(X23) & ~predt(X23) & room(X23))) & (? [X26] : (predz(X26) & room(X26)) | ! [X25] : (((predh(X25) | predl(X25)) & (~predh(X25) | ~predl(X25))) | room(X25))) & (? [X28] : ((predb(X28) | predl(X28)) & (~predb(X28) | ~predl(X28)) & room(X28)) | sP0) & (! [X32] : (~prede(X32) | predu(X32) | ~anywhere(X32)) | ? [X31] : (predu(X31) & predc(X31) & room(X31))) & (! [X34] : (~predu(X34) | ~predc(X34) | ~room(X34)) | ? [X33] : (predm(X33) & anywhere(X33))) & (! [X36] : (predq(X36) | ~predl(X36) | room(X36)) | ? [X35] : (predg(X35) & ~predq(X35) & room(X35))) & (! [X38] : (~predg(X38) | predq(X38) | ~room(X38)) | ? [X37] : (~predl(X37) | predl(X37) | ~room(X37))) [flattening 138]
140. ! [X0] : (predu(X0) | ~prede(X0) | room(X0)) & ? [X1] : (~prede(X1) & (predn(X1) | ~predm(X1)) & (~predn(X1) | predm(X1)) & room(X1)) & ! [X2] : (predq(X2) | predr(X2) | ~room(X2)) & ? [X3] : (preda(X3) & ~predz(X3) & room(X3)) & ! [X4] : (~predz(X4) | ~predt(X4) | predm(X4) | ~room(X4)) & ! [X5,X6] : (X5 = X6 | ~predn(X6) | ~predm(X6) | ~predn(X5) | ~predm(X5) | ~room(X6) | ~room(X5)) & ? [X7] : (predn(X7) & predm(X7) & room(X7)) & ! [X8] : (prede(X8) | predm(X8) | ~room(X8)) & ! [X9] : (~predm(X9) | preda(X9) | ~room(X9)) & ! [X10] : (~predg(X10) | ~predz(X10) | ~room(X10)) & ! [X11,X12] : (X11 = X12 | ~predy(X12) | ~predy(X11) | ~anywhere(X12) | ~anywhere(X11)) & ? [X13] : (predy(X13) & anywhere(X13)) & ! [X14] : ((~predc(X14) & predw(X14)) | ~room(X14)) & ! [X15] : (((~predb(X15) | ~predt(X15)) & (predb(X15) | predt(X15))) | preda(X15) | room(X15)) & (? [X16] : (preda(X16) & ~predz(X16) & room(X16)) | ? [X17] : (predz(X17) & room(X17))) & (! [X18] : (((preda(X18) | ~predy(X18)) & (predy(X18) | ~preda(X18))) | ~room(X18)) | ? [X19] : (~predw(X19) & anywhere(X19))) & (? [X20] : (~predr(X20) & room(X20)) | ? [X21] : (predz(X21) & ~predt(X21) & room(X21))) & (? [X22] : (predz(X22) & room(X22)) | ! [X23] : (((predh(X23) | predl(X23)) & (~predh(X23) | ~predl(X23))) | room(X23))) & (? [X24] : ((predb(X24) | predl(X24)) & (~predb(X24) | ~predl(X24)) & room(X24)) | sP0) & (! [X25] : (~prede(X25) | predu(X25) | ~anywhere(X25)) | ? [X26] : (predu(X26) & predc(X26) & room(X26))) & (! [X27] : (~predu(X27) | ~predc(X27) | ~room(X27)) | ? [X28] : (predm(X28) & anywhere(X28))) & (! [X29] : (predq(X29) | ~predl(X29) | room(X29)) | ? [X30] : (predg(X30) & ~predq(X30) & room(X30))) & (! [X31] : (~predg(X31) | predq(X31) | ~room(X31)) | ? [X32] : (~predl(X32) | predl(X32) | ~room(X32))) [rectify 139]
141. ? [X1] : (~prede(X1) & (predn(X1) | ~predm(X1)) & (~predn(X1) | predm(X1)) & room(X1)) => (~prede(sK2) & (predn(sK2) | ~predm(sK2)) & (~predn(sK2) | predm(sK2)) & room(sK2)) [choice axiom]
142. ? [X3] : (preda(X3) & ~predz(X3) & room(X3)) => (preda(sK3) & ~predz(sK3) & room(sK3)) [choice axiom]
143. ? [X7] : (predn(X7) & predm(X7) & room(X7)) => (predn(sK4) & predm(sK4) & room(sK4)) [choice axiom]
144. ? [X13] : (predy(X13) & anywhere(X13)) => (predy(sK5) & anywhere(sK5)) [choice axiom]
145. ? [X16] : (preda(X16) & ~predz(X16) & room(X16)) => (preda(sK6) & ~predz(sK6) & room(sK6)) [choice axiom]
146. ? [X17] : (predz(X17) & room(X17)) => (predz(sK7) & room(sK7)) [choice axiom]
147. ? [X19] : (~predw(X19) & anywhere(X19)) => (~predw(sK8) & anywhere(sK8)) [choice axiom]
148. ? [X20] : (~predr(X20) & room(X20)) => (~predr(sK9) & room(sK9)) [choice axiom]
149. ? [X21] : (predz(X21) & ~predt(X21) & room(X21)) => (predz(sK10) & ~predt(sK10) & room(sK10)) [choice axiom]
150. ? [X22] : (predz(X22) & room(X22)) => (predz(sK11) & room(sK11)) [choice axiom]
151. ? [X24] : ((predb(X24) | predl(X24)) & (~predb(X24) | ~predl(X24)) & room(X24)) => ((predb(sK12) | predl(sK12)) & (~predb(sK12) | ~predl(sK12)) & room(sK12)) [choice axiom]
152. ? [X26] : (predu(X26) & predc(X26) & room(X26)) => (predu(sK13) & predc(sK13) & room(sK13)) [choice axiom]
153. ? [X28] : (predm(X28) & anywhere(X28)) => (predm(sK14) & anywhere(sK14)) [choice axiom]
154. ? [X30] : (predg(X30) & ~predq(X30) & room(X30)) => (predg(sK15) & ~predq(sK15) & room(sK15)) [choice axiom]
155. ? [X32] : (~predl(X32) | predl(X32) | ~room(X32)) => (~predl(sK16) | predl(sK16) | ~room(sK16)) [choice axiom]
156. ! [X0] : (predu(X0) | ~prede(X0) | room(X0)) & (~prede(sK2) & (predn(sK2) | ~predm(sK2)) & (~predn(sK2) | predm(sK2)) & room(sK2)) & ! [X2] : (predq(X2) | predr(X2) | ~room(X2)) & (preda(sK3) & ~predz(sK3) & room(sK3)) & ! [X4] : (~predz(X4) | ~predt(X4) | predm(X4) | ~room(X4)) & ! [X5,X6] : (X5 = X6 | ~predn(X6) | ~predm(X6) | ~predn(X5) | ~predm(X5) | ~room(X6) | ~room(X5)) & (predn(sK4) & predm(sK4) & room(sK4)) & ! [X8] : (prede(X8) | predm(X8) | ~room(X8)) & ! [X9] : (~predm(X9) | preda(X9) | ~room(X9)) & ! [X10] : (~predg(X10) | ~predz(X10) | ~room(X10)) & ! [X11,X12] : (X11 = X12 | ~predy(X12) | ~predy(X11) | ~anywhere(X12) | ~anywhere(X11)) & (predy(sK5) & anywhere(sK5)) & ! [X14] : ((~predc(X14) & predw(X14)) | ~room(X14)) & ! [X15] : (((~predb(X15) | ~predt(X15)) & (predb(X15) | predt(X15))) | preda(X15) | room(X15)) & ((preda(sK6) & ~predz(sK6) & room(sK6)) | (predz(sK7) & room(sK7))) & (! [X18] : (((preda(X18) | ~predy(X18)) & (predy(X18) | ~preda(X18))) | ~room(X18)) | (~predw(sK8) & anywhere(sK8))) & ((~predr(sK9) & room(sK9)) | (predz(sK10) & ~predt(sK10) & room(sK10))) & ((predz(sK11) & room(sK11)) | ! [X23] : (((predh(X23) | predl(X23)) & (~predh(X23) | ~predl(X23))) | room(X23))) & (((predb(sK12) | predl(sK12)) & (~predb(sK12) | ~predl(sK12)) & room(sK12)) | sP0) & (! [X25] : (~prede(X25) | predu(X25) | ~anywhere(X25)) | (predu(sK13) & predc(sK13) & room(sK13))) & (! [X27] : (~predu(X27) | ~predc(X27) | ~room(X27)) | (predm(sK14) & anywhere(sK14))) & (! [X29] : (predq(X29) | ~predl(X29) | room(X29)) | (predg(sK15) & ~predq(sK15) & room(sK15))) & (! [X31] : (~predg(X31) | predq(X31) | ~room(X31)) | (~predl(sK16) | predl(sK16) | ~room(sK16))) [skolemisation 140,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141]
257. room(sK9) | room(sK10) [cnf transformation 156]
276. ~predc(X14) | ~room(X14) [cnf transformation 156]
297. predc(X0) | ~room(X0) [cnf transformation 129]
382. 18 <=> room(sK10) [avatar definition]
384. room(sK10) <- (18) [avatar component clause 382]
387. 19 <=> room(sK9) [avatar definition]
389. room(sK9) <- (19) [avatar component clause 387]
392. 18 | 19 [avatar split clause 257,387,382]
465. ~room(X0) [subsumption resolution 297,276]
471. $false <- (18) [subsumption resolution 384,465]
472. ~18 [avatar contradiction clause 471]
475. $false <- (19) [subsumption resolution 389,465]
476. ~19 [avatar contradiction clause 475]
479. $false [avatar sat refutation 392,472,476]
% SZS output end Proof for 6721980247881708955525176
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.041 s
% ------------------------------
% ------------------------------
| 0.127352 |
Claud, Marcelle, Victor are the only persons in the room.
If “everyone in the room does not collect classic novels or can play the flute” then “at least one person in the room does not enjoy mountain biking”.
If “everyone anywhere does not collect first edition books or participates in long-distance cycling events across the country” then “everyone outside the room cannot play the flute if they does not collect first edition books” otherwise “if someone enjoys salsa dancing then he/she uses a Windows laptop”.
If “Claud enjoys salsa dancing” then “everyone in the room practices urban gardening if they uses a Windows laptop and uses an ios phone”.
If “no one in the room collects classic novels or does not participate in long-distance cycling events across the country” then “everyone in the room does enjoy mountain biking or is not an enthusiastic bird watcher who travels for rare sightings”.
If someone enjoys coding in Python then he/she uses a Windows laptop.
Claud can play the flute.
Everyone in the room collects classic novels if they collects first edition books.
Claud does not participate in long-distance cycling events across the country.
Everyone in the room makes homemade pastries if and only if they does enjoy mountain biking.
Everyone in the room who does enjoy mountain biking practices digital art.
Everyone in the room who practices digital art drives a hybrid car.
If someone owns a 3D printer then he/she uses a Windows laptop, drives a hybrid car and enjoys coding in Python.
Claud either does enjoy mountain biking or drives a hybrid car but not both.
Everyone in the room who uses a Windows laptop uses a Windows laptop and drives a hybrid car.
Claud collects classic novels, can play the flute or does not enjoy virtual reality gaming.
Everyone in the room enjoys salsa dancing.
Everyone in the room does enjoy mountain biking if they does not own a 3D printer.
Everyone in the room who enjoys virtual reality gaming or practices digital art or both collects luxury watches.
If someone does enjoy mountain biking, enjoys virtual reality gaming or uses an ios phone then he/she does enjoy mountain biking and vice versa.
Claud practices graffiti art. | Claud enjoys coding in Python. | entailment | room(claud)&room(marcelle)&room(victor)&(![X]:(room(X)=>(X='claud'|X='marcelle'|X='victor')))&
((![X]:(room(X)=>(((can_play_the_flute(X))|(does_not_collect_classic_novels(X))))))=>(((?[X]:(room(X)&does_not_enjoy_mountain_biking(X))))))&
(((![X]:(anywhere(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))|(does_not_collect_first_edition_books(X))))))=>(![X]:(~room(X)=>(((does_not_collect_first_edition_books(X))=>(cannot_play_the_flute(X)))))))&((~(![X]:(anywhere(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))|(does_not_collect_first_edition_books(X)))))))=>((![X]:((enjoys_salsa_dancing(X))=>(uses_a_Windows_laptop(X)))))))&
((enjoys_salsa_dancing(claud))=>(![X]:(room(X)=>(((((uses_a_Windows_laptop(X))&(uses_an_ios_phone(X))))=>(practices_urban_gardening(X)))))))&
((~?[X]:(room(X)=>(((does_not_participate_in_long-distance_cycling_events_across_the_country(X))|(collects_classic_novels(X))))))=>(![X]:(room(X)=>(((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(does_enjoy_mountain_biking(X)))))))&
((![X]:((enjoys_coding_in_Python(X))=>(uses_a_Windows_laptop(X)))))&
(can_play_the_flute(claud))&
(![X]:(room(X)=>(((collects_first_edition_books(X))=>(collects_classic_novels(X))))))&
(does_not_participate_in_long-distance_cycling_events_across_the_country(claud))&
(![X]:(room(X)=>(((makes_homemade_pastries(X))<=>(does_enjoy_mountain_biking(X))))))&
(![X]:(room(X)=>(((does_enjoy_mountain_biking(X))=>(practices_digital_art(X))))))&
(![X]:(room(X)=>(((practices_digital_art(X))=>(drives_a_hybrid_car(X))))))&
((![X]:((owns_a_3D_printer(X))=>(((uses_a_Windows_laptop(X))&(drives_a_hybrid_car(X))&(enjoys_coding_in_Python(X)))))))&
(((does_enjoy_mountain_biking(claud))<~>(drives_a_hybrid_car(claud))))&
(![X]:(room(X)=>(((uses_a_Windows_laptop(X))=>(((uses_a_Windows_laptop(X))&(drives_a_hybrid_car(X))))))))&
(((collects_classic_novels(claud))|(can_play_the_flute(claud))|(does_not_enjoy_virtual_reality_gaming(claud))))&
(![X]:(room(X)=>(enjoys_salsa_dancing(X))))&
(![X]:(room(X)=>(((does_not_own_a_3D_printer(X))=>(does_enjoy_mountain_biking(X))))))&
(![X]:(room(X)=>(((((enjoys_virtual_reality_gaming(X))|(practices_digital_art(X))))=>(collects_luxury_watches(X))))))&
((![X]:((((does_enjoy_mountain_biking(X))|(enjoys_virtual_reality_gaming(X))|(uses_an_ios_phone(X))))<=>(does_enjoy_mountain_biking(X)))))&
(practices_graffiti_art(claud)) | room(claud)&room(marcelle)&room(victor)&(![X]:(room(X)=>(X='claud'|X='marcelle'|X='victor')))&
enjoys_coding_in_Python(claud) | [
"p0",
"p10",
"p11",
"p12",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5639558885481725553947758
% SZS output start Proof for 5639558885481725553947758
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
54. ! [X0] : (room(X0) => (predb(X0) => predq(X0))) [input p10]
55. ! [X0] : (room(X0) => (predq(X0) => prede(X0))) [input p11]
56. ! [X0] : (predk(X0) => (predn(X0) & prede(X0) & predg(X0))) [input p12]
57. predb(mary) <~> prede(mary) [input p13]
61. ! [X0] : (room(X0) => (~predk(X0) => predb(X0))) [input p17]
65. ~(predn(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis]
147. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
148. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 147]
154. ! [X0] : ((predq(X0) | ~predb(X0)) | ~room(X0)) [ennf transformation 54]
155. ! [X0] : (predq(X0) | ~predb(X0) | ~room(X0)) [flattening 154]
156. ! [X0] : ((prede(X0) | ~predq(X0)) | ~room(X0)) [ennf transformation 55]
157. ! [X0] : (prede(X0) | ~predq(X0) | ~room(X0)) [flattening 156]
158. ! [X0] : ((predn(X0) & prede(X0) & predg(X0)) | ~predk(X0)) [ennf transformation 56]
162. ! [X0] : ((predb(X0) | predk(X0)) | ~room(X0)) [ennf transformation 61]
163. ! [X0] : (predb(X0) | predk(X0) | ~room(X0)) [flattening 162]
164. ~predn(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 65]
165. ~predn(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 164]
175. (~prede(mary) | ~predb(mary)) & (prede(mary) | predb(mary)) [nnf transformation 57]
178. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) [choice axiom]
179. ~predn(mary) | (fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 165,178]
261. room(mary) [cnf transformation 148]
262. room(paul) [cnf transformation 148]
263. room(fred) [cnf transformation 148]
264. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 148]
278. ~predb(X0) | predq(X0) | ~room(X0) [cnf transformation 155]
279. ~predq(X0) | prede(X0) | ~room(X0) [cnf transformation 157]
282. ~predk(X0) | predn(X0) [cnf transformation 158]
284. ~prede(mary) | ~predb(mary) [cnf transformation 175]
288. ~room(X0) | predk(X0) | predb(X0) [cnf transformation 163]
293. ~predn(mary) | room(sK3) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 179]
294. ~predn(mary) | mary != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 179]
295. ~predn(mary) | paul != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 179]
296. ~predn(mary) | fred != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 179]
339. 10 <=> predb(mary) [avatar definition]
340. predb(mary) <- (10) [avatar component clause 339]
341. ~predb(mary) <- (~10) [avatar component clause 339]
343. 11 <=> prede(mary) [avatar definition]
345. ~prede(mary) <- (~11) [avatar component clause 343]
346. ~10 | ~11 [avatar split clause 284,343,339]
348. ~predn(mary) | fred != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 296,263]
349. ~predn(mary) | fred != sK3 | ~room(mary) [subsumption resolution 348,262]
350. ~predn(mary) | fred != sK3 [subsumption resolution 349,261]
352. 12 <=> fred = sK3 [avatar definition]
354. fred != sK3 <- (~12) [avatar component clause 352]
356. 13 <=> predn(mary) [avatar definition]
359. ~12 | ~13 [avatar split clause 350,356,352]
360. ~predn(mary) | paul != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 295,263]
361. ~predn(mary) | paul != sK3 | ~room(mary) [subsumption resolution 360,262]
362. ~predn(mary) | paul != sK3 [subsumption resolution 361,261]
364. 14 <=> paul = sK3 [avatar definition]
366. paul != sK3 <- (~14) [avatar component clause 364]
367. ~14 | ~13 [avatar split clause 362,356,364]
368. ~predn(mary) | mary != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 294,263]
369. ~predn(mary) | mary != sK3 | ~room(mary) [subsumption resolution 368,262]
370. ~predn(mary) | mary != sK3 [subsumption resolution 369,261]
372. 15 <=> mary = sK3 [avatar definition]
374. mary != sK3 <- (~15) [avatar component clause 372]
375. ~15 | ~13 [avatar split clause 370,356,372]
376. ~predn(mary) | room(sK3) | ~room(paul) | ~room(mary) [subsumption resolution 293,263]
377. ~predn(mary) | room(sK3) | ~room(mary) [subsumption resolution 376,262]
378. ~predn(mary) | room(sK3) [subsumption resolution 377,261]
380. 16 <=> room(sK3) [avatar definition]
382. room(sK3) <- (16) [avatar component clause 380]
383. 16 | ~13 [avatar split clause 378,356,380]
398. predq(mary) | ~room(mary) <- (10) [resolution 278,340]
399. predq(mary) <- (10) [subsumption resolution 398,261]
400. prede(mary) | ~room(mary) <- (10) [resolution 279,399]
401. ~room(mary) <- (10, ~11) [subsumption resolution 400,345]
402. $false <- (10, ~11) [subsumption resolution 401,261]
403. ~10 | 11 [avatar contradiction clause 402]
411. predk(mary) | predb(mary) [resolution 288,261]
415. predk(mary) <- (~10) [subsumption resolution 411,341]
446. predn(mary) <- (~10) [resolution 415,282]
451. 13 | 10 [avatar split clause 446,339,356]
531. paul = sK3 | mary = sK3 | fred = sK3 <- (16) [resolution 264,382]
545. mary = sK3 | fred = sK3 <- (~14, 16) [subsumption resolution 531,366]
546. fred = sK3 <- (~14, ~15, 16) [subsumption resolution 545,374]
547. $false <- (~12, ~14, ~15, 16) [subsumption resolution 546,354]
548. 12 | 14 | 15 | ~16 [avatar contradiction clause 547]
549. $false [avatar sat refutation 346,359,367,375,383,403,451,548]
% SZS output end Proof for 5639558885481725553947758
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.041 s
% ------------------------------
% ------------------------------
| 0.021768 |
There is a room.
Everyone in the room enjoys bird watching if and only if they either is dedicated to sustainable living and zero-waste practices or makes intricate hand-cut paper art for exhibitions but not both.
Everyone in the room who either is dedicated to sustainable living and zero-waste practices or makes intricate hand-cut paper art for exhibitions but not both enjoys logic puzzles.
Everyone outside the room enjoys logic puzzles or is not dedicated to sustainable living and zero-waste practices.
Everyone in the room plays as a goalkeeper for a local amateur soccer team or does not collect antique clocks.
Everyone in the room is a client of LVMH if they plays as a goalkeeper for a local amateur soccer team.
Everyone in the room who travels domestically frequently is dedicated to sustainable living and zero-waste practices and enjoys bird watching.
Everyone anywhere has a curated collection of mid-century modern furniture only if they enjoys logic puzzles.
Everyone in the room who either enjoys bird watching or travels domestically frequently but not both makes intricate hand-cut paper art for exhibitions, enjoys logic puzzles or is dedicated to sustainable living and zero-waste practices.
Everyone in the room neither has a curated collection of mid-century modern furniture nor makes intricate hand-cut paper art for exhibitions if and only if they makes intricate hand-cut paper art for exhibitions, enjoys bird watching or is dedicated to sustainable living and zero-waste practices.
Everyone in the room who makes intricate hand-cut paper art for exhibitions, enjoys bird watching or is dedicated to sustainable living and zero-waste practices is a client of LVMH.
Everyone anywhere who enjoys fishing enjoys logic puzzles.
Everyone in the room who enjoys logic puzzles collects antique clocks. | Everyone in the room does not collect antique clocks or enjoys fishing. | neutral | (there_is_a_room)&
(![X]:(room(X)=>(((enjoys_bird_watching(X))<=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))<~>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))))&
(![X]:(room(X)=>(((((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))<~>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))=>(enjoys_logic_puzzles(X))))))&
(![X]:(~room(X)=>(((is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(enjoys_logic_puzzles(X))))))&
(![X]:(room(X)=>(((does_not_collect_antique_clocks(X))|(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))))))&
(![X]:(room(X)=>(((plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))=>(is_a_client_of_LVMH(X))))))&
(![X]:(room(X)=>(((travels_domestically_frequently(X))=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))&(enjoys_bird_watching(X))))))))&
(![X]:(anywhere(X)=>(((enjoys_logic_puzzles(X))<=(has_a_curated_collection_of_mid-century_modern_furniture(X))))))&
(![X]:(room(X)=>(((((enjoys_bird_watching(X))<~>(travels_domestically_frequently(X))))=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))|(enjoys_logic_puzzles(X))|(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))))&
(![X]:(room(X)=>(((~((has_a_curated_collection_of_mid-century_modern_furniture(X))|(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))<=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))|(enjoys_bird_watching(X))|(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))))))&
(![X]:(room(X)=>(((((makes_intricate_hand-cut_paper_art_for_exhibitions(X))|(enjoys_bird_watching(X))|(is_dedicated_to_sustainable_living_and_zero-waste_practices(X))))=>(is_a_client_of_LVMH(X))))))&
(![X]:(anywhere(X)=>(((enjoys_fishing(X))=>(enjoys_logic_puzzles(X))))))&
(![X]:(room(X)=>(((enjoys_logic_puzzles(X))=>(collects_antique_clocks(X)))))) | (there_is_a_room)&
![X]:(room(X)=>(((enjoys_fishing(X))|(does_not_collect_antique_clocks(X))))) | [] | null | 0.001674 |
There is a room. Everyone in the room who is quieter than Ethel is older than Teresa, is not a tall quiet old person and is a kind person. No tall person is kind. Everyone anywhere is older than Ethel if they is kind. Only one person in the room either is a tall person or is not a old kind person but not both. Everyone in the room is not a kind person, is older than Irene and is a tall person if they is kind, is quiet and is a tall person. All quiet persons are kind. Everyone in the room who is quieter than Ethel neither is quieter than Nancy nor is not a old kind tall person. Everyone in the room who is a quiet person or is older than Teresa or both is not a kind tall person. No one in the room who is not a kind tall person neither is tall nor is not a quiet person. Everyone in the room is old if they is quieter than Tony. Everyone anywhere is richer than Ethel if they is old. Everyone in the room either is quieter than Nancy or is kind but not both if they is tall. No one in the room is quieter than Ethel if they either is quieter than Nancy or is kind but not both. Everyone outside the room is tall if they is quieter than Ethel. Everyone in the room is a quiet person if they is not a quiet person, is a old person and is a tall person. If someone is quieter than Ethel then he/she is not a kind person. Everyone in the room who is a quiet person is richer than Tony. Everyone in the room is not a old person if they is not a kind person. Everyone in the room who is old either is not a kind person or is a kind person but not both. Everyone anywhere who is older than Teresa is not a quiet person. Everyone in the room is not a old person if they is not a quiet person. Everyone in the room is not a tall kind quiet person if they is not a old person. | Everyone in the room is a old person or is quieter than Irene or both. | contradiction | (there_is_a_room)&
(![X]:(room(X)=>(((quieter(ethel,X))=>(((older(teresa,X))&(~(tall(X)&quiet(X)&old(X)&person(X)))&(kind(X)&person(X))))))))&
(~?[X]:(tall(X)=>kind(X)))&
(![X]:(anywhere(X)=>(((kind(X))=>(older(ethel,X))))))&
(((?[X]:(room(X)&((tall(X)&person(X))<~>(~(old(X)&kind(X)&person(X))))))&(![X,Y]:((room(X)&room(Y)&(((tall(X)&person(X))<~>(~(old(X)&kind(X)&person(X)))))&(((tall(Y)&person(Y))<~>(~(old(Y)&kind(Y)&person(Y))))))=>(X=Y)))))&
(![X]:(room(X)=>(((((kind(X))&(quiet(X))&(tall(X)&person(X))))=>(((~(kind(X)&person(X)))&(older(irene,X))&(tall(X)&person(X))))))))&
(![X]:(quiet(X)=>kind(X)))&
(![X]:(room(X)=>(((quieter(ethel,X))=>(~((quieter(nancy,X))|(~(old(X)&kind(X)&tall(X)&person(X)))))))))&
(![X]:(room(X)=>(((((quiet(X)&person(X))|(older(teresa,X))))=>(~(kind(X)&tall(X)&person(X)))))))&
(~?[X]:(room(X)=>(((~(kind(X)&tall(X)&person(X)))=>(~((tall(X))|(~(quiet(X)&person(X)))))))))&
(![X]:(room(X)=>(((quieter(tony,X))=>(old(X))))))&
(![X]:(anywhere(X)=>(((old(X))=>(richer(ethel,X))))))&
(![X]:(room(X)=>(((tall(X))=>(((quieter(nancy,X))<~>(kind(X))))))))&
(~?[X]:(room(X)=>(((((quieter(nancy,X))<~>(kind(X))))=>(quieter(ethel,X))))))&
(![X]:(~room(X)=>(((quieter(ethel,X))=>(tall(X))))))&
(![X]:(room(X)=>(((((~(quiet(X)&person(X)))&(old(X)&person(X))&(tall(X)&person(X))))=>(quiet(X)&person(X))))))&
((![X]:((quieter(ethel,X))=>(~(kind(X)&person(X))))))&
(![X]:(room(X)=>(((quiet(X)&person(X))=>(richer(tony,X))))))&
(![X]:(room(X)=>(((~(kind(X)&person(X)))=>(~(old(X)&person(X)))))))&
(![X]:(room(X)=>(((old(X))=>(((~(kind(X)&person(X)))<~>(kind(X)&person(X))))))))&
(![X]:(anywhere(X)=>(((older(teresa,X))=>(~(quiet(X)&person(X)))))))&
(![X]:(room(X)=>(((~(quiet(X)&person(X)))=>(~(old(X)&person(X)))))))&
(![X]:(room(X)=>(((~(old(X)&person(X)))=>(~(tall(X)&kind(X)&quiet(X)&person(X))))))) | (there_is_a_room)&
![X]:(room(X)=>(((old(X)&person(X))|(quieter(irene,X))))) | [
"b13",
"b42",
"p2",
"p6",
"p9",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5988873702348191364803531
% SZS output start Proof for 5988873702348191364803531
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]
46. ~? [X0] : (tall(X0) => kind(X0)) [input p2]
50. ! [X0] : (quiet(X0) => kind(X0)) [input p6]
53. ~? [X0] : (room(X0) => (~(person(X0) & tall(X0) & kind(X0)) => ~(~(person(X0) & quiet(X0)) | tall(X0)))) [input p9]
56. ! [X0] : (room(X0) => (tall(X0) => (quieter(fred,X0) <~> kind(X0)))) [input p12]
59. ! [X0] : (room(X0) => ((person(X0) & tall(X0) & person(X0) & old(X0) & ~(person(X0) & quiet(X0))) => (person(X0) & quiet(X0)))) [input p15]
67. ! [X0] : (room(X0) => (quieter(mary,X0) | (person(X0) & old(X0)))) & there_is_a_room [input hypothesis]
70. ! [X0] : (room(X0) => (quieter(mary,X0) | (person(X0) & old(X0)))) [pure predicate removal 67]
89. ! [X0,X1] : ((~quieter(X1,X0) | ~quieter(X0,X1)) | X0 = X1) [ennf transformation 14]
90. ! [X0,X1] : (~quieter(X1,X0) | ~quieter(X0,X1) | X0 = X1) [flattening 89]
144. ! [X0] : (~kind(X0) & tall(X0)) [ennf transformation 46]
151. ! [X0] : (kind(X0) | ~quiet(X0)) [ennf transformation 50]
156. ! [X0] : ((((~person(X0) | ~quiet(X0)) | tall(X0)) & (~person(X0) | ~tall(X0) | ~kind(X0))) & room(X0)) [ennf transformation 53]
157. ! [X0] : ((~person(X0) | ~quiet(X0) | tall(X0)) & (~person(X0) | ~tall(X0) | ~kind(X0)) & room(X0)) [flattening 156]
162. ! [X0] : (((quieter(fred,X0) <~> kind(X0)) | ~tall(X0)) | ~room(X0)) [ennf transformation 56]
163. ! [X0] : ((quieter(fred,X0) <~> kind(X0)) | ~tall(X0) | ~room(X0)) [flattening 162]
168. ! [X0] : (((person(X0) & quiet(X0)) | (~person(X0) | ~tall(X0) | ~person(X0) | ~old(X0) | (person(X0) & quiet(X0)))) | ~room(X0)) [ennf transformation 59]
169. ! [X0] : ((person(X0) & quiet(X0)) | ~person(X0) | ~tall(X0) | ~person(X0) | ~old(X0) | (person(X0) & quiet(X0)) | ~room(X0)) [flattening 168]
184. ! [X0] : ((quieter(mary,X0) | (person(X0) & old(X0))) | ~room(X0)) [ennf transformation 70]
185. ! [X0] : (quieter(mary,X0) | (person(X0) & old(X0)) | ~room(X0)) [flattening 184]
195. ! [X0] : (((~kind(X0) | ~quieter(fred,X0)) & (kind(X0) | quieter(fred,X0))) | ~tall(X0) | ~room(X0)) [nnf transformation 163]
210. ~quieter(X1,X0) | ~quieter(X0,X1) | X0 = X1 [cnf transformation 90]
251. mary != fred [cnf transformation 43]
285. tall(X0) [cnf transformation 144]
286. ~kind(X0) [cnf transformation 144]
312. kind(X0) | ~quiet(X0) [cnf transformation 151]
320. room(X0) [cnf transformation 157]
325. kind(X0) | quieter(fred,X0) | ~tall(X0) | ~room(X0) [cnf transformation 195]
332. quiet(X0) | ~person(X0) | ~tall(X0) | ~person(X0) | ~old(X0) | quiet(X0) | ~room(X0) [cnf transformation 169]
349. quieter(mary,X0) | old(X0) | ~room(X0) [cnf transformation 185]
350. quieter(mary,X0) | person(X0) | ~room(X0) [cnf transformation 185]
351. quiet(X0) | ~person(X0) | ~tall(X0) | ~old(X0) | ~room(X0) [duplicate literal removal 332]
364. ~quiet(X0) [subsumption resolution 312,286]
367. quieter(fred,X0) | ~tall(X0) | ~room(X0) [subsumption resolution 325,286]
368. quieter(fred,X0) | ~room(X0) [subsumption resolution 367,285]
369. quieter(fred,X0) [subsumption resolution 368,320]
370. ~person(X0) | ~tall(X0) | ~old(X0) | ~room(X0) [subsumption resolution 351,364]
371. ~person(X0) | ~old(X0) | ~room(X0) [subsumption resolution 370,285]
372. ~old(X0) | ~person(X0) [subsumption resolution 371,320]
373. quieter(mary,X0) | person(X0) [subsumption resolution 350,320]
374. quieter(mary,X0) | old(X0) [subsumption resolution 349,320]
379. ~quieter(X0,fred) | fred = X0 [resolution 210,369]
383. mary = fred | old(fred) [resolution 379,374]
384. mary = fred | person(fred) [resolution 379,373]
385. old(fred) [subsumption resolution 383,251]
386. person(fred) [subsumption resolution 384,251]
390. ~person(fred) [resolution 385,372]
391. $false [subsumption resolution 390,386]
% SZS output end Proof for 5988873702348191364803531
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.204901 |
Roy, David are the only persons in the room.
If 'at least one person in the room is older than Lydia' then 'if someone is a old person or is a generous old person or both then he/she is a old person'.
David is older than Lydia.
Someone in the room is a generous person.
David is the oldest anywhere.
Roy is older than Lydia and is older than Goldie. | Rea is older than Roy. | neutral | room(roy)&room(david)&(![X]:(room(X)=>(X='roy'|X='david')))&
((((?[X]:(room(X)&older(lydia,X)))))=>((![X]:((((old(X)&person(X))|(generous(X)&old(X)&person(X))))=>(old(X)&person(X))))))&
(older(lydia,david))&
(?[X]:(room(X)&(generous(X)&person(X))))&
(![X]:((anywhere(X)&(X!=david))=>older(X,david)))&
(((older(lydia,roy))&(older(goldie,roy))))&
(~(~(generous(david)&person(david))))&
(![X]:((~room(X)&(X!=david))=>older(X,david)))&
(~(generous(roy)&person(roy)))&
(?[X,Y]:((old(X)&generous(X)&person(X))&(older(rea,Y))&(older(X,Y))))&
(?[X]:(room(X)&(older(rea,X))))&
(older(rea,david))&
(older(goldie,david))&
((![X]:((((old(X)&person(X))&(~old(X))))=>(((old(X)&generous(X)&person(X))&(generous(X)&person(X)))))))&
(?[X]:(room(X)&(((old(X)&generous(X)&person(X))|(~(old(X)&person(X)))|(generous(X)&person(X))))))&
(~(old(roy)&generous(roy)&person(roy)))&
(?[X,Y]:((~old(X))&(~(old(Y)&person(Y)))&(older(X,Y)))) | room(roy)&room(david)&(![X]:(room(X)=>(X='roy'|X='david')))&
older(roy,rea) | [] | null | 0.372508 |
Marylynn, Elizabeth, Gloria, Lillian are the only persons in the room.
“It is not the case that “Gloria is an avid mountain climber who has scaled several peaks”” only if “Gloria enjoys windsurfing or collects action figures or both”.
“Everyone in the room does not enjoy stargazing or can play the harmonica” only if “Lillian builds model airplanes”.
“Everyone in the room does not compose and performs experimental electronic music or practices calligraphy” if “Lillian owns an Android phone” and vice versa.
Either “not everyone in the room does not practice calligraphy or practices calligraphy” or “Gloria owns a smart tv” but not both.
Either “Gloria enjoys making ceramics, is right-handed or collects luxury watches” or “everyone in the room is a certified yoga instructor teaching classes weekly or is not right-handed” but not both.
Everyone in the room who is a certified yoga instructor teaching classes weekly enjoys kayaking.
Everyone in the room who collects luxury watches is a Linux enthusiast.
Marylynn practices calligraphy.
Everyone in the room volunteers for local environmental conservation projects if and only if they is right-handed.
Everyone in the room who does practice yoga has completed a triathlon.
Someone in the room hosts regular workshops on creative writing.
Someone in the room is a certified yoga instructor teaching classes weekly.
Elizabeth hosts regular workshops on creative writing, enjoys kayaking or composes and performs experimental electronic music.
Everyone in the room who enjoys stargazing can play the harmonica.
Lillian practices calligraphy.
Everyone in the room who can play the harmonica, is an enthusiastic bird watcher who travels for rare sightings or is an avid mountain climber who has scaled several peaks practices calligraphy or is a certified yoga instructor teaching classes weekly or both.
Gloria volunteers for local environmental conservation projects.
Gloria owns a smart tv.
Marylynn is an avid mountain climber who has scaled several peaks and is a certified yoga instructor teaching classes weekly.
Everyone in the room does practice yoga or cannot play the harmonica.
Elizabeth practices calligraphy.
Someone in the room enjoys stargazing.
Marylynn is a certified yoga instructor teaching classes weekly, has completed a triathlon or enjoys stargazing.
Someone in the room practices calligraphy. | Marylynn enjoys kayaking. | entailment | room(marylynnlynn)&room(elizabeth)&room(gloria)&room(lillian)&(![X]:(room(X)=>(X='marylynnlynn'|X='elizabeth'|X='gloria'|X='lillian')))&
((~(is_an_avid_mountain_climber_who_has_scaled_several_peaks(gloria)))=>(((enjoys_windsurfing(gloria))|(collects_action_figures(gloria)))))&
((![X]:(room(X)=>(((can_play_the_harmonica(X))|(does_not_enjoy_stargazing(X))))))=>(builds_model_airplanes(lillian)))&
((owns_an_Android_phone(lillian))<=>(![X]:(room(X)=>(((practices_calligraphy(X))|(does_not_compose_and_performs_experimental_electronic_music(X)))))))&
((~![X]:(room(X)=>(((practices_calligraphy(X))|(does_not_practice_calligraphy(X))))))<~>(owns_a_smart_tv(gloria)))&
((((enjoys_making_ceramics(gloria))|(is_right-handed(gloria))|(collects_luxury_watches(gloria))))<~>(![X]:(room(X)=>(((is_not_right-handed(X))|(is_a_certified_yoga_instructor_teaching_classes_weekly(X)))))))&
(![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(enjoys_kayaking(X))))))&
(![X]:(room(X)=>(((collects_luxury_watches(X))=>(is_a_Linux_enthusiast(X))))))&
(practices_calligraphy(marylynnlynn))&
(![X]:(room(X)=>(((volunteers_for_local_environmental_conservation_projects(X))<=>(is_right-handed(X))))))&
(![X]:(room(X)=>(((does_practice_yoga(X))=>(has_completed_a_triathlon(X))))))&
(?[X]:(room(X)&(hosts_regular_workshops_on_creative_writing(X))))&
(?[X]:(room(X)&(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))&
(((hosts_regular_workshops_on_creative_writing(elizabeth))|(enjoys_kayaking(elizabeth))|(composes_and_performs_experimental_electronic_music(elizabeth))))&
(![X]:(room(X)=>(((enjoys_stargazing(X))=>(can_play_the_harmonica(X))))))&
(practices_calligraphy(lillian))&
(![X]:(room(X)=>(((((can_play_the_harmonica(X))|(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))=>(((practices_calligraphy(X))|(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))))&
(volunteers_for_local_environmental_conservation_projects(gloria))&
(owns_a_smart_tv(gloria))&
(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(marylynnlynn))&(is_a_certified_yoga_instructor_teaching_classes_weekly(marylynnlynn))))&
(![X]:(room(X)=>(((cannot_play_the_harmonica(X))|(does_practice_yoga(X))))))&
(practices_calligraphy(elizabeth))&
(?[X]:(room(X)&(enjoys_stargazing(X))))&
(((is_a_certified_yoga_instructor_teaching_classes_weekly(marylynnlynn))|(has_completed_a_triathlon(marylynnlynn))|(enjoys_stargazing(marylynnlynn))))&
(?[X]:(room(X)&(practices_calligraphy(X))))&
(is_not_right-handed(elizabeth))&
(((is_a_certified_yoga_instructor_teaching_classes_weekly(gloria))&(makes_homemade_pastries(gloria))&(owns_a_smart_tv(gloria))))&
(volunteers_for_local_environmental_conservation_projects(marylynnlynn)) | room(marylynnlynn)&room(elizabeth)&room(gloria)&room(lillian)&(![X]:(room(X)=>(X='marylynnlynn'|X='elizabeth'|X='gloria'|X='lillian')))&
enjoys_kayaking(marylynnlynn) | [
"p0",
"p6",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3474845517899292611820872
% SZS output start Proof for 3474845517899292611820872
44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
50. ! [X0] : (room(X0) => (predh(X0) => predg(X0))) [input p6]
63. predh(mary) & predk(mary) [input p19]
72. ~(predg(mary) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis]
155. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
156. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 155]
163. ! [X0] : ((predg(X0) | ~predh(X0)) | ~room(X0)) [ennf transformation 50]
164. ! [X0] : (predg(X0) | ~predh(X0) | ~room(X0)) [flattening 163]
170. ~predg(mary) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 72]
171. ~predg(mary) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 170]
195. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK7 & fred != sK7 & paul != sK7 & mary != sK7 & room(sK7)) [choice axiom]
196. ~predg(mary) | (alice != sK7 & fred != sK7 & paul != sK7 & mary != sK7 & room(sK7)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 171,195]
277. room(mary) [cnf transformation 156]
278. room(paul) [cnf transformation 156]
279. room(fred) [cnf transformation 156]
280. room(alice) [cnf transformation 156]
281. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 156]
300. ~predh(X0) | predg(X0) | ~room(X0) [cnf transformation 164]
314. predh(mary) [cnf transformation 63]
324. ~predg(mary) | room(sK7) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 196]
325. ~predg(mary) | mary != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 196]
326. ~predg(mary) | paul != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 196]
327. ~predg(mary) | fred != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 196]
328. ~predg(mary) | alice != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 196]
406. ~predg(mary) | alice != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 328,280]
407. ~predg(mary) | alice != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 406,279]
408. ~predg(mary) | alice != sK7 | ~room(mary) [subsumption resolution 407,278]
409. ~predg(mary) | alice != sK7 [subsumption resolution 408,277]
411. 16 <=> alice = sK7 [avatar definition]
413. alice != sK7 <- (~16) [avatar component clause 411]
415. 17 <=> predg(mary) [avatar definition]
418. ~16 | ~17 [avatar split clause 409,415,411]
419. ~predg(mary) | fred != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 327,280]
420. ~predg(mary) | fred != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 419,279]
421. ~predg(mary) | fred != sK7 | ~room(mary) [subsumption resolution 420,278]
422. ~predg(mary) | fred != sK7 [subsumption resolution 421,277]
424. 18 <=> fred = sK7 [avatar definition]
426. fred != sK7 <- (~18) [avatar component clause 424]
427. ~18 | ~17 [avatar split clause 422,415,424]
428. ~predg(mary) | paul != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 326,280]
429. ~predg(mary) | paul != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 428,279]
430. ~predg(mary) | paul != sK7 | ~room(mary) [subsumption resolution 429,278]
431. ~predg(mary) | paul != sK7 [subsumption resolution 430,277]
433. 19 <=> paul = sK7 [avatar definition]
435. paul != sK7 <- (~19) [avatar component clause 433]
436. ~19 | ~17 [avatar split clause 431,415,433]
437. ~predg(mary) | mary != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 325,280]
438. ~predg(mary) | mary != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 437,279]
439. ~predg(mary) | mary != sK7 | ~room(mary) [subsumption resolution 438,278]
440. ~predg(mary) | mary != sK7 [subsumption resolution 439,277]
442. 20 <=> mary = sK7 [avatar definition]
444. mary != sK7 <- (~20) [avatar component clause 442]
445. ~20 | ~17 [avatar split clause 440,415,442]
446. ~predg(mary) | room(sK7) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 324,280]
447. ~predg(mary) | room(sK7) | ~room(paul) | ~room(mary) [subsumption resolution 446,279]
448. ~predg(mary) | room(sK7) | ~room(mary) [subsumption resolution 447,278]
449. ~predg(mary) | room(sK7) [subsumption resolution 448,277]
451. 21 <=> room(sK7) [avatar definition]
453. room(sK7) <- (21) [avatar component clause 451]
454. 21 | ~17 [avatar split clause 449,415,451]
456. predg(mary) | ~room(mary) [resolution 300,314]
463. predg(mary) [subsumption resolution 456,277]
464. 17 [avatar split clause 463,415]
539. fred = sK7 | paul = sK7 | mary = sK7 | alice = sK7 <- (21) [resolution 281,453]
625. paul = sK7 | mary = sK7 | alice = sK7 <- (~18, 21) [subsumption resolution 539,426]
626. mary = sK7 | alice = sK7 <- (~18, ~19, 21) [subsumption resolution 625,435]
627. alice = sK7 <- (~18, ~19, ~20, 21) [subsumption resolution 626,444]
628. $false <- (~16, ~18, ~19, ~20, 21) [subsumption resolution 627,413]
629. 16 | 18 | 19 | 20 | ~21 [avatar contradiction clause 628]
630. $false [avatar sat refutation 418,427,436,445,454,464,629]
% SZS output end Proof for 3474845517899292611820872
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0.007196 |
Brandon is the only person in the room. If everyone in the room is a sibling of Caroline or does not collect action figures then Brandon is a sibling of Caroline. If someone in the room is a sibling of Margaret then Brandon who is a sibling of Margaret collects action figures. If Margaret is a sibling of Brandon then everyone in the room who is a sibling of Caroline collects action figures. If everyone anywhere is a sibling of Margaret or does not frequently participates in hackathons and coding competitions then someone anywhere collects action figures. If everyone in the room is a sibling of Caroline or does not collect action figures then Brandon is a sibling of Margaret. If at least one person in the room is a sibling of Caroline then Margaret is a sibling of Brandon. If everyone outside the room is a sibling of Caroline or does not frequently participates in hackathons and coding competitions then someone in the room is a sibling of Margaret. Caroline is a sibling of Brandon. Everyone in the room who either is a sibling of Caroline or is a sibling of Margaret but not both frequently participates in hackathons and coding competitions. Everyone in the room who frequently participates in hackathons and coding competitions is a sibling of Margaret. Someone who frequently participates in hackathons and coding competitions hate someone who collects action figures. Someone in the room is a sibling of Margaret. Margaret is a sibling of Brandon. Brandon who collects action figures frequently participates in hackathons and coding competitions. At least one person in the room is a sibling of Caroline. | Brandon is a sibling of Caroline. | entailment | room(brandon)&(![X]:(room(X)=>(X='brandon')))&
((![X]:(room(X)=>(((does_not_collect_action_figures(X))|(sibling(caroline,X))))))=>(sibling(caroline,brandon)))&
((?[X]:(room(X)&(sibling(margaret,X))))=>((sibling(margaret,brandon))&(collects_action_figures(brandon))))&
((sibling(brandon,margaret))=>(![X]:(room(X)=>(((sibling(caroline,X))=>(collects_action_figures(X)))))))&
((![X]:(anywhere(X)=>(((does_not_frequently_participates_in_hackathons_and_coding_competitions(X))|(sibling(margaret,X))))))=>(?[X]:(anywhere(X)&(collects_action_figures(X)))))&
((![X]:(room(X)=>(((does_not_collect_action_figures(X))|(sibling(caroline,X))))))=>(sibling(margaret,brandon)))&
((((?[X]:(room(X)&sibling(caroline,X)))))=>(sibling(brandon,margaret)))&
((![X]:(~room(X)=>(((does_not_frequently_participates_in_hackathons_and_coding_competitions(X))|(sibling(caroline,X))))))=>(?[X]:(room(X)&(sibling(margaret,X)))))&
(sibling(brandon,caroline))&
(![X]:(room(X)=>(((((sibling(caroline,X))<~>(sibling(margaret,X))))=>(frequently_participates_in_hackathons_and_coding_competitions(X))))))&
(![X]:(room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))=>(sibling(margaret,X))))))&
(?[X,Y]:((frequently_participates_in_hackathons_and_coding_competitions(X))&(collects_action_figures(Y))&(hate(X,Y))))&
(?[X]:(room(X)&(sibling(margaret,X))))&
(sibling(brandon,margaret))&
((collects_action_figures(brandon))&(frequently_participates_in_hackathons_and_coding_competitions(brandon)))&
(frequently_participates_in_hackathons_and_coding_competitions(brandon))&
(((?[X]:(room(X)&sibling(caroline,X)))))&
(![X]:(room(X)=>(((((frequently_participates_in_hackathons_and_coding_competitions(X))|(collects_action_figures(X))))=>(frequently_participates_in_hackathons_and_coding_competitions(X)))))) | room(brandon)&(![X]:(room(X)=>(X='brandon')))&
sibling(caroline,brandon) | [
"p0",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5356551851761150036884364
% SZS output start Proof for 5356551851761150036884364
44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
60. ? [X0] : (sibling(paul,X0) & room(X0)) [input p16]
62. ~(sibling(paul,mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis]
139. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
157. ~sibling(paul,mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 62]
176. ? [X0] : (sibling(paul,X0) & room(X0)) => (sibling(paul,sK9) & room(sK9)) [choice axiom]
177. sibling(paul,sK9) & room(sK9) [skolemisation 60,176]
178. ? [X0] : (mary != X0 & room(X0)) => (mary != sK10 & room(sK10)) [choice axiom]
179. ~sibling(paul,mary) | (mary != sK10 & room(sK10)) | ~room(mary) [skolemisation 157,178]
260. room(mary) [cnf transformation 139]
261. ~room(X0) | mary = X0 [cnf transformation 139]
292. room(sK9) [cnf transformation 177]
293. sibling(paul,sK9) [cnf transformation 177]
296. ~sibling(paul,mary) | room(sK10) | ~room(mary) [cnf transformation 179]
297. ~sibling(paul,mary) | mary != sK10 | ~room(mary) [cnf transformation 179]
303. 2 <=> sibling(paul,mary) [avatar definition]
399. ~sibling(paul,mary) | mary != sK10 [subsumption resolution 297,260]
401. 22 <=> mary = sK10 [avatar definition]
403. mary != sK10 <- (~22) [avatar component clause 401]
404. ~22 | ~2 [avatar split clause 399,303,401]
405. ~sibling(paul,mary) | room(sK10) [subsumption resolution 296,260]
407. 23 <=> room(sK10) [avatar definition]
409. room(sK10) <- (23) [avatar component clause 407]
410. 23 | ~2 [avatar split clause 405,303,407]
414. mary = sK9 [resolution 261,292]
421. sibling(paul,mary) [backward demodulation 293,414]
424. 2 [avatar split clause 421,303]
426. mary = sK10 <- (23) [resolution 409,261]
427. $false <- (~22, 23) [subsumption resolution 426,403]
428. 22 | ~23 [avatar contradiction clause 427]
429. $false [avatar sat refutation 404,410,424,428]
% SZS output end Proof for 5356551851761150036884364
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.136832 |
Robert, Iris, Christina are the only persons in the room. If “Robert is a tall old quiet person” then “Iris is a patient wise person”. Everyone in the room is humble if and only if they is a brave person. Iris is humble. Iris is funny. All old persons are patient. Iris is a patient wise person. Someone anywhere is a funny brave person, is a creative person and is a happy person. Robert is the oldest in the room. | Everyone anywhere is a quiet person. | neutral | room(robert)&room(iris)&room(christina)&(![X]:(room(X)=>(X='robert'|X='iris'|X='christina')))&
((tall(robert)&old(robert)&quiet(robert)&person(robert))=>(patient(iris)&wise(iris)&person(iris)))&
(![X]:(room(X)=>(((humble(X))<=>(brave(X)&person(X))))))&
(humble(iris))&
(funny(iris))&
(![X]:(old(X)=>patient(X)))&
(patient(iris)&wise(iris)&person(iris))&
(?[X]:(anywhere(X)&(((funny(X)&brave(X)&person(X))&(creative(X)&person(X))&(happy(X)&person(X))))))&
(![X]:((room(X)&(X!=robert))=>older(X,robert)))&
(?[X]:(room(X)&(happy(X))))&
(~(generous(robert)&old(robert)&wise(robert)&person(robert)))&
(![X]:(room(X)=>(((~(tall(X)&curious(X)&happy(X)&old(X)&person(X)))<=>(calm(X)&person(X))))))&
(![X]:(room(X)=>(((calm(X)&person(X))=>(~(tall(X)&person(X)))))))&
((![X]:((calm(X)&patient(X)&tall(X)&curious(X)&kind(X)&humble(X)&person(X))=>(((~(calm(X)&person(X)))|(humble(X)&curious(X)&person(X)))))))&
(![X]:(old(X)=>funny(X)))&
(~(tall(robert)&curious(robert)&happy(robert)&old(robert)&person(robert)))&
(~(generous(iris)&person(iris)))&
(happy(robert)&happy(iris)) | room(robert)&room(iris)&room(christina)&(![X]:(room(X)=>(X='robert'|X='iris'|X='christina')))&
![X]:(anywhere(X)=>(quiet(X)&person(X))) | [] | null | 0 |
There is a room.
It is not the case that 'at least one person in the room plays video games'.
At least one person anywhere collects historical artifacts related to ancient civilizations.
Someone outside the room writes and illustrates their own graphic novels.
More than one person anywhere writes and illustrates their own graphic novels.
More than one person in the room has lived in exactly three countries.
At least one person anywhere plays video games. | Everyone in the room collects historical artifacts related to ancient civilizations. | neutral | (there_is_a_room)&
(~(((?[X]:(room(X)&plays_video_games(X))))))&
(((?[X]:(anywhere(X)&collects_historical_artifacts_related_to_ancient_civilizations(X)))))&
(?[X]:(~room(X)&(writes_and_illustrates_their_own_graphic_novels(X))))&
((?[X,Y]:(anywhere(X)&anywhere(Y)&(writes_and_illustrates_their_own_graphic_novels(X)&writes_and_illustrates_their_own_graphic_novels(Y))&(X!=Y))))&
((?[X,Y]:(room(X)&room(Y)&(has_lived_in_exactly_three_countries(X)&has_lived_in_exactly_three_countries(Y))&(X!=Y))))&
(((?[X]:(anywhere(X)&plays_video_games(X))))) | (there_is_a_room)&
![X]:(room(X)=>(collects_historical_artifacts_related_to_ancient_civilizations(X))) | [] | null | 0.209465 |
Juan, Amber are the only persons in the room.
If “everyone in the room is not a culinary enthusiast who experiments with international cuisines or collects rare and antique scientific instruments” then “everyone in the room has a specialized collection of handmade artisan pottery if they is not a culinary enthusiast who experiments with international cuisines”.
Either “everyone in the room has a specialized collection of handmade artisan pottery” or “everyone in the room does not have a specialized collection of handmade artisan pottery or is a culinary enthusiast who experiments with international cuisines” but not both.
Either “everyone in the room has lived in exactly three countries or does not write and illustrates their own graphic novels” or “everyone anywhere does not enjoy mountain biking or is not a Linux enthusiast” but not both.
Either “Juan is a Linux enthusiast” or “Amber enjoys landscape photography” but not both.
Juan has a specialized collection of handmade artisan pottery.
Amber enjoys landscape photography.
Juan is a culinary enthusiast who experiments with international cuisines.
Everyone in the room has lived in exactly three countries.
Amber does enjoy mountain biking.
Amber collects rare and antique scientific instruments. | Only one person in the room enjoys landscape photography. | neutral | room(juan)&room(amber)&(![X]:(room(X)=>(X='juan'|X='amber')))&
((![X]:(room(X)=>(((collects_rare_and_antique_scientific_instruments(X))|(is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))))))=>(![X]:(room(X)=>(((is_not_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))=>(has_a_specialized_collection_of_handmade_artisan_pottery(X)))))))&
((![X]:(room(X)=>(has_a_specialized_collection_of_handmade_artisan_pottery(X))))<~>(![X]:(room(X)=>(((is_a_culinary_enthusiast_who_experiments_with_international_cuisines(X))|(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X)))))))&
((![X]:(room(X)=>(((does_not_write_and_illustrates_their_own_graphic_novels(X))|(has_lived_in_exactly_three_countries(X))))))<~>(![X]:(anywhere(X)=>(((is_not_a_Linux_enthusiast(X))|(does_not_enjoy_mountain_biking(X)))))))&
((is_a_Linux_enthusiast(juan))<~>(enjoys_landscape_photography(amber)))&
(has_a_specialized_collection_of_handmade_artisan_pottery(juan))&
(enjoys_landscape_photography(amber))&
(is_a_culinary_enthusiast_who_experiments_with_international_cuisines(juan))&
(![X]:(room(X)=>(has_lived_in_exactly_three_countries(X))))&
(does_enjoy_mountain_biking(amber))&
(collects_rare_and_antique_scientific_instruments(amber)) | room(juan)&room(amber)&(![X]:(room(X)=>(X='juan'|X='amber')))&
((?[X]:(room(X)&enjoys_landscape_photography(X)))&(![X,Y]:((room(X)&room(Y)&(enjoys_landscape_photography(X))&(enjoys_landscape_photography(Y)))=>(X=Y)))) | [] | null | 0 |
Joseph is the only person in the room.
“Everyone outside the room does not practice zumba” if “everyone outside the room does not own a telescope or is a certified yoga instructor teaching classes weekly”.
“Everyone anywhere who makes intricate hand-cut paper art for exhibitions neither collects action figures nor hosts regular workshops on creative writing” unless “everyone in the room practices zumba or does not have a piercing”.
If “everyone anywhere is an expert in identifying and foraging wild edible plants or does not use an ios phone” then “everyone in the room practices zumba”.
No one anywhere is an expert in identifying and foraging wild edible plants only if they practices pilates.
Everyone in the room regularly contributes to tech forums and online communities only if they is a member of a local theater group specializing in improv.
Everyone outside the room has a piercing if they neither hosts regular game nights featuring complex strategy games nor hosts regular workshops on creative writing. | Joseph practices zumba. | entailment | room(joseph)&(![X]:(room(X)=>(X='joseph')))&
((![X]:(~room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))|(does_not_own_a_telescope(X))))))=>(![X]:(~room(X)=>(does_not_practice_zumba(X)))))&
(~(![X]:(room(X)=>(((does_not_have_a_piercing(X))|(practices_zumba(X))))))=>(![X]:(anywhere(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))=>(~((collects_action_figures(X))|(hosts_regular_workshops_on_creative_writing(X)))))))))&
((![X]:(anywhere(X)=>(((does_not_use_an_ios_phone(X))|(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))=>(![X]:(room(X)=>(practices_zumba(X)))))&
(~?[X]:(anywhere(X)=>(((practices_pilates(X))<=(is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))))))&
(![X]:(room(X)=>(((is_a_member_of_a_local_theater_group_specializing_in_improv(X))<=(regularly_contributes_to_tech_forums_and_online_communities(X))))))&
(![X]:(~room(X)=>(((~((hosts_regular_game_nights_featuring_complex_strategy_games(X))|(hosts_regular_workshops_on_creative_writing(X))))=>(has_a_piercing(X))))))&
((![X]:((((enjoys_making_ceramics(X))|(collects_action_figures(X))|(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))<=>(does_not_enjoy_windsurfing(X)))))&
(![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(regularly_contributes_to_tech_forums_and_online_communities(X))))))&
(![X]:(~room(X)=>(((regularly_contributes_to_tech_forums_and_online_communities(X))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X)))))) | room(joseph)&(![X]:(room(X)=>(X='joseph')))&
practices_zumba(joseph) | [
"p0",
"p3",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 20410044457004300500318
% SZS output start Proof for 20410044457004300500318
44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
47. ! [X0] : (anywhere(X0) => (predu(X0) | ~predw(X0))) => ! [X0] : (room(X0) => predl(X0)) [input p3]
48. ~? [X0] : (anywhere(X0) => (predu(X0) => predh(X0))) [input p4]
54. ~(predl(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis]
57. ! [X0] : (anywhere(X0) => (predu(X0) | ~predw(X0))) => ! [X1] : (room(X1) => predl(X1)) [rectify 47]
61. ~? [X0] : (predu(X0) => predh(X0)) [pure predicate removal 48]
62. ! [X0] : (predu(X0) | ~predw(X0)) => ! [X1] : (room(X1) => predl(X1)) [pure predicate removal 57]
65. ~? [X0] : ~predu(X0) [pure predicate removal 61]
66. ! [X0] : predu(X0) => ! [X1] : (room(X1) => predl(X1)) [pure predicate removal 62]
139. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
141. ! [X1] : (predl(X1) | ~room(X1)) | ? [X0] : ~predu(X0) [ennf transformation 66]
142. ! [X0] : predu(X0) [ennf transformation 65]
147. ~predl(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 54]
152. ! [X0] : (predl(X0) | ~room(X0)) | ? [X1] : ~predu(X1) [rectify 141]
153. ? [X1] : ~predu(X1) => ~predu(sK1) [choice axiom]
154. ! [X0] : (predl(X0) | ~room(X0)) | ~predu(sK1) [skolemisation 152,153]
155. ? [X0] : (mary != X0 & room(X0)) => (mary != sK2 & room(sK2)) [choice axiom]
156. ~predl(mary) | (mary != sK2 & room(sK2)) | ~room(mary) [skolemisation 147,155]
237. room(mary) [cnf transformation 139]
238. ~room(X0) | mary = X0 [cnf transformation 139]
241. predl(X0) | ~room(X0) | ~predu(sK1) [cnf transformation 154]
242. predu(X0) [cnf transformation 142]
245. ~predl(mary) | room(sK2) | ~room(mary) [cnf transformation 156]
246. ~predl(mary) | mary != sK2 | ~room(mary) [cnf transformation 156]
261. 4 <=> predu(sK1) [avatar definition]
263. ~predu(sK1) <- (~4) [avatar component clause 261]
265. 5 <=> ! [X0] : (predl(X0) | ~room(X0)) [avatar definition]
266. ~room(X0) | predl(X0) <- (5) [avatar component clause 265]
267. ~4 | 5 [avatar split clause 241,265,261]
268. ~predl(mary) | mary != sK2 [subsumption resolution 246,237]
270. 6 <=> mary = sK2 [avatar definition]
272. mary != sK2 <- (~6) [avatar component clause 270]
274. 7 <=> predl(mary) [avatar definition]
277. ~6 | ~7 [avatar split clause 268,274,270]
278. ~predl(mary) | room(sK2) [subsumption resolution 245,237]
280. 8 <=> room(sK2) [avatar definition]
282. room(sK2) <- (8) [avatar component clause 280]
283. 8 | ~7 [avatar split clause 278,274,280]
284. $false <- (~4) [subsumption resolution 263,242]
285. 4 [avatar contradiction clause 284]
286. predl(mary) <- (5) [resolution 266,237]
289. 7 | ~5 [avatar split clause 286,265,274]
292. mary = sK2 <- (8) [resolution 238,282]
293. $false <- (~6, 8) [subsumption resolution 292,272]
294. 6 | ~8 [avatar contradiction clause 293]
295. $false [avatar sat refutation 267,277,283,285,289,294]
% SZS output end Proof for 20410044457004300500318
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0.002044 |
Renee, Jeffrey, Stephen are the only persons in the room.
If “everyone in the room is a certified yoga instructor teaching classes weekly or is not a Linux enthusiast” then “everyone in the room who watches fantasy movies hosts a YouTube channel dedicated to art tutorials”.
“Everyone in the room enjoys stand-up paddleboarding or does not enjoy snowboarding” if “everyone in the room does enjoy trail running or does not enjoy trail running” and vice versa.
If “it is not the case that “Jeffrey collect rare sneakers”” then “not everyone in the room collects vintage stamps if they is a Linux enthusiast”.
Everyone in the room who collects vintage stamps does enjoy trail running.
Stephen is a Linux enthusiast.
Not everyone in the room collects vintage stamps if they is a Linux enthusiast.
Everyone anywhere enjoys kayaking and exploring remote waterways only if they owns a telescope.
Stephen enjoys snowboarding.
Someone in the room is a Linux enthusiast.
Everyone in the room watches fantasy movies if they collects vintage stamps.
Everyone in the room who watches fantasy movies enjoys writing detailed reviews of new and classic board games.
Everyone in the room practices kickboxing.
Everyone anywhere enjoys writing detailed reviews of new and classic board games only if they hosts a YouTube channel dedicated to art tutorials.
If someone does not practice kickboxing then he/she does enjoy trail running and vice versa.
Everyone in the room who collects comic books collects vintage stamps.
Stephen is a certified yoga instructor teaching classes weekly.
Everyone in the room enjoys kayaking and exploring remote waterways if they enjoys origami.
Stephen regularly contributes to tech forums and online communities.
Everyone in the room collects rare minerals if they enjoys snowboarding.
Everyone in the room enjoys kayaking and exploring remote waterways if they collects rare minerals.
Not everyone in the room who enjoys kayaking and exploring remote waterways enjoys snowboarding. | Jeffrey collects comic books. | contradiction | room(renee)&room(jeffrey)&room(stephen)&(![X]:(room(X)=>(X='renee'|X='jeffrey'|X='stephen')))&
((![X]:(room(X)=>(((is_not_a_Linux_enthusiast(X))|(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))=>(![X]:(room(X)=>(((watches_fantasy_movies(X))=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X)))))))&
((![X]:(room(X)=>(((does_not_enjoy_trail_running(X))|(does_enjoy_trail_running(X))))))<=>(![X]:(room(X)=>(((does_not_enjoy_snowboarding(X))|(enjoys_stand-up_paddleboarding(X)))))))&
((~(collect_rare_sneakers(jeffrey)))=>(~![X]:(room(X)=>(((is_a_Linux_enthusiast(X))=>(collects_vintage_stamps(X)))))))&
(![X]:(room(X)=>(((collects_vintage_stamps(X))=>(does_enjoy_trail_running(X))))))&
(is_a_Linux_enthusiast(stephen))&
(~![X]:(room(X)=>(((is_a_Linux_enthusiast(X))=>(collects_vintage_stamps(X))))))&
(![X]:(anywhere(X)=>(((owns_a_telescope(X))<=(enjoys_kayaking_and_exploring_remote_waterways(X))))))&
(enjoys_snowboarding(stephen))&
(?[X]:(room(X)&(is_a_Linux_enthusiast(X))))&
(![X]:(room(X)=>(((collects_vintage_stamps(X))=>(watches_fantasy_movies(X))))))&
(![X]:(room(X)=>(((watches_fantasy_movies(X))=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))))&
(![X]:(room(X)=>(practices_kickboxing(X))))&
(![X]:(anywhere(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))<=(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))))&
((![X]:((does_not_practice_kickboxing(X))<=>(does_enjoy_trail_running(X)))))&
(![X]:(room(X)=>(((collects_comic_books(X))=>(collects_vintage_stamps(X))))))&
(is_a_certified_yoga_instructor_teaching_classes_weekly(stephen))&
(![X]:(room(X)=>(((enjoys_origami(X))=>(enjoys_kayaking_and_exploring_remote_waterways(X))))))&
(regularly_contributes_to_tech_forums_and_online_communities(stephen))&
(![X]:(room(X)=>(((enjoys_snowboarding(X))=>(collects_rare_minerals(X))))))&
(![X]:(room(X)=>(((collects_rare_minerals(X))=>(enjoys_kayaking_and_exploring_remote_waterways(X))))))&
(~![X]:(room(X)=>(((enjoys_kayaking_and_exploring_remote_waterways(X))=>(enjoys_snowboarding(X)))))) | room(renee)&room(jeffrey)&room(stephen)&(![X]:(room(X)=>(X='renee'|X='jeffrey'|X='stephen')))&
collects_comic_books(jeffrey) | [
"p0",
"p4",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 303053723107784485554320
% SZS output start Proof for 303053723107784485554320
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
48. ! [X0] : (room(X0) => (preda(X0) => predd(X0))) [input p4]
56. ! [X0] : (room(X0) => predp(X0)) [input p12]
58. ! [X0] : (~predp(X0) <=> predd(X0)) [input p14]
59. ! [X0] : (room(X0) => (predf(X0) => preda(X0))) [input p15]
66. predf(paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis]
69. ! [X0] : (predd(X0) => ~predp(X0)) [unused predicate definition removal 58]
157. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
158. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 157]
161. ! [X0] : ((predd(X0) | ~preda(X0)) | ~room(X0)) [ennf transformation 48]
162. ! [X0] : (predd(X0) | ~preda(X0) | ~room(X0)) [flattening 161]
164. ! [X0] : (predp(X0) | ~room(X0)) [ennf transformation 56]
165. ! [X0] : (~predp(X0) | ~predd(X0)) [ennf transformation 69]
166. ! [X0] : ((preda(X0) | ~predf(X0)) | ~room(X0)) [ennf transformation 59]
167. ! [X0] : (preda(X0) | ~predf(X0) | ~room(X0)) [flattening 166]
169. predf(paul) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 66]
170. predf(paul) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 169]
264. room(paul) [cnf transformation 158]
273. ~preda(X0) | predd(X0) | ~room(X0) [cnf transformation 162]
278. ~room(X0) | predp(X0) [cnf transformation 164]
279. ~predp(X0) | ~predd(X0) [cnf transformation 165]
280. ~predf(X0) | preda(X0) | ~room(X0) [cnf transformation 167]
287. predf(paul) [cnf transformation 170]
303. predp(paul) [resolution 278,264]
309. ~predd(paul) [resolution 303,279]
310. preda(paul) | ~room(paul) [resolution 280,287]
311. preda(paul) [subsumption resolution 310,264]
318. predd(paul) | ~room(paul) [resolution 311,273]
319. ~room(paul) [subsumption resolution 318,309]
320. $false [subsumption resolution 319,264]
% SZS output end Proof for 303053723107784485554320
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.686612 |
Diane, Lupe, Maria, Deanna, Ashley are the only persons in the room.
Everyone in the room creates augmented reality experiences for mobile applications if they has a vast collection of first-edition science fiction novels.
Diane enjoys writing detailed reviews of new and classic board games.
Everyone outside the room writes and illustrates their own graphic novels if they is an avid mountain climber who has scaled several peaks.
Everyone in the room writes and illustrates their own graphic novels if they writes and illustrates their own graphic novels and hosts a YouTube channel dedicated to art tutorials and vice versa.
Everyone anywhere writes and illustrates their own graphic novels and hosts a YouTube channel dedicated to art tutorials only if they has a vast collection of first-edition science fiction novels.
Diane is a cybersecurity expert or collects rare and antique scientific instruments or both.
Diane collect rare sneakers.
Diane who does practice yoga is an avid mountain climber who has scaled several peaks.
Everyone in the room does not collect action figures if they writes and illustrates their own graphic novels and vice versa.
Everyone in the room does not host themed dinner parties featuring gourmet home-cooked meals or writes and illustrates their own graphic novels.
If someone either owns a high-end gaming PC with custom-built components or is an avid mountain climber who has scaled several peaks but not both then he/she does practice yoga and vice versa.
Diane hosts themed dinner parties featuring gourmet home-cooked meals.
Everyone in the room who does practice yoga plays the drums.
Diane collect rare sneakers or is a cybersecurity expert or both.
Diane who creates augmented reality experiences for mobile applications plays the violin.
Everyone anywhere who is an avid mountain climber who has scaled several peaks creates augmented reality experiences for mobile applications.
Everyone in the room does not collect comic books or creates augmented reality experiences for mobile applications.
Everyone in the room does not host themed dinner parties featuring gourmet home-cooked meals or does not have lived in exactly three countries.
Everyone in the room who does not host themed dinner parties featuring gourmet home-cooked meals hosts a YouTube channel dedicated to art tutorials.
Everyone in the room who hosts a YouTube channel dedicated to art tutorials is not a cybersecurity expert and does practice yoga.
It is not the case that “Diane owns a high-end gaming PC with custom-built components”.
Someone in the room collects rare and antique scientific instruments, enjoys writing detailed reviews of new and classic board games and writes a travel blog.
At least one person in the room is not a member of a local theater group specializing in improv.
Everyone anywhere plays the drums. | Diane has a vast collection of first-edition science fiction novels. | entailment | room(diane)&room(lupe)&room(maria)&room(deanna)&room(ashley)&(![X]:(room(X)=>(X='diane'|X='lupe'|X='maria'|X='deanna'|X='ashley')))&
(![X]:(room(X)=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))=>(creates_augmented_reality_experiences_for_mobile_applications(X))))))&
(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(diane))&
(![X]:(~room(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(writes_and_illustrates_their_own_graphic_novels(X))))))&
(![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))<=>(((writes_and_illustrates_their_own_graphic_novels(X))&(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))))&
(![X]:(anywhere(X)=>(((has_a_vast_collection_of_first-edition_science_fiction_novels(X))<=(((writes_and_illustrates_their_own_graphic_novels(X))&(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))))&
(((is_a_cybersecurity_expert(diane))|(collects_rare_and_antique_scientific_instruments(diane))))&
(collect_rare_sneakers(diane))&
((does_practice_yoga(diane))&(is_an_avid_mountain_climber_who_has_scaled_several_peaks(diane)))&
(![X]:(room(X)=>(((does_not_collect_action_figures(X))<=>(writes_and_illustrates_their_own_graphic_novels(X))))))&
(![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))|(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))&
((![X]:((((owns_a_high-end_gaming_PC_with_custom-built_components(X))<~>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))<=>(does_practice_yoga(X)))))&
(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(diane))&
(![X]:(room(X)=>(((does_practice_yoga(X))=>(plays_the_drums(X))))))&
(((collect_rare_sneakers(diane))|(is_a_cybersecurity_expert(diane))))&
((creates_augmented_reality_experiences_for_mobile_applications(diane))&(plays_the_violin(diane)))&
(![X]:(anywhere(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))=>(creates_augmented_reality_experiences_for_mobile_applications(X))))))&
(![X]:(room(X)=>(((creates_augmented_reality_experiences_for_mobile_applications(X))|(does_not_collect_comic_books(X))))))&
(![X]:(room(X)=>(((does_not_have_lived_in_exactly_three_countries(X))|(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))&
(![X]:(room(X)=>(((does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))&
(![X]:(room(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))=>(((is_not_a_cybersecurity_expert(X))&(does_practice_yoga(X))))))))&
(~(owns_a_high-end_gaming_PC_with_custom-built_components(diane)))&
(?[X]:(room(X)&(((collects_rare_and_antique_scientific_instruments(X))&(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))&(writes_a_travel_blog(X))))))&
(((?[X]:(room(X)&is_not_a_member_of_a_local_theater_group_specializing_in_improv(X)))))&
(![X]:(anywhere(X)=>(plays_the_drums(X)))) | room(diane)&room(lupe)&room(maria)&room(deanna)&room(ashley)&(![X]:(room(X)=>(X='diane'|X='lupe'|X='maria'|X='deanna'|X='ashley')))&
has_a_vast_collection_of_first-edition_science_fiction_novels(diane) | [
"b4",
"p0",
"p4",
"p5",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1050902077376939858580357
% SZS output start Proof for 1050902077376939858580357
5. ! [X0] : anywhere(X0) [input b4]
44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
48. ! [X0] : (room(X0) => (predk(X0) <=> (predf(X0) & predk(X0)))) [input p4]
49. ! [X0] : (anywhere(X0) => ((predf(X0) & predk(X0)) => predn(X0))) [input p5]
54. ! [X0] : (room(X0) => (~preda(X0) | predk(X0))) [input p10]
56. preda(mary) [input p12]
69. ~(predn(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]
159. ! [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]
160. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 159]
163. ! [X0] : ((predk(X0) <=> (predf(X0) & predk(X0))) | ~room(X0)) [ennf transformation 48]
164. ! [X0] : ((predn(X0) | (~predf(X0) | ~predk(X0))) | ~anywhere(X0)) [ennf transformation 49]
165. ! [X0] : (predn(X0) | ~predf(X0) | ~predk(X0) | ~anywhere(X0)) [flattening 164]
167. ! [X0] : ((~preda(X0) | predk(X0)) | ~room(X0)) [ennf transformation 54]
168. ! [X0] : (~preda(X0) | predk(X0) | ~room(X0)) [flattening 167]
174. ~predn(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 69]
175. ~predn(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 174]
177. ! [X0] : (((predk(X0) | (~predf(X0) | ~predk(X0))) & ((predf(X0) & predk(X0)) | ~predk(X0))) | ~room(X0)) [nnf transformation 163]
178. ! [X0] : (((predk(X0) | ~predf(X0) | ~predk(X0)) & ((predf(X0) & predk(X0)) | ~predk(X0))) | ~room(X0)) [flattening 177]
185. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK2 & alice != sK2 & fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) [choice axiom]
186. ~predn(mary) | (john != sK2 & alice != sK2 & fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 175,185]
187. anywhere(X0) [cnf transformation 5]
268. room(mary) [cnf transformation 160]
269. room(paul) [cnf transformation 160]
270. room(fred) [cnf transformation 160]
271. room(alice) [cnf transformation 160]
272. room(john) [cnf transformation 160]
273. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 160]
276. ~predk(X0) | predf(X0) | ~room(X0) [cnf transformation 178]
278. predn(X0) | ~predf(X0) | ~predk(X0) | ~anywhere(X0) [cnf transformation 165]
283. ~preda(X0) | predk(X0) | ~room(X0) [cnf transformation 168]
286. preda(mary) [cnf transformation 56]
292. ~predn(mary) | room(sK2) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 186]
293. ~predn(mary) | mary != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 186]
294. ~predn(mary) | paul != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 186]
295. ~predn(mary) | fred != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 186]
296. ~predn(mary) | alice != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 186]
297. ~predn(mary) | john != sK2 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 186]
298. ~predf(X0) | predn(X0) | ~predk(X0) [subsumption resolution 278,187]
299. ~predn(mary) | john != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 297,272]
300. ~predn(mary) | john != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 299,271]
301. ~predn(mary) | john != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 300,270]
302. ~predn(mary) | john != sK2 | ~room(mary) [subsumption resolution 301,269]
303. ~predn(mary) | john != sK2 [subsumption resolution 302,268]
305. 1 <=> john = sK2 [avatar definition]
307. john != sK2 <- (~1) [avatar component clause 305]
309. 2 <=> predn(mary) [avatar definition]
312. ~1 | ~2 [avatar split clause 303,309,305]
313. ~predn(mary) | alice != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 296,272]
314. ~predn(mary) | alice != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 313,271]
315. ~predn(mary) | alice != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 314,270]
316. ~predn(mary) | alice != sK2 | ~room(mary) [subsumption resolution 315,269]
317. ~predn(mary) | alice != sK2 [subsumption resolution 316,268]
319. 3 <=> alice = sK2 [avatar definition]
321. alice != sK2 <- (~3) [avatar component clause 319]
322. ~3 | ~2 [avatar split clause 317,309,319]
323. ~predn(mary) | fred != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 295,272]
324. ~predn(mary) | fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 323,271]
325. ~predn(mary) | fred != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 324,270]
326. ~predn(mary) | fred != sK2 | ~room(mary) [subsumption resolution 325,269]
327. ~predn(mary) | fred != sK2 [subsumption resolution 326,268]
329. 4 <=> fred = sK2 [avatar definition]
331. fred != sK2 <- (~4) [avatar component clause 329]
332. ~4 | ~2 [avatar split clause 327,309,329]
333. ~predn(mary) | paul != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 294,272]
334. ~predn(mary) | paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 333,271]
335. ~predn(mary) | paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 334,270]
336. ~predn(mary) | paul != sK2 | ~room(mary) [subsumption resolution 335,269]
337. ~predn(mary) | paul != sK2 [subsumption resolution 336,268]
339. 5 <=> paul = sK2 [avatar definition]
341. paul != sK2 <- (~5) [avatar component clause 339]
342. ~5 | ~2 [avatar split clause 337,309,339]
343. ~predn(mary) | mary != sK2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 293,272]
344. ~predn(mary) | mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 343,271]
345. ~predn(mary) | mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 344,270]
346. ~predn(mary) | mary != sK2 | ~room(mary) [subsumption resolution 345,269]
347. ~predn(mary) | mary != sK2 [subsumption resolution 346,268]
349. 6 <=> mary = sK2 [avatar definition]
351. mary != sK2 <- (~6) [avatar component clause 349]
352. ~6 | ~2 [avatar split clause 347,309,349]
353. ~predn(mary) | room(sK2) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 292,272]
354. ~predn(mary) | room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 353,271]
355. ~predn(mary) | room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 354,270]
356. ~predn(mary) | room(sK2) | ~room(mary) [subsumption resolution 355,269]
357. ~predn(mary) | room(sK2) [subsumption resolution 356,268]
359. 7 <=> room(sK2) [avatar definition]
361. room(sK2) <- (7) [avatar component clause 359]
362. 7 | ~2 [avatar split clause 357,309,359]
372. 8 <=> predk(mary) [avatar definition]
374. predk(mary) <- (8) [avatar component clause 372]
434. predf(mary) | ~room(mary) <- (8) [resolution 374,276]
435. predf(mary) <- (8) [subsumption resolution 434,268]
438. predk(mary) | ~room(mary) [resolution 283,286]
481. predn(mary) | ~predk(mary) <- (8) [resolution 435,298]
486. predn(mary) <- (8) [subsumption resolution 481,374]
487. 2 | ~8 [avatar split clause 486,372,309]
508. predk(mary) [subsumption resolution 438,268]
509. 8 [avatar split clause 508,372]
645. alice = sK2 | fred = sK2 | paul = sK2 | mary = sK2 | john = sK2 <- (7) [resolution 273,361]
688. fred = sK2 | paul = sK2 | mary = sK2 | john = sK2 <- (~3, 7) [subsumption resolution 645,321]
689. paul = sK2 | mary = sK2 | john = sK2 <- (~3, ~4, 7) [subsumption resolution 688,331]
690. mary = sK2 | john = sK2 <- (~3, ~4, ~5, 7) [subsumption resolution 689,341]
691. john = sK2 <- (~3, ~4, ~5, ~6, 7) [subsumption resolution 690,351]
692. $false <- (~1, ~3, ~4, ~5, ~6, 7) [subsumption resolution 691,307]
693. 1 | 3 | 4 | 5 | 6 | ~7 [avatar contradiction clause 692]
694. $false [avatar sat refutation 312,322,332,342,352,362,487,509,693]
% SZS output end Proof for 1050902077376939858580357
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
There is a room.
If "everyone in the room owns an extensive assortment of vintage comic book memorabilia or is not a wine connoisseur with a private cellar of vintage wines" then "everyone outside the room who owns an extensive assortment of vintage comic book memorabilia bakes bread at home and owns an extensive assortment of vintage comic book memorabilia".
Everyone in the room creates augmented reality experiences for mobile applications only if they practices digital art.
Everyone in the room who practices digital art enjoys making ceramics.
If someone practices digital art then he/she enjoys watercolor painting and vice versa.
Everyone in the room who practices pilates neither uses an ios phone nor hosts regular game nights featuring complex strategy games.
No one in the room neither uses an ios phone nor hosts regular game nights featuring complex strategy games if they practices digital art and vice versa.
Only one person in the room writes poetry and enjoys making ceramics.
If someone is a client of LVMH then he/she enjoys watercolor painting and vice versa.
Everyone anywhere collects antique jewelry or is not a dedicated advocate for digital privacy and encryption.
Someone in the room is a client of LVMH.
If someone collects antique jewelry then he/she bakes bread at home or practices kickboxing or both and vice versa.
Everyone in the room practices kickboxing if and only if they is a certified yoga instructor teaching classes weekly. | Everyone in the room practices pilates. | contradiction | (there_is_a_room)&
((![X]:(room(X)=>(((is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))|(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))))=>(![X]:(~room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))=>(((bakes_bread_at_home(X))&(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X)))))))))&
(![X]:(room(X)=>(((practices_digital_art(X))<=(creates_augmented_reality_experiences_for_mobile_applications(X))))))&
(![X]:(room(X)=>(((practices_digital_art(X))=>(enjoys_making_ceramics(X))))))&
((![X]:((practices_digital_art(X))<=>(enjoys_watercolor_painting(X)))))&
(![X]:(room(X)=>(((practices_pilates(X))=>(~((uses_an_ios_phone(X))|(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))))&
(~?[X]:(room(X)=>(((~((uses_an_ios_phone(X))|(hosts_regular_game_nights_featuring_complex_strategy_games(X))))<=>(practices_digital_art(X))))))&
(((?[X]:(room(X)&((writes_poetry(X))&(enjoys_making_ceramics(X)))))&(![X,Y]:((room(X)&room(Y)&(((writes_poetry(X))&(enjoys_making_ceramics(X))))&(((writes_poetry(Y))&(enjoys_making_ceramics(Y)))))=>(X=Y)))))&
((![X]:((is_a_client_of_LVMH(X))<=>(enjoys_watercolor_painting(X)))))&
(![X]:(anywhere(X)=>(((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))|(collects_antique_jewelry(X))))))&
(?[X]:(room(X)&(is_a_client_of_LVMH(X))))&
((![X]:((collects_antique_jewelry(X))<=>(((bakes_bread_at_home(X))|(practices_kickboxing(X)))))))&
(![X]:(room(X)=>(((practices_kickboxing(X))<=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X)))))) | (there_is_a_room)&
![X]:(room(X)=>(practices_pilates(X))) | [
"p4",
"p5",
"p6",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7313111840518234780419423
% SZS output start Proof for 7313111840518234780419423
48. ! [X0] : (predm(X0) <=> predf(X0)) [input p4]
49. ! [X0] : (room(X0) => (predk(X0) => ~(predn(X0) | predp(X0)))) [input p5]
50. ~? [X0] : (room(X0) => (~(predn(X0) | predp(X0)) <=> predm(X0))) [input p6]
52. ! [X0] : (predt(X0) <=> predf(X0)) [input p8]
54. ? [X0] : (predt(X0) & room(X0)) [input p10]
57. ! [X0] : (room(X0) => predk(X0)) & there_is_a_room [input hypothesis]
61. ! [X0] : (predt(X0) => predf(X0)) [unused predicate definition removal 52]
69. ! [X0] : (room(X0) => predk(X0)) [pure predicate removal 57]
145. ! [X0] : (((~predn(X0) & ~predp(X0)) | ~predk(X0)) | ~room(X0)) [ennf transformation 49]
146. ! [X0] : ((~predn(X0) & ~predp(X0)) | ~predk(X0) | ~room(X0)) [flattening 145]
147. ! [X0] : (((~predn(X0) & ~predp(X0)) <~> predm(X0)) & room(X0)) [ennf transformation 50]
150. ! [X0] : (predf(X0) | ~predt(X0)) [ennf transformation 61]
152. ! [X0] : (predk(X0) | ~room(X0)) [ennf transformation 69]
157. ! [X0] : ((predm(X0) | ~predf(X0)) & (predf(X0) | ~predm(X0))) [nnf transformation 48]
158. ! [X0] : (((~predm(X0) | (predn(X0) | predp(X0))) & (predm(X0) | (~predn(X0) & ~predp(X0)))) & room(X0)) [nnf transformation 147]
159. ! [X0] : ((~predm(X0) | predn(X0) | predp(X0)) & (predm(X0) | (~predn(X0) & ~predp(X0))) & room(X0)) [flattening 158]
162. ? [X0] : (predt(X0) & room(X0)) => (predt(sK2) & room(sK2)) [choice axiom]
163. predt(sK2) & room(sK2) [skolemisation 54,162]
249. ~predf(X0) | predm(X0) [cnf transformation 157]
250. ~predp(X0) | ~predk(X0) | ~room(X0) [cnf transformation 146]
251. ~predn(X0) | ~predk(X0) | ~room(X0) [cnf transformation 146]
252. room(X0) [cnf transformation 159]
255. ~predm(X0) | predn(X0) | predp(X0) [cnf transformation 159]
260. ~predt(X0) | predf(X0) [cnf transformation 150]
262. predt(sK2) [cnf transformation 163]
265. predk(X0) | ~room(X0) [cnf transformation 152]
270. predk(X0) [subsumption resolution 265,252]
271. predf(sK2) [resolution 260,262]
272. predm(sK2) [resolution 271,249]
276. predn(sK2) | predp(sK2) [resolution 255,272]
278. 1 <=> predp(sK2) [avatar definition]
280. predp(sK2) <- (1) [avatar component clause 278]
282. 2 <=> predn(sK2) [avatar definition]
284. predn(sK2) <- (2) [avatar component clause 282]
285. 1 | 2 [avatar split clause 276,282,278]
286. ~predk(sK2) | ~room(sK2) <- (2) [resolution 284,251]
288. ~room(sK2) <- (2) [subsumption resolution 286,270]
289. $false <- (2) [subsumption resolution 288,252]
290. ~2 [avatar contradiction clause 289]
291. ~predk(sK2) | ~room(sK2) <- (1) [resolution 280,250]
293. ~room(sK2) <- (1) [subsumption resolution 291,270]
294. $false <- (1) [subsumption resolution 293,252]
295. ~1 [avatar contradiction clause 294]
296. $false [avatar sat refutation 285,290,295]
% SZS output end Proof for 7313111840518234780419423
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.04029 |
There is a room. Everyone in the room does not play video games and enjoys stargazing if they makes intricate hand-cut paper art for exhibitions. Everyone anywhere makes intricate hand-cut paper art for exhibitions if they does not play video games and enjoys stargazing. Everyone outside the room neither is an amateur astronomer who builds and uses custom telescopes nor is not an amateur astronomer who builds and uses custom telescopes if they makes intricate hand-cut paper art for exhibitions. If someone either does not play video games or makes intricate hand-cut paper art for exhibitions but not both then he/she enjoys stargazing and vice versa. Everyone in the room does not play video games and plays video games if and only if they enjoys stargazing. Everyone in the room who enjoys stargazing either plays video games or does not work on fridays but not both. | Everyone outside the room works on fridays. | neutral | (there_is_a_room)&
(![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))=>(((does_not_play_video_games(X))&(enjoys_stargazing(X))))))))&
(![X]:(anywhere(X)=>(((((does_not_play_video_games(X))&(enjoys_stargazing(X))))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))&
(![X]:(~room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))=>(~((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))|(is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))))&
((![X]:((((does_not_play_video_games(X))<~>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))<=>(enjoys_stargazing(X)))))&
(![X]:(room(X)=>(((((does_not_play_video_games(X))&(plays_video_games(X))))<=>(enjoys_stargazing(X))))))&
(![X]:(room(X)=>(((enjoys_stargazing(X))=>(((plays_video_games(X))<~>(does_not_work_on_fridays(X)))))))) | (there_is_a_room)&
![X]:(~room(X)=>(works_on_fridays(X))) | [] | null | 0.031228 |
Efrain, David, Elizabeth, Melissa are the only persons in the room. If “Efrain is happy” then “A clock does not measure time in various colors.”. If ““There is no planet where the oceans are in the sky.” or “A car does not run solely on saltwater.” but not both” then “everyone in the room is calm or does not enjoy spelunking”. “Everyone in the room who is a cybersecurity expert enjoys coding in Python” unless “Melissa is not a calm person”. If “Elizabeth and Melissa are calm persons” then “Melissa enjoys spelunking”. At least one person in the room is not a happy patient calm person. “All swans in one park are blue.” or “There is no planet where the oceans are in the sky.” but not both. Elizabeth neither enjoys spelunking nor enjoys coding in Python. It is not the case that “Elizabeth is calm”. Melissa does not enjoy spelunking. Everyone in the room is not a calm person if they enjoys spelunking. | Efrain is happy. | neutral | room(efrain)&room(david)&room(elizabeth)&room(melissa)&(![X]:(room(X)=>(X='efrain'|X='david'|X='elizabeth'|X='melissa')))&
((happy(efrain))=>(A_clock_does_not_measure_time_in_various_colors.))&
((((There_is_no_planet_where_the_oceans_are_in_the_sky.)<~>(A_car_does_not_run_solely_on_saltwater.)))=>(![X]:(room(X)=>(((does_not_enjoy_spelunking(X))|(calm(X)))))))&
(~(~(calm(melissa)&person(melissa)))=>(![X]:(room(X)=>(((is_a_cybersecurity_expert(X))=>(enjoys_coding_in_Python(X)))))))&
((calm(elizabeth)&person(elizabeth)&calm(melissa)&person(melissa))=>(enjoys_spelunking(melissa)))&
(((?[X]:(room(X)&~(happy(X)&patient(X)&calm(X)&person(X))))))&
(((All_swans_in_one_park_are_blue.)<~>(There_is_no_planet_where_the_oceans_are_in_the_sky.)))&
(~((enjoys_spelunking(elizabeth))|(enjoys_coding_in_Python(elizabeth))))&
(~(calm(elizabeth)))&
(does_not_enjoy_spelunking(melissa))&
(![X]:(room(X)=>(((enjoys_spelunking(X))=>(~(calm(X)&person(X)))))))&
((?[X,Y]:(room(X)&room(Y)&(patient(X)&patient(Y))&(X!=Y))))&
(((?[X]:(room(X)&enjoys_spelunking(X)))))&
((calm(melissa))&(patient(efrain)))&
(~(patient(elizabeth)&person(elizabeth)))&
(?[X]:(room(X)&(patient(X)&person(X))))&
(![X]:((room(X)&(X!=elizabeth))=>poorer(X,elizabeth)))&
(![X]:(room(X)=>(((is_a_cybersecurity_expert(X))=>(((happy(X))|(is_a_cybersecurity_expert(X))))))))&
(~(happy(efrain)&patient(efrain)&calm(efrain)&person(efrain))&~(happy(elizabeth)&patient(elizabeth)&calm(elizabeth)&person(elizabeth)))&
(~![X]:(room(X)=>(((is_a_cybersecurity_expert(X))=>(enjoys_coding_in_Python(X))))))&
(((?[X]:(~room(X)&enjoys_spelunking(X))))) | room(efrain)&room(david)&room(elizabeth)&room(melissa)&(![X]:(room(X)=>(X='efrain'|X='david'|X='elizabeth'|X='melissa')))&
happy(efrain) | [] | null | 0.026548 |
Barry, Barbara, James are the only persons in the room.
Everyone in the room does not compete in national level swimming championships.
James bakes bread at home.
Barry bakes bread at home.
Not everyone outside the room bakes bread at home and enjoys stargazing only if they does not enjoy stargazing.
If someone enjoys skydiving then he/she enjoys skydiving, bakes bread at home and writes and illustrates their own graphic novels.
Everyone in the room enjoys skydiving, does not enjoy stargazing or bakes bread at home if they enjoys skydiving.
It is not the case that “Barbara does not enjoy stargazing”.
Everyone in the room enjoys deep-sea diving and exploring underwater caves only if they enjoys stargazing. | Everyone in the room writes and illustrates their own graphic novels. | neutral | room(barry)&room(barbara)&room(james)&(![X]:(room(X)=>(X='barry'|X='barbara'|X='james')))&
(![X]:(room(X)=>(does_not_compete_in_national_level_swimming_championships(X))))&
(bakes_bread_at_home(james))&
(bakes_bread_at_home(barry))&
(~![X]:(~room(X)=>(((does_not_enjoy_stargazing(X))<=(((bakes_bread_at_home(X))&(enjoys_stargazing(X))))))))&
((![X]:((enjoys_skydiving(X))=>(((enjoys_skydiving(X))&(bakes_bread_at_home(X))&(writes_and_illustrates_their_own_graphic_novels(X)))))))&
(![X]:(room(X)=>(((enjoys_skydiving(X))=>(((enjoys_skydiving(X))|(does_not_enjoy_stargazing(X))|(bakes_bread_at_home(X))))))))&
(~(does_not_enjoy_stargazing(barbara)))&
(![X]:(room(X)=>(((enjoys_stargazing(X))<=(enjoys_deep-sea_diving_and_exploring_underwater_caves(X)))))) | room(barry)&room(barbara)&room(james)&(![X]:(room(X)=>(X='barry'|X='barbara'|X='james')))&
![X]:(room(X)=>(writes_and_illustrates_their_own_graphic_novels(X))) | [] | null | 0 |
Tiffany, Nancy, Gerald, Anna, Anna are the only persons in the room.
If “everyone in the room has a specialized collection of handmade artisan pottery or does not build model airplanes” then “Tiffany does not have a specialized collection of handmade artisan pottery”.
If “Tiffany does not build model airplanes” then “Tiffany works on fridays”.
If “Tiffany has a tattoo” then “everyone in the room has a specialized collection of handmade artisan pottery”.
At least one person in the room does not work on fridays.
It is true that “Tiffany collects vintage vinyl records”.
Only one person in the room does not build model airplanes.
It is not the case that “Tiffany competes in national level swimming championships”.
Everyone in the room works on fridays if they practices urban gardening.
It is true that “everyone in the room has a tattoo if they practices and performs acrobatic dance routines”. | Tiffany practices and performs acrobatic dance routines. | contradiction | room(tiffany)&room(nancy)&room(gerald)&room(anna)&room(anna)&(![X]:(room(X)=>(X='tiffany'|X='nancy'|X='gerald'|X='anna'|X='anna')))&
((![X]:(room(X)=>(((does_not_build_model_airplanes(X))|(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))=>(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(tiffany)))&
((does_not_build_model_airplanes(tiffany))=>(works_on_fridays(tiffany)))&
((has_a_tattoo(tiffany))=>(![X]:(room(X)=>(has_a_specialized_collection_of_handmade_artisan_pottery(X)))))&
(((?[X]:(room(X)&does_not_work_on_fridays(X)))))&
(collects_vintage_vinyl_records(tiffany))&
(((?[X]:(room(X)&does_not_build_model_airplanes(X)))&(![X,Y]:((room(X)&room(Y)&(does_not_build_model_airplanes(X))&(does_not_build_model_airplanes(Y)))=>(X=Y)))))&
(~(competes_in_national_level_swimming_championships(tiffany)))&
(![X]:(room(X)=>(((practices_urban_gardening(X))=>(works_on_fridays(X))))))&
(![X]:(room(X)=>(((does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X))=>(is_an_active_member_of_a_local_robotics_club(X))))))&
(![X]:(room(X)=>(((practices_and_performs_acrobatic_dance_routines(X))=>(has_a_tattoo(X)))))) | room(tiffany)&room(nancy)&room(gerald)&room(anna)&room(anna)&(![X]:(room(X)=>(X='tiffany'|X='nancy'|X='gerald'|X='anna'|X='anna')))&
practices_and_performs_acrobatic_dance_routines(tiffany) | [
"p0",
"p1",
"p3",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 316172402298248814745293
% SZS output start Proof for 316172402298248814745293
44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
45. ! [X0] : (room(X0) => (predh(X0) | ~predf(X0))) => ~predh(mary) [input p1]
47. predb(mary) => ! [X0] : (room(X0) => predh(X0)) [input p3]
54. ! [X0] : (room(X0) => (predg(X0) => predb(X0))) [input p10]
55. predg(mary) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis]
133. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
134. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 133]
135. ~predh(mary) | ? [X0] : ((~predh(X0) & predf(X0)) & room(X0)) [ennf transformation 45]
136. ~predh(mary) | ? [X0] : (~predh(X0) & predf(X0) & room(X0)) [flattening 135]
138. ! [X0] : (predh(X0) | ~room(X0)) | ~predb(mary) [ennf transformation 47]
141. ! [X0] : ((predb(X0) | ~predg(X0)) | ~room(X0)) [ennf transformation 54]
142. ! [X0] : (predb(X0) | ~predg(X0) | ~room(X0)) [flattening 141]
143. predg(mary) & ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 55]
144. predg(mary) & ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 143]
146. ? [X0] : (~predh(X0) & predf(X0) & room(X0)) => (~predh(sK0) & predf(sK0) & room(sK0)) [choice axiom]
147. ~predh(mary) | (~predh(sK0) & predf(sK0) & room(sK0)) [skolemisation 136,146]
232. room(mary) [cnf transformation 134]
238. ~predh(mary) | room(sK0) [cnf transformation 147]
240. ~predh(mary) | ~predh(sK0) [cnf transformation 147]
242. predh(X0) | ~room(X0) | ~predb(mary) [cnf transformation 138]
248. ~predg(X0) | predb(X0) | ~room(X0) [cnf transformation 142]
255. predg(mary) [cnf transformation 144]
257. 1 <=> predh(sK0) [avatar definition]
259. ~predh(sK0) <- (~1) [avatar component clause 257]
261. 2 <=> predh(mary) [avatar definition]
264. ~1 | ~2 [avatar split clause 240,261,257]
271. 4 <=> room(sK0) [avatar definition]
273. room(sK0) <- (4) [avatar component clause 271]
274. 4 | ~2 [avatar split clause 238,261,271]
285. 7 <=> predb(mary) [avatar definition]
289. 8 <=> ! [X0] : (predh(X0) | ~room(X0)) [avatar definition]
290. ~room(X0) | predh(X0) <- (8) [avatar component clause 289]
291. ~7 | 8 [avatar split clause 242,289,285]
292. predb(mary) | ~room(mary) [resolution 248,255]
296. predb(mary) [subsumption resolution 292,232]
297. 7 [avatar split clause 296,285]
298. predh(mary) <- (8) [resolution 290,232]
307. 2 | ~8 [avatar split clause 298,289,261]
308. predh(sK0) <- (4, 8) [resolution 273,290]
309. $false <- (~1, 4, 8) [subsumption resolution 308,259]
310. 1 | ~4 | ~8 [avatar contradiction clause 309]
311. $false [avatar sat refutation 264,274,291,297,307,310]
% SZS output end Proof for 316172402298248814745293
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.37327 |
There is a room. "Everyone in the room either does not compete in national level swimming championships or cannot play the flute but not both" only if "everyone in the room does not host regular game nights featuring complex strategy games, is not a craft beer aficionado and does not collect vintage vinyl records". "Everyone outside the room is not an amateur astronomer who builds and uses custom telescopes, does not have completed a triathlon and does not enjoy fishing" unless "everyone anywhere cannot play the flute, does not compete in national level swimming championships and does not practice tai chi". Everyone in the room does not compete in national level swimming championships and does not practice tai chi. Someone in the room neither does not have a vast collection of first-edition science fiction novels nor does not collect historical artifacts related to ancient civilizations. Everyone in the room either does not compete in national level swimming championships or cannot play the flute but not both. Everyone in the room does not enjoy macrame, does not collect action figures and does not enjoy virtual reality gaming. Everyone in the room does not host regular game nights featuring complex strategy games, is not a craft beer aficionado and does not collect vintage vinyl records. Everyone in the room either is not a wine connoisseur or does not enjoy fishing but not both. Everyone in the room does not practice urban gardening, does not enjoy trail running and does not collect vintage vinyl records. | Everyone in the room practices urban gardening. | contradiction | (there_is_a_room)&
((![X]:(room(X)=>(((does_not_compete_in_national_level_swimming_championships(X))<~>(cannot_play_the_flute(X))))))=>(![X]:(room(X)=>(((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))&(is_not_a_craft_beer_aficionado(X))&(does_not_collect_vintage_vinyl_records(X)))))))&
(~(![X]:(anywhere(X)=>(((cannot_play_the_flute(X))&(does_not_compete_in_national_level_swimming_championships(X))&(does_not_practice_tai_chi(X))))))=>(![X]:(~room(X)=>(((is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))&(does_not_have_completed_a_triathlon(X))&(does_not_enjoy_fishing(X)))))))&
(![X]:(room(X)=>(((does_not_compete_in_national_level_swimming_championships(X))&(does_not_practice_tai_chi(X))))))&
(?[X]:(room(X)&(~((does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))|(does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))))))&
(![X]:(room(X)=>(((does_not_compete_in_national_level_swimming_championships(X))<~>(cannot_play_the_flute(X))))))&
(![X]:(room(X)=>(((does_not_enjoy_macrame(X))&(does_not_collect_action_figures(X))&(does_not_enjoy_virtual_reality_gaming(X))))))&
(![X]:(room(X)=>(((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))&(is_not_a_craft_beer_aficionado(X))&(does_not_collect_vintage_vinyl_records(X))))))&
(![X]:(room(X)=>(((is_not_a_wine_connoisseur(X))<~>(does_not_enjoy_fishing(X))))))&
(![X]:(room(X)=>(is_not_a_craft_beer_aficionado(X))))&
(![X]:(room(X)=>(((does_not_enjoy_trail_running(X))<~>(does_not_own_an_Android_phone(X))))))&
(![X]:(room(X)=>(((does_not_write_poetry(X))&(is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))&
(![X]:(room(X)=>(((is_not_a_wine_connoisseur(X))<~>(does_not_enjoy_virtual_reality_gaming(X))))))&
(![X]:(room(X)=>(((does_not_practice_urban_gardening(X))&(does_not_enjoy_trail_running(X))&(does_not_collect_vintage_vinyl_records(X)))))) | (there_is_a_room)&
![X]:(room(X)=>(practices_urban_gardening(X))) | [
"p4",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 657832500408548553379380
% SZS output start Proof for 657832500408548553379380
48. ? [X0] : (~(~predu(X0) | ~predv(X0)) & room(X0)) [input p4]
57. ! [X0] : (room(X0) => (~predj(X0) & ~predq(X0) & ~predk(X0))) [input p13]
58. ! [X0] : (room(X0) => predk(X0)) & there_is_a_room [input hypothesis]
64. ? [X0] : (~~predv(X0) & room(X0)) [pure predicate removal 48]
65. ? [X0] : room(X0) [pure predicate removal 64]
73. ! [X0] : (room(X0) => (~predq(X0) & ~predk(X0))) [pure predicate removal 57]
79. ! [X0] : (room(X0) => predk(X0)) [pure predicate removal 58]
159. ! [X0] : ((~predq(X0) & ~predk(X0)) | ~room(X0)) [ennf transformation 73]
160. ! [X0] : (predk(X0) | ~room(X0)) [ennf transformation 79]
163. ? [X0] : room(X0) => room(sK0) [choice axiom]
164. room(sK0) [skolemisation 65,163]
253. room(sK0) [cnf transformation 164]
263. ~predk(X0) | ~room(X0) [cnf transformation 159]
265. predk(X0) | ~room(X0) [cnf transformation 160]
281. ~room(X0) [subsumption resolution 265,263]
283. $false [resolution 281,253]
% SZS output end Proof for 657832500408548553379380
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0.192277 |
Linda, Mark, Margaret, Clara are the only persons in the room.
Not everyone in the room is not a strong person if they neither is not a generous calm person nor is not a quiet creative person.
Everyone in the room is not a strong person only if they is not not patient.
Everyone in the room is not not patient only if they is brave.
Clara is curious.
It is not the case that “it is not the case that “at least one person in the room is a calm humble quiet old person””.
More than one person in the room is patient.
Everyone in the room is a wise person if and only if they is not a quiet person.
Everyone in the room is funny if they is strong.
Not everyone anywhere who is a curious old person is not a wise person.
It is true that “all kind persons are tall”.
Margaret neither is not a generous calm person nor is not a quiet creative person.
Everyone in the room is not a strong person if they is a patient person.
Linda is a patient person.
Mark is not not not patient.
Everyone outside the room who either is not a calm strong curious brave person or is a wise old creative generous person but not both is quiet.
Clara is the least old in the room.
Linda is brave.
Mark is the oldest in the room.
Mark is a strong person. | Mark and Linda are not a kind persons or are kind or both. | entailment | room(linda)&room(mark)&room(margaret)&room(clara)&(![X]:(room(X)=>(X='linda'|X='mark'|X='margaret'|X='clara')))&
(~![X]:(room(X)=>(((~((~(generous(X)&calm(X)&person(X)))|(~(quiet(X)&creative(X)&person(X)))))=>(~(strong(X)&person(X)))))))&
(![X]:(room(X)=>(((~~patient(X))<=(~(strong(X)&person(X)))))))&
(![X]:(room(X)=>(((brave(X))<=(~~patient(X))))))&
(curious(clara))&
(~(~(((?[X]:(room(X)&calm(X)&humble(X)&quiet(X)&old(X)&person(X)))))))&
((?[X,Y]:(room(X)&room(Y)&(patient(X)&patient(Y))&(X!=Y))))&
(![X]:(room(X)=>(((wise(X)&person(X))<=>(~(quiet(X)&person(X)))))))&
(![X]:(room(X)=>(((strong(X))=>(funny(X))))))&
(~![X]:(anywhere(X)=>(((curious(X)&old(X)&person(X))=>(~(wise(X)&person(X)))))))&
(![X]:(kind(X)=>tall(X)))&
(~((~(generous(margaret)&calm(margaret)&person(margaret)))|(~(quiet(margaret)&creative(margaret)&person(margaret)))))&
(![X]:(room(X)=>(((patient(X)&person(X))=>(~(strong(X)&person(X)))))))&
(patient(linda)&person(linda))&
(~~~patient(mark))&
(![X]:(~room(X)=>(((((~(calm(X)&strong(X)&curious(X)&brave(X)&person(X)))<~>(wise(X)&old(X)&creative(X)&generous(X)&person(X))))=>(quiet(X))))))&
(![X]:((room(X)&(X!=clara))=>older(clara,X)))&
(brave(linda))&
(![X]:((room(X)&(X!=mark))=>older(X,mark)))&
(strong(mark)&person(mark)) | room(linda)&room(mark)&room(margaret)&room(clara)&(![X]:(room(X)=>(X='linda'|X='mark'|X='margaret'|X='clara')))&
((~(kind(mark)&person(mark)))|(kind(mark)))&((~(kind(linda)&person(linda)))|(kind(linda))) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 2685863631112061595926681
% SZS output start Proof for 2685863631112061595926681
44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
64. ~((kind(mary) | ~(person(mary) & kind(mary))) & (kind(paul) | ~(person(paul) & kind(paul))) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis]
142. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
143. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 142]
163. (~kind(mary) & (person(mary) & kind(mary))) | (~kind(paul) & (person(paul) & kind(paul))) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 64]
164. (~kind(mary) & person(mary) & kind(mary)) | (~kind(paul) & person(paul) & kind(paul)) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 163]
168. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~sP2 [predicate definition introduction]
169. (~kind(paul) & person(paul) & kind(paul)) | ~sP3 [predicate definition introduction]
170. (~kind(mary) & person(mary) & kind(mary)) | sP3 | sP2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [definition folding 164,169,168]
186. (~kind(paul) & person(paul) & kind(paul)) | ~sP3 [nnf transformation 169]
187. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~sP2 [nnf transformation 168]
188. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK9 & fred != sK9 & paul != sK9 & mary != sK9 & room(sK9)) [choice axiom]
189. (alice != sK9 & fred != sK9 & paul != sK9 & mary != sK9 & room(sK9)) | ~sP2 [skolemisation 187,188]
270. room(mary) [cnf transformation 143]
271. room(paul) [cnf transformation 143]
272. room(fred) [cnf transformation 143]
273. room(alice) [cnf transformation 143]
274. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 143]
336. kind(paul) | ~sP3 [cnf transformation 186]
338. ~kind(paul) | ~sP3 [cnf transformation 186]
339. room(sK9) | ~sP2 [cnf transformation 189]
340. mary != sK9 | ~sP2 [cnf transformation 189]
341. paul != sK9 | ~sP2 [cnf transformation 189]
342. fred != sK9 | ~sP2 [cnf transformation 189]
343. alice != sK9 | ~sP2 [cnf transformation 189]
344. kind(mary) | sP3 | sP2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 170]
346. ~kind(mary) | sP3 | sP2 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 170]
353. 1 <=> sP3 [avatar definition]
357. 2 <=> kind(paul) [avatar definition]
360. ~1 | ~2 [avatar split clause 338,357,353]
361. ~1 | 2 [avatar split clause 336,357,353]
363. 3 <=> sP2 [avatar definition]
367. 4 <=> alice = sK9 [avatar definition]
369. alice != sK9 <- (~4) [avatar component clause 367]
370. ~3 | ~4 [avatar split clause 343,367,363]
372. 5 <=> fred = sK9 [avatar definition]
374. fred != sK9 <- (~5) [avatar component clause 372]
375. ~3 | ~5 [avatar split clause 342,372,363]
377. 6 <=> paul = sK9 [avatar definition]
379. paul != sK9 <- (~6) [avatar component clause 377]
380. ~3 | ~6 [avatar split clause 341,377,363]
382. 7 <=> mary = sK9 [avatar definition]
384. mary != sK9 <- (~7) [avatar component clause 382]
385. ~3 | ~7 [avatar split clause 340,382,363]
387. 8 <=> room(sK9) [avatar definition]
389. room(sK9) <- (8) [avatar component clause 387]
390. ~3 | 8 [avatar split clause 339,387,363]
391. ~kind(mary) | sP3 | sP2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 346,273]
392. ~kind(mary) | sP3 | sP2 | ~room(paul) | ~room(mary) [subsumption resolution 391,272]
393. ~kind(mary) | sP3 | sP2 | ~room(mary) [subsumption resolution 392,271]
394. ~kind(mary) | sP3 | sP2 [subsumption resolution 393,270]
396. 9 <=> kind(mary) [avatar definition]
399. 3 | 1 | ~9 [avatar split clause 394,396,353,363]
400. kind(mary) | sP3 | sP2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 344,273]
401. kind(mary) | sP3 | sP2 | ~room(paul) | ~room(mary) [subsumption resolution 400,272]
402. kind(mary) | sP3 | sP2 | ~room(mary) [subsumption resolution 401,271]
403. kind(mary) | sP3 | sP2 [subsumption resolution 402,270]
404. 3 | 1 | 9 [avatar split clause 403,396,353,363]
696. fred = sK9 | paul = sK9 | mary = sK9 | alice = sK9 <- (8) [resolution 274,389]
765. paul = sK9 | mary = sK9 | alice = sK9 <- (~5, 8) [subsumption resolution 696,374]
766. mary = sK9 | alice = sK9 <- (~5, ~6, 8) [subsumption resolution 765,379]
767. alice = sK9 <- (~5, ~6, ~7, 8) [subsumption resolution 766,384]
768. $false <- (~4, ~5, ~6, ~7, 8) [subsumption resolution 767,369]
769. 4 | 5 | 6 | 7 | ~8 [avatar contradiction clause 768]
770. $false [avatar sat refutation 360,361,370,375,380,385,390,399,404,769]
% SZS output end Proof for 2685863631112061595926681
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.041 s
% ------------------------------
% ------------------------------
| 0.095021 |
Logan, Adam, Veronica, Mary are the only persons in the room.
“Logan is a curious person, is old and is not brave, not kind, not calm” if “Logan is a creative generous humble person” and vice versa.
“Logan who is a patient wise person is a humble strong person” unless “Logan is quiet”.
“Logan is not old, not funny” if “Logan is brave” and vice versa.
If “Logan is a humble happy kind person, is a generous calm person and is tall” then “no old person is tall”.
If “it is not the case that “Logan is not quiet”” then “all generous persons are strong” otherwise “Logan is a humble person”.
More than one person in the room is not a wise quiet person and is a wise person.
Logan is the least old in the room.
All creative persons are curious.
At least one person anywhere is not wise.
All creative persons are generous.
All brave persons are quiet.
If someone is calm then he/she is a old creative humble calm funny person.
All old persons are brave.
All tall persons are brave.
All funny persons are creative. | Everyone anywhere neither is a happy person nor is a kind happy person. | neutral | room(logan)&room(adam)&room(veronica)&room(mary)&(![X]:(room(X)=>(X='logan'|X='adam'|X='veronica'|X='mary')))&
((creative(logan)&generous(logan)&humble(logan)&person(logan))<=>(((curious(logan)&person(logan))&(old(logan))&(~brave(logan)&~kind(logan)&~calm(logan)))))&
(~(quiet(logan))=>((patient(logan)&wise(logan)&person(logan))&(humble(logan)&strong(logan)&person(logan))))&
((brave(logan))<=>(~old(logan)&~funny(logan)))&
((((humble(logan)&happy(logan)&kind(logan)&person(logan))&(generous(logan)&calm(logan)&person(logan))&(tall(logan))))=>(~?[X]:(old(X)=>tall(X))))&
(((~(~quiet(logan)))=>(![X]:(generous(X)=>strong(X))))&((~(~(~quiet(logan))))=>(humble(logan)&person(logan))))&
((?[X,Y]:(room(X)&room(Y)&(((~(wise(X)&quiet(X)&person(X)))&(wise(X)&person(X)))&((~(wise(Y)&quiet(Y)&person(Y)))&(wise(Y)&person(Y))))&(X!=Y))))&
(![X]:((room(X)&(X!=logan))=>older(logan,X)))&
(![X]:(creative(X)=>curious(X)))&
(((?[X]:(anywhere(X)&~wise(X)))))&
(![X]:(creative(X)=>generous(X)))&
(![X]:(brave(X)=>quiet(X)))&
((![X]:((calm(X))=>(old(X)&creative(X)&humble(X)&calm(X)&funny(X)&person(X)))))&
(![X]:(old(X)=>brave(X)))&
(![X]:(tall(X)=>brave(X)))&
(![X]:(funny(X)=>creative(X))) | room(logan)&room(adam)&room(veronica)&room(mary)&(![X]:(room(X)=>(X='logan'|X='adam'|X='veronica'|X='mary')))&
![X]:(anywhere(X)=>(~((happy(X)&person(X))|(kind(X)&happy(X)&person(X))))) | [] | null | 0.143697 |
Debra is the only person in the room.
If “it is true that “someone in the room regularly goes on multi-day backpacking trips in national parks”” then “it is not the case that “it is true that “someone in the room is a drone photographer”””.
Someone in the room is an avid mountain climber who has scaled several peaks.
It is not the case that “someone in the room practices urban gardening”.
It is not the case that “someone in the room does not regularly goes on multi-day backpacking trips in national parks”.
If someone enjoys salsa dancing then he/she is an avid mountain climber who has scaled several peaks. | It is not the case that “Debra practices urban gardening”. | entailment | room(debra)&(![X]:(room(X)=>(X='debra')))&
((?[X]:(room(X)&(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))=>(~(?[X]:(room(X)&(is_a_drone_photographer(X))))))&
(?[X]:(room(X)&(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))&
(~(?[X]:(room(X)&(practices_urban_gardening(X)))))&
(~(?[X]:(room(X)&(does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X)))))&
((![X]:((enjoys_salsa_dancing(X))=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X)))))&
((![X]:((enjoys_salsa_dancing(X))=>(is_a_drone_photographer(X)))))&
((![X]:((is_a_night_owl(X))=>(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))))&
(((?[X]:(~room(X)&enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X)))))&
(((?[X]:(anywhere(X)&practices_urban_gardening(X)))))&
(?[X]:(~room(X)&(enjoys_salsa_dancing(X))))&
((![X]:((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))<=>(is_a_night_owl(X)))))&
(?[X]:(room(X)&(collects_action_figures(X))))&
((debra_dream=>((![X]:((watches_fantasy_movies(X))<=>(is_a_night_owl(X)))))))&
((![X]:((is_a_drone_photographer(X))=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X)))))&
(?[X]:(room(X)&(is_a_night_owl(X)))) | room(debra)&(![X]:(room(X)=>(X='debra')))&
~(practices_urban_gardening(debra)) | [
"p0",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 6525140002407477040468216
% SZS output start Proof for 6525140002407477040468216
44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
47. ~? [X0] : (preda(X0) & room(X0)) [input p3]
60. ~(~preda(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis]
145. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
147. ! [X0] : (~preda(X0) | ~room(X0)) [ennf transformation 47]
150. preda(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 60]
165. ? [X0] : (mary != X0 & room(X0)) => (mary != sK6 & room(sK6)) [choice axiom]
166. preda(mary) | (mary != sK6 & room(sK6)) | ~room(mary) [skolemisation 150,165]
247. room(mary) [cnf transformation 145]
248. ~room(X0) | mary = X0 [cnf transformation 145]
251. ~preda(X0) | ~room(X0) [cnf transformation 147]
260. preda(mary) | room(sK6) | ~room(mary) [cnf transformation 166]
261. preda(mary) | mary != sK6 | ~room(mary) [cnf transformation 166]
269. preda(mary) | mary != sK6 [subsumption resolution 261,247]
271. 3 <=> mary = sK6 [avatar definition]
273. mary != sK6 <- (~3) [avatar component clause 271]
275. 4 <=> preda(mary) [avatar definition]
277. preda(mary) <- (4) [avatar component clause 275]
278. ~3 | 4 [avatar split clause 269,275,271]
279. preda(mary) | room(sK6) [subsumption resolution 260,247]
281. 5 <=> room(sK6) [avatar definition]
283. room(sK6) <- (5) [avatar component clause 281]
284. 5 | 4 [avatar split clause 279,275,281]
286. ~room(mary) <- (4) [resolution 251,277]
287. $false <- (4) [subsumption resolution 286,247]
288. ~4 [avatar contradiction clause 287]
299. mary = sK6 <- (5) [resolution 248,283]
306. $false <- (~3, 5) [subsumption resolution 299,273]
307. 3 | ~5 [avatar contradiction clause 306]
308. $false [avatar sat refutation 278,284,288,307]
% SZS output end Proof for 6525140002407477040468216
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.498908 |
Juan, Cynthia are the only persons in the room.
Either “Cynthia is a member of a local theater group specializing in improv” or “it is not the case that “it is not the case that “Cynthia enjoys spelunking””” but not both.
Either “Cynthia develops open-source software projects in their free time” or “Juan does enjoy mountain biking” but not both.
“Juan does not enjoy rooftop gardening or has a tattoo or both” only if “Juan enjoys rooftop gardening, enjoys spelunking and makes homemade pastries”.
“Cynthia develops open-source software projects in their free time” only if “Cynthia does not enjoy mountain biking”.
“Juan dreamt that “Juan either collects historical artifacts related to ancient civilizations or enjoys snowboarding but not both”” unless “Juan does not develop open-source software projects in their free time”.
If “Cynthia practices digital art” then “Juan has a saltwater aquarium”.
If someone hosts a popular podcast about emerging technologies then he/she enjoys rooftop gardening.
Cynthia develops open-source software projects in their free time.
If someone enjoys bird watching then he/she practices tai chi and vice versa.
Cynthia practices digital art.
At least one person in the room practices kickboxing.
It is not the case that “Cynthia has a tattoo”.
Cynthia enjoys macrame.
Cynthia makes homemade pastries.
Cynthia is a member of a local theater group specializing in improv.
Cynthia knows morse code.
Juan has a saltwater aquarium.
More than one person in the room practices kickboxing.
If someone collects historical artifacts related to ancient civilizations then he/she enjoys spelunking and does not enjoy rooftop gardening and vice versa.
Juan does not develop open-source software projects in their free time.
At least one person in the room is not a member of a local theater group specializing in improv.
At least one person in the room neither enjoys bird watching nor does not enjoy spelunking.
Juan owns a microscope.
Cynthia has completed a triathlon.
Cynthia participates in long-distance cycling events across the country. | Juan is a member of a local theater group specializing in improv. | contradiction | room(juan)&room(cynthia)&(![X]:(room(X)=>(X='juan'|X='cynthia')))&
((is_a_member_of_a_local_theater_group_specializing_in_improv(cynthia))<~>(~(~(enjoys_spelunking(cynthia)))))&
((develops_open-source_software_projects_in_their_free_time(cynthia))<~>(does_enjoy_mountain_biking(juan)))&
((((does_not_enjoy_rooftop_gardening(juan))|(has_a_tattoo(juan))))=>(((enjoys_rooftop_gardening(juan))&(enjoys_spelunking(juan))&(makes_homemade_pastries(juan)))))&
((develops_open-source_software_projects_in_their_free_time(cynthia))=>(does_not_enjoy_mountain_biking(cynthia)))&
(~(does_not_develop_open-source_software_projects_in_their_free_time(juan))=>((juan_dream=>(((collects_historical_artifacts_related_to_ancient_civilizations(juan))<~>(enjoys_snowboarding(juan)))))))&
((practices_digital_art(cynthia))=>(has_a_saltwater_aquarium(juan)))&
((![X]:((hosts_a_popular_podcast_about_emerging_technologies(X))=>(enjoys_rooftop_gardening(X)))))&
(develops_open-source_software_projects_in_their_free_time(cynthia))&
((![X]:((enjoys_bird_watching(X))<=>(practices_tai_chi(X)))))&
(practices_digital_art(cynthia))&
(((?[X]:(room(X)&practices_kickboxing(X)))))&
(~(has_a_tattoo(cynthia)))&
(enjoys_macrame(cynthia))&
(makes_homemade_pastries(cynthia))&
(is_a_member_of_a_local_theater_group_specializing_in_improv(cynthia))&
(knows_morse_code(cynthia))&
(has_a_saltwater_aquarium(juan))&
((?[X,Y]:(room(X)&room(Y)&(practices_kickboxing(X)&practices_kickboxing(Y))&(X!=Y))))&
((![X]:((collects_historical_artifacts_related_to_ancient_civilizations(X))<=>(((enjoys_spelunking(X))&(does_not_enjoy_rooftop_gardening(X)))))))&
(does_not_develop_open-source_software_projects_in_their_free_time(juan))&
(((?[X]:(room(X)&is_not_a_member_of_a_local_theater_group_specializing_in_improv(X)))))&
(((?[X]:(room(X)&~((enjoys_bird_watching(X))|(does_not_enjoy_spelunking(X)))))))&
(owns_a_microscope(juan))&
(has_completed_a_triathlon(cynthia))&
(participates_in_long-distance_cycling_events_across_the_country(cynthia)) | room(juan)&room(cynthia)&(![X]:(room(X)=>(X='juan'|X='cynthia')))&
is_a_member_of_a_local_theater_group_specializing_in_improv(juan) | [
"p0",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7479537241510736142305373
% SZS output start Proof for 7479537241510736142305373
44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0]
59. predo(paul) [input p15]
65. ? [X0] : (~predo(X0) & room(X0)) [input p21]
70. predo(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis]
163. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44]
164. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 163]
167. predo(mary) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 70]
168. predo(mary) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 167]
176. ? [X0] : (~predo(X0) & room(X0)) => (~predo(sK3) & room(sK3)) [choice axiom]
177. ~predo(sK3) & room(sK3) [skolemisation 65,176]
262. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 164]
270. predo(paul) [cnf transformation 59]
275. room(sK3) [cnf transformation 177]
276. ~predo(sK3) [cnf transformation 177]
282. predo(mary) [cnf transformation 168]
284. 1 <=> predo(paul) [avatar definition]
285. predo(paul) <- (1) [avatar component clause 284]
309. 1 [avatar split clause 270,284]
315. mary = sK3 | paul = sK3 [resolution 262,275]
345. 12 <=> paul = sK3 [avatar definition]
347. paul = sK3 <- (12) [avatar component clause 345]
349. 13 <=> mary = sK3 [avatar definition]
351. mary = sK3 <- (13) [avatar component clause 349]
352. 12 | 13 [avatar split clause 315,349,345]
367. ~predo(paul) <- (12) [backward demodulation 276,347]
368. $false <- (1, 12) [subsumption resolution 367,285]
369. ~1 | ~12 [avatar contradiction clause 368]
379. ~predo(mary) <- (13) [backward demodulation 276,351]
380. $false <- (13) [subsumption resolution 379,282]
381. ~13 [avatar contradiction clause 380]
385. $false [avatar sat refutation 309,352,369,381]
% SZS output end Proof for 7479537241510736142305373
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0.172463 |
Maria is the only person in the room.
Everyone in the room who composes and performs experimental electronic music enjoys spelunking.
Only one person in the room has a piercing.
Maria travels domestically frequently.
Everyone in the room is not a night owl or enjoys spelunking.
Everyone in the room who is not a night owl neither composes and performs experimental electronic music nor has a specialized collection of handmade artisan pottery.
Maria composes and performs experimental electronic music. | Maria has a specialized collection of handmade artisan pottery. | neutral | room(maria)&(![X]:(room(X)=>(X='maria')))&
(![X]:(room(X)=>(((composes_and_performs_experimental_electronic_music(X))=>(enjoys_spelunking(X))))))&
(((?[X]:(room(X)&has_a_piercing(X)))&(![X,Y]:((room(X)&room(Y)&(has_a_piercing(X))&(has_a_piercing(Y)))=>(X=Y)))))&
(travels_domestically_frequently(maria))&
(![X]:(room(X)=>(((enjoys_spelunking(X))|(is_not_a_night_owl(X))))))&
(![X]:(room(X)=>(((is_not_a_night_owl(X))=>(~((composes_and_performs_experimental_electronic_music(X))|(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))))&
(composes_and_performs_experimental_electronic_music(maria))&
(has_a_piercing(maria))&
(![X]:(room(X)=>(((has_a_specialized_collection_of_handmade_artisan_pottery(X))=>(enjoys_spelunking(X))))))&
(![X]:(room(X)=>(((((composes_and_performs_experimental_electronic_music(X))&(travels_domestically_frequently(X))&(is_a_night_owl(X))))<=>(travels_domestically_frequently(X)))))) | room(maria)&(![X]:(room(X)=>(X='maria')))&
has_a_specialized_collection_of_handmade_artisan_pottery(maria) | [] | null | 0.195161 |
There is a room. Everyone in the room who writes poetry practices archery. Everyone in the room who practices archery practices archery, enjoys stand-up paddleboarding and owns a 3D printer. Everyone in the room practices archery, enjoys stand-up paddleboarding and owns a 3D printer only if they enjoys stand-up paddleboarding. Efrain dreamt that “everyone in the room enjoys stand-up paddleboarding if they practices archery and vice versa”. Everyone in the room who enjoys stand-up paddleboarding writes poetry, practices archery and enjoys stand-up paddleboarding. Not everyone in the room enjoys writing detailed reviews of new and classic board games, owns a 3D printer and writes poetry if they enjoys stand-up paddleboarding and vice versa. Everyone in the room who enjoys stand-up paddleboarding owns a 3D printer. Everyone in the room neither enjoys stand-up paddleboarding nor writes poetry only if they practices archery. | Everyone in the room enjoys writing detailed reviews of new and classic board games. | contradiction | (there_is_a_room)&
(![X]:(room(X)=>(((writes_poetry(X))=>(practices_archery(X))))))&
(![X]:(room(X)=>(((practices_archery(X))=>(((practices_archery(X))&(enjoys_stand-up_paddleboarding(X))&(owns_a_3D_printer(X))))))))&
(![X]:(room(X)=>(((enjoys_stand-up_paddleboarding(X))<=(((practices_archery(X))&(enjoys_stand-up_paddleboarding(X))&(owns_a_3D_printer(X))))))))&
((efrain_dream=>(![X]:(room(X)=>(((enjoys_stand-up_paddleboarding(X))<=>(practices_archery(X))))))))&
(![X]:(room(X)=>(((enjoys_stand-up_paddleboarding(X))=>(((writes_poetry(X))&(practices_archery(X))&(enjoys_stand-up_paddleboarding(X))))))))&
(~![X]:(room(X)=>(((((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))&(owns_a_3D_printer(X))&(writes_poetry(X))))<=>(enjoys_stand-up_paddleboarding(X))))))&
(![X]:(room(X)=>(((enjoys_stand-up_paddleboarding(X))=>(owns_a_3D_printer(X))))))&
(![X]:(room(X)=>(((practices_archery(X))<=(~((enjoys_stand-up_paddleboarding(X))|(writes_poetry(X)))))))) | (there_is_a_room)&
![X]:(room(X)=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))) | [
"p1",
"p2",
"p5",
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8980664276975790318338901
% SZS output start Proof for 8980664276975790318338901
45. ! [X0] : (room(X0) => (prede(X0) => preda(X0))) [input p1]
46. ! [X0] : (room(X0) => (preda(X0) => (predb(X0) & predd(X0) & preda(X0)))) [input p2]
49. ! [X0] : (room(X0) => (predd(X0) => (predd(X0) & preda(X0) & prede(X0)))) [input p5]
50. ~! [X0] : (room(X0) => ((prede(X0) & predb(X0) & predc(X0)) <=> predd(X0))) [input p6]
52. ! [X0] : (room(X0) => (~(prede(X0) | predd(X0)) => preda(X0))) [input p8]
53. ! [X0] : (room(X0) => predc(X0)) & there_is_a_room [input hypothesis]
56. ! [X0] : (room(X0) => predc(X0)) [pure predicate removal 53]
129. ! [X0] : ((preda(X0) | ~prede(X0)) | ~room(X0)) [ennf transformation 45]
130. ! [X0] : (preda(X0) | ~prede(X0) | ~room(X0)) [flattening 129]
131. ! [X0] : (((predb(X0) & predd(X0) & preda(X0)) | ~preda(X0)) | ~room(X0)) [ennf transformation 46]
132. ! [X0] : ((predb(X0) & predd(X0) & preda(X0)) | ~preda(X0) | ~room(X0)) [flattening 131]
135. ! [X0] : (((predd(X0) & preda(X0) & prede(X0)) | ~predd(X0)) | ~room(X0)) [ennf transformation 49]
136. ! [X0] : ((predd(X0) & preda(X0) & prede(X0)) | ~predd(X0) | ~room(X0)) [flattening 135]
137. ? [X0] : (((prede(X0) & predb(X0) & predc(X0)) <~> predd(X0)) & room(X0)) [ennf transformation 50]
140. ! [X0] : ((preda(X0) | (prede(X0) | predd(X0))) | ~room(X0)) [ennf transformation 52]
141. ! [X0] : (preda(X0) | prede(X0) | predd(X0) | ~room(X0)) [flattening 140]
142. ! [X0] : (predc(X0) | ~room(X0)) [ennf transformation 56]
144. ? [X0] : (((~predd(X0) | (~prede(X0) | ~predb(X0) | ~predc(X0))) & (predd(X0) | (prede(X0) & predb(X0) & predc(X0)))) & room(X0)) [nnf transformation 137]
145. ? [X0] : ((~predd(X0) | ~prede(X0) | ~predb(X0) | ~predc(X0)) & (predd(X0) | (prede(X0) & predb(X0) & predc(X0))) & room(X0)) [flattening 144]
146. ? [X0] : ((~predd(X0) | ~prede(X0) | ~predb(X0) | ~predc(X0)) & (predd(X0) | (prede(X0) & predb(X0) & predc(X0))) & room(X0)) => ((~predd(sK0) | ~prede(sK0) | ~predb(sK0) | ~predc(sK0)) & (predd(sK0) | (prede(sK0) & predb(sK0) & predc(sK0))) & room(sK0)) [choice axiom]
147. (~predd(sK0) | ~prede(sK0) | ~predb(sK0) | ~predc(sK0)) & (predd(sK0) | (prede(sK0) & predb(sK0) & predc(sK0))) & room(sK0) [skolemisation 145,146]
228. ~prede(X0) | preda(X0) | ~room(X0) [cnf transformation 130]
230. ~preda(X0) | predd(X0) | ~room(X0) [cnf transformation 132]
231. ~preda(X0) | predb(X0) | ~room(X0) [cnf transformation 132]
233. prede(X0) | ~predd(X0) | ~room(X0) [cnf transformation 136]
236. room(sK0) [cnf transformation 147]
240. ~predd(sK0) | ~prede(sK0) | ~predb(sK0) | ~predc(sK0) [cnf transformation 147]
242. preda(X0) | prede(X0) | predd(X0) | ~room(X0) [cnf transformation 141]
243. ~room(X0) | predc(X0) [cnf transformation 142]
245. 1 <=> predc(sK0) [avatar definition]
249. 2 <=> predb(sK0) [avatar definition]
253. 3 <=> prede(sK0) [avatar definition]
254. prede(sK0) <- (3) [avatar component clause 253]
257. 4 <=> predd(sK0) [avatar definition]
260. ~1 | ~2 | ~3 | ~4 [avatar split clause 240,257,253,249,245]
264. prede(X0) | predd(X0) | ~room(X0) [subsumption resolution 242,230]
265. ~room(X0) | prede(X0) [subsumption resolution 264,233]
266. predc(sK0) [resolution 243,236]
267. 1 [avatar split clause 266,245]
268. prede(sK0) [resolution 265,236]
269. 3 [avatar split clause 268,253]
270. preda(sK0) | ~room(sK0) <- (3) [resolution 228,254]
271. preda(sK0) <- (3) [subsumption resolution 270,236]
272. predd(sK0) | ~room(sK0) <- (3) [resolution 230,271]
273. predb(sK0) | ~room(sK0) <- (3) [resolution 231,271]
277. predb(sK0) <- (3) [subsumption resolution 273,236]
278. 2 | ~3 [avatar split clause 277,253,249]
279. predd(sK0) <- (3) [subsumption resolution 272,236]
280. 4 | ~3 [avatar split clause 279,253,257]
281. $false [avatar sat refutation 260,267,269,278,280]
% SZS output end Proof for 8980664276975790318338901
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.331969 |
Betty is the only person in the room. “Everyone outside the room does not drive a hybrid car only if they hosts a YouTube channel dedicated to art tutorials” if “everyone in the room does not drive a hybrid car or plays video games”. “Everyone in the room who writes poetry is a member of a local theater group specializing in improv” unless “everyone in the room is not allergic to anything or writes poetry”. “Everyone in the room writes poetry only if they drives a hybrid car” if “everyone in the room does not travel domestically frequently or has a piercing”. Everyone anywhere who drives a hybrid car enjoys deep-sea diving and exploring underwater caves. Not everyone outside the room who is a coffee connoisseur, is a Linux enthusiast or bakes bread at home is a Linux enthusiast. Everyone in the room who is a Linux enthusiast enjoys deep-sea diving and exploring underwater caves. Everyone in the room plays video games if and only if they is allergic to anything. Everyone in the room who is a Linux enthusiast has a curated collection of mid-century modern furniture. Everyone in the room who is an avid hiker is an avid collector of autographed memorabilia from famous musicians, plays video games and has a curated collection of mid-century modern furniture. Not everyone in the room does not practice calligraphy or is an avid collector of autographed memorabilia from famous musicians, plays video games and has a curated collection of mid-century modern furniture. | Betty writes poetry. | neutral | room(betty)&(![X]:(room(X)=>(X='betty')))&
((![X]:(room(X)=>(((plays_video_games(X))|(does_not_drive_a_hybrid_car(X))))))=>(![X]:(~room(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))<=(does_not_drive_a_hybrid_car(X)))))))&
(~(![X]:(room(X)=>(((writes_poetry(X))|(is_not_allergic_to_anything(X))))))=>(![X]:(room(X)=>(((writes_poetry(X))=>(is_a_member_of_a_local_theater_group_specializing_in_improv(X)))))))&
((![X]:(room(X)=>(((has_a_piercing(X))|(does_not_travel_domestically_frequently(X))))))=>(![X]:(room(X)=>(((drives_a_hybrid_car(X))<=(writes_poetry(X)))))))&
(![X]:(anywhere(X)=>(((drives_a_hybrid_car(X))=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))&
(~![X]:(~room(X)=>(((((is_a_coffee_connoisseur(X))|(is_a_Linux_enthusiast(X))|(bakes_bread_at_home(X))))=>(is_a_Linux_enthusiast(X))))))&
(![X]:(room(X)=>(((is_a_Linux_enthusiast(X))=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X))))))&
(![X]:(room(X)=>(((plays_video_games(X))<=>(is_allergic_to_anything(X))))))&
(![X]:(room(X)=>(((is_a_Linux_enthusiast(X))=>(has_a_curated_collection_of_mid-century_modern_furniture(X))))))&
(![X]:(room(X)=>(((is_an_avid_hiker(X))=>(((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))&(plays_video_games(X))&(has_a_curated_collection_of_mid-century_modern_furniture(X))))))))&
(~![X]:(room(X)=>(((((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))&(plays_video_games(X))&(has_a_curated_collection_of_mid-century_modern_furniture(X))))|(does_not_practice_calligraphy(X))))))&
(![X]:(room(X)=>(((is_a_coffee_connoisseur(X))<=>(practices_calligraphy(X))))))&
(((?[X]:(room(X)&has_completed_a_triathlon(X)))))&
(![X]:(room(X)=>(((plays_eSports_competitively(X))=>(writes_poetry(X))))))&
((![X]:((has_completed_a_triathlon(X))=>(enjoys_deep-sea_diving_and_exploring_underwater_caves(X)))))&
((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(betty))&(writes_a_travel_blog(betty)))&
(~![X]:(room(X)=>(((travels_domestically_frequently(X))=>(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))&
(![X]:(anywhere(X)=>(((((is_an_avid_hiker(X))&(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))<=(drives_a_hybrid_car(X))))))&
(~?[X]:(anywhere(X)=>(((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))=>(((drives_a_hybrid_car(X))&(is_a_coffee_connoisseur(X))))))))&
(![X]:(room(X)=>(((((drives_a_hybrid_car(X))&(is_a_coffee_connoisseur(X))))=>(plays_video_games(X))))))&
(~![X]:(~room(X)=>(((plays_video_games(X))=>(is_allergic_to_anything(X))))))&
(![X]:(room(X)=>(((plays_video_games(X))<=(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))&
(~![X]:(anywhere(X)=>(((plays_video_games(X))=>(is_a_Linux_enthusiast(X))))))&
(![X]:(room(X)=>(((writes_poetry(X))<=(is_a_Linux_enthusiast(X))))))&
((betty_dream=>(![X]:(room(X)=>(((plays_video_games(X))<=(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X)))))))) | room(betty)&(![X]:(room(X)=>(X='betty')))&
writes_poetry(betty) | [] | null | 0.207322 |
Laura, Thomas, Alan are the only persons in the room.
“If someone does not play eSports competitively then he/she is not old, not patient and vice versa” if “Alan writes poetry”.
Laura is the quietest in the room.
If someone does not play eSports competitively then he/she is not old, not patient and vice versa.
Everyone in the room who is a client of Valerie collects vintage vinyl records.
Someone who is a client of Valerie hate someone who collect rare sneakers.
It is true that “no kind person is wise”.
Everyone in the room does not collect rare sneakers or watches fantasy movies.
Everyone in the room collects comic books only if they is right-handed.
Laura is poorer than Valerie.
Someone who collects vintage vinyl records hate someone who is a old funny creative patient calm strong tourist.
Thomas who is a old funny european is not a humble person.
Alan is not liked by Rochelle.
Everyone anywhere does not write poetry if they does not hate Rochelle.
Everyone in the room has a saltwater aquarium if they owns an extensive assortment of vintage comic book memorabilia.
Someone who enjoys origami is poorer than someone who does not hate Robert.
Alan is not quiet, plays the violin and writes poetry.
It is not the case that “Laura and Rochelle hate each other”.
Alan is a client of Valerie.
Thomas and Alan like Cheryl.
Laura owns an extensive assortment of vintage comic book memorabilia.
Alan does not drive a hybrid car and is not tall, not strong, not happy, not generous. | Alan is strong. | contradiction | room(laura)&room(thomas)&room(alan)&(![X]:(room(X)=>(X='laura'|X='thomas'|X='alan')))&
((writes_poetry(alan))=>((![X]:((does_not_play_eSports_competitively(X))<=>(~old(X)&~patient(X))))))&
(![X]:((room(X)&(X!=laura))=>quieter(X,laura)))&
((![X]:((does_not_play_eSports_competitively(X))<=>(~old(X)&~patient(X)))))&
(![X]:(room(X)=>(((client(valerie,X))=>(collects_vintage_vinyl_records(X))))))&
(?[X,Y]:((client(valerie,X))&(collect_rare_sneakers(Y))&(hate(X,Y))))&
(~?[X]:(kind(X)=>wise(X)))&
(![X]:(room(X)=>(((watches_fantasy_movies(X))|(does_not_collect_rare_sneakers(X))))))&
(![X]:(room(X)=>(((is_right-handed(X))<=(collects_comic_books(X))))))&
(poorer(valerie,laura))&
(?[X,Y]:((collects_vintage_vinyl_records(X))&(old(Y)&funny(Y)&creative(Y)&patient(Y)&calm(Y)&strong(Y)&tourist(Y))&(hate(X,Y))))&
((old(thomas)&funny(thomas)&european(thomas))&(~(humble(thomas)&person(thomas))))&
(~like(alan,rochelle))&
(![X]:(anywhere(X)=>(((~hate(rochelle,X))=>(does_not_write_poetry(X))))))&
(![X]:(room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))=>(has_a_saltwater_aquarium(X))))))&
(?[X,Y]:((enjoys_origami(X))&(~hate(robert,Y))&(poorer(X,Y))))&
(((~quiet(alan))&(plays_the_violin(alan))&(writes_poetry(alan))))&
(~((hate(laura,rochelle) & hate(rochelle,laura))))&
(client(valerie,alan))&
(like(cheryl,thomas)&like(cheryl,alan))&
(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(laura))&
((![X]:((((~(happy(X)&european(X)))|(generous(X)&wise(X)&tourist(X))|(enjoys_salsa_dancing(X))))=>(client(cheryl,X)))))&
(![X]:((room(X)&(X!=thomas))=>poorer(thomas,X)))&
(![X]:(room(X)=>(((does_not_play_eSports_competitively(X))|(is_not_a_scotch_connoisseur(X))))))&
(![X]:(room(X)=>(((is_not_a_scotch_connoisseur(X))=>(~~quiet(X))))))&
(![X]:(~room(X)=>(((~~quiet(X))=>(younger(rochelle,X))))))&
(![X]:(room(X)=>(((enjoys_camping_and_organizing_outdoor_survival_workshops(X))=>(wise(X)&strong(X)&generous(X)&european(X))))))&
(((does_not_drive_a_hybrid_car(alan))&(~tall(alan)&~strong(alan)&~happy(alan)&~generous(alan)))) | room(laura)&room(thomas)&room(alan)&(![X]:(room(X)=>(X='laura'|X='thomas'|X='alan')))&
strong(alan) | [
"p27",
"hypothesis"
] | % SZS status Unsatisfiable for 3550238769235829471721731
% SZS output start Proof for 3550238769235829471721731
71. ~generous(fred) & ~happy(fred) & ~strong(fred) & ~tall(fred) & ~prede(fred) [input p27]
72. strong(fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis]
73. ~generous(fred) & ~happy(fred) & ~strong(fred) & ~prede(fred) [pure predicate removal 71]
74. ~generous(fred) & ~happy(fred) & ~strong(fred) [pure predicate removal 73]
77. ~happy(fred) & ~strong(fred) [pure predicate removal 74]
103. ~strong(fred) [pure predicate removal 77]
191. strong(fred) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 72]
192. strong(fred) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 191]
318. ~strong(fred) [cnf transformation 103]
323. strong(fred) [cnf transformation 192]
354. $false [subsumption resolution 323,318]
% SZS output end Proof for 3550238769235829471721731
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0.062385 |
David is the only person in the room. If “everyone in the room is not a wine connoisseur or is a wine connoisseur” then “everyone in the room does not enjoy coding in Python”. “Everyone outside the room does not create bespoke furniture pieces from reclaimed wood or is a certified yoga instructor teaching classes weekly” if “everyone in the room does not have a piercing or does not host a YouTube channel dedicated to art tutorials” and vice versa. If “everyone anywhere is not a scotch connoisseur or has a tattoo” then “David who does not create large-scale murals for public art installations either creates bespoke furniture pieces from reclaimed wood or enjoys cross-country skiing but not both” otherwise “only one person in the room works on fridays”. Not everyone in the room uses a Windows laptop. Everyone in the room is a certified yoga instructor teaching classes weekly if they does not create bespoke furniture pieces from reclaimed wood and vice versa. Everyone in the room does not practice yoga if they does not create bespoke furniture pieces from reclaimed wood. Everyone in the room is a certified yoga instructor teaching classes weekly if they does practice yoga. | David does practice yoga. | contradiction | room(david)&(![X]:(room(X)=>(X='david')))&
((![X]:(room(X)=>(((is_a_wine_connoisseur(X))|(is_not_a_wine_connoisseur(X))))))=>(![X]:(room(X)=>(does_not_enjoy_coding_in_Python(X)))))&
((![X]:(room(X)=>(((does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))|(does_not_have_a_piercing(X))))))<=>(![X]:(~room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))|(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X)))))))&
(((![X]:(anywhere(X)=>(((has_a_tattoo(X))|(is_not_a_scotch_connoisseur(X))))))=>((does_not_create_large-scale_murals_for_public_art_installations(david))&(((creates_bespoke_furniture_pieces_from_reclaimed_wood(david))<~>(enjoys_cross-country_skiing(david))))))&((~(![X]:(anywhere(X)=>(((has_a_tattoo(X))|(is_not_a_scotch_connoisseur(X)))))))=>(((?[X]:(room(X)&works_on_fridays(X)))&(![X,Y]:((room(X)&room(Y)&(works_on_fridays(X))&(works_on_fridays(Y)))=>(X=Y)))))))&
(~![X]:(room(X)=>(uses_a_Windows_laptop(X))))&
(![X]:(room(X)=>(((writes_and_illustrates_their_own_graphic_novels(X))=>(uses_a_Windows_laptop(X))))))&
(![X]:(anywhere(X)=>(((has_a_tattoo(X))|(is_not_a_scotch_connoisseur(X))))))&
(![X]:(room(X)=>(((does_not_host_a_YouTube_channel_dedicated_to_art_tutorials(X))|(does_not_have_a_piercing(X))))))&
(![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))<=>(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))))&
(![X]:(room(X)=>(((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))=>(does_not_practice_yoga(X))))))&
(![X]:(~room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))|(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))))&
(![X]:(room(X)=>(((((is_a_wine_connoisseur(X))|(is_not_a_scotch_connoisseur(X))))=>(enjoys_coding_in_Python(X))))))&
(![X]:(room(X)=>(((enjoys_macrame(X))<~>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))&
(![X]:(room(X)=>(((does_practice_yoga(X))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))&
((does_not_create_large-scale_murals_for_public_art_installations(david))&(((creates_bespoke_furniture_pieces_from_reclaimed_wood(david))<~>(enjoys_cross-country_skiing(david)))))&
(![X]:(room(X)=>(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))&
(![X]:(room(X)=>(((enjoys_macrame(X))=>(does_not_create_large-scale_murals_for_public_art_installations(X))))))&
(![X]:(room(X)=>(((does_not_create_large-scale_murals_for_public_art_installations(X))=>(does_not_collect_rare_and_antique_scientific_instruments(X)))))) | room(david)&(![X]:(room(X)=>(X='david')))&
does_practice_yoga(david) | [
"p0",
"p8",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7270999799740723883168758
% SZS output start Proof for 7270999799740723883168758
44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
52. ! [X0] : (room(X0) => (predl(X0) <=> ~predt(X0))) [input p8]
53. ! [X0] : (room(X0) => (~predt(X0) => ~predw(X0))) [input p9]
57. ! [X0] : (room(X0) => (predw(X0) => predl(X0))) [input p13]
62. predw(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis]
144. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
156. ! [X0] : ((predl(X0) <=> ~predt(X0)) | ~room(X0)) [ennf transformation 52]
157. ! [X0] : ((~predw(X0) | predt(X0)) | ~room(X0)) [ennf transformation 53]
158. ! [X0] : (~predw(X0) | predt(X0) | ~room(X0)) [flattening 157]
164. ! [X0] : ((predl(X0) | ~predw(X0)) | ~room(X0)) [ennf transformation 57]
165. ! [X0] : (predl(X0) | ~predw(X0) | ~room(X0)) [flattening 164]
166. predw(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 62]
183. ! [X0] : (((predl(X0) | predt(X0)) & (~predt(X0) | ~predl(X0))) | ~room(X0)) [nnf transformation 156]
267. room(mary) [cnf transformation 144]
290. ~predt(X0) | ~predl(X0) | ~room(X0) [cnf transformation 183]
292. ~predw(X0) | predt(X0) | ~room(X0) [cnf transformation 158]
298. ~predw(X0) | predl(X0) | ~room(X0) [cnf transformation 165]
303. predw(mary) [cnf transformation 166]
379. 17 <=> predt(mary) [avatar definition]
380. predt(mary) <- (17) [avatar component clause 379]
403. ~predl(mary) | ~room(mary) <- (17) [resolution 290,380]
404. ~predl(mary) <- (17) [subsumption resolution 403,267]
406. predt(mary) | ~room(mary) [resolution 292,303]
431. predl(mary) | ~room(mary) [resolution 298,303]
432. ~room(mary) <- (17) [subsumption resolution 431,404]
433. $false <- (17) [subsumption resolution 432,267]
434. ~17 [avatar contradiction clause 433]
436. predt(mary) [subsumption resolution 406,267]
437. 17 [avatar split clause 436,379]
438. $false [avatar sat refutation 434,437]
% SZS output end Proof for 7270999799740723883168758
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0.476674 |
Everyone in the room practices zumba and writes and illustrates their own graphic novels.
Everyone in the room does not play eSports competitively and practices zumba if they neither does not practice zumba nor does not write and illustrates their own graphic novels.
If someone does not practice zumba then he/she does not play eSports competitively.
Everyone outside the room either does not practice zumba or does not play eSports competitively but not both. | Kenneth plays eSports competitively. | contradiction | room(christine)&room(kenneth)&room(roger)&room(darren)&room(myra)&(![X]:(room(X)=>(X='christine'|X='kenneth'|X='roger'|X='darren'|X='myra')))&
(~![X]:(anywhere(X)=>(~((practices_zumba(X))|(does_not_write_and_illustrates_their_own_graphic_novels(X))))))&
(![X]:(room(X)=>(((practices_zumba(X))&(writes_and_illustrates_their_own_graphic_novels(X))))))&
(![X]:(room(X)=>(((~((does_not_practice_zumba(X))|(does_not_write_and_illustrates_their_own_graphic_novels(X))))=>(((does_not_play_eSports_competitively(X))&(practices_zumba(X))))))))&
((![X]:((does_not_practice_zumba(X))=>(does_not_play_eSports_competitively(X)))))&
(![X]:(~room(X)=>(((does_not_practice_zumba(X))<~>(does_not_play_eSports_competitively(X))))))&
(![X]:(room(X)=>(((practices_zumba(X))&(does_not_play_eSports_competitively(X)))))) | room(christine)&room(kenneth)&room(roger)&room(darren)&room(myra)&(![X]:(room(X)=>(X='christine'|X='kenneth'|X='roger'|X='darren'|X='myra')))&
plays_eSports_competitively(kenneth) | [
"p2",
"p3",
"p4",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 8177674940751593169979624
% SZS output start Proof for 8177674940751593169979624
46. ! [X0] : (room(X0) => (predc(X0) & predb(X0))) [input p2]
47. ! [X0] : (room(X0) => (~(~predc(X0) | ~predb(X0)) => (predb(X0) & ~preda(X0)))) [input p3]
48. ! [X0] : (~predb(X0) => ~preda(X0)) [input p4]
49. ! [X0] : (~room(X0) => (~predb(X0) <~> ~preda(X0))) [input p5]
51. preda(paul) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis]
128. ! [X0] : ((predc(X0) & predb(X0)) | ~room(X0)) [ennf transformation 46]
129. ! [X0] : (((predb(X0) & ~preda(X0)) | (~predc(X0) | ~predb(X0))) | ~room(X0)) [ennf transformation 47]
130. ! [X0] : ((predb(X0) & ~preda(X0)) | ~predc(X0) | ~predb(X0) | ~room(X0)) [flattening 129]
131. ! [X0] : (~preda(X0) | predb(X0)) [ennf transformation 48]
132. ! [X0] : ((~predb(X0) <~> ~preda(X0)) | room(X0)) [ennf transformation 49]
134. preda(paul) & ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 51]
135. preda(paul) & ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 134]
139. ! [X0] : (((preda(X0) | predb(X0)) & (~preda(X0) | ~predb(X0))) | room(X0)) [nnf transformation 132]
227. predb(X0) | ~room(X0) [cnf transformation 128]
228. predc(X0) | ~room(X0) [cnf transformation 128]
229. ~preda(X0) | ~predc(X0) | ~predb(X0) | ~room(X0) [cnf transformation 130]
231. ~preda(X0) | predb(X0) [cnf transformation 131]
232. ~preda(X0) | ~predb(X0) | room(X0) [cnf transformation 139]
233. preda(X0) | predb(X0) | room(X0) [cnf transformation 139]
242. preda(paul) [cnf transformation 135]
252. ~preda(X0) | ~predb(X0) | ~room(X0) [subsumption resolution 229,228]
253. ~preda(X0) | ~room(X0) [subsumption resolution 252,227]
254. predb(X0) | room(X0) [subsumption resolution 233,231]
255. predb(X0) [subsumption resolution 254,227]
256. ~preda(X0) | room(X0) [subsumption resolution 232,255]
257. ~preda(X0) [subsumption resolution 256,253]
258. $false [subsumption resolution 242,257]
% SZS output end Proof for 8177674940751593169979624
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0.470114 |
There is a room.
'Everyone in the room hosts regular game nights featuring complex strategy games if they collects vintage vinyl records' if 'everyone in the room does not own a significant collection of rare gemstones and minerals or owns an Android phone'.
'Everyone in the room who does not practice digital art is not a certified scuba diver with advanced underwater photography skills' if 'everyone in the room does not practice digital art or hosts a YouTube channel dedicated to art tutorials'.
More than one person in the room is a Linux enthusiast.
Everyone in the room composes and performs experimental electronic music if they does not enjoy stargazing, owns a significant collection of rare gemstones and minerals or uses a Windows laptop.
Not everyone anywhere plays the drums if they composes and performs experimental electronic music.
Everyone in the room who plays the drums owns an Android phone.
Someone outside the room enjoys wildlife photography.
If someone knows morse code then he/she uses a Windows laptop.
More than one person in the room hosts regular game nights featuring complex strategy games or enjoys wildlife photography or both.
Everyone in the room plays the drums if they is a certified scuba diver with advanced underwater photography skills, creates YouTube content and is not a wine connoisseur with a private cellar of vintage wines.
Not everyone in the room is not an active member of a local robotics club only if they is a skilled home brewer experimenting with craft beer recipes, does not write poetry and hosts a popular podcast about emerging technologies.
Everyone outside the room practices digital art or hosts a YouTube channel dedicated to art tutorials or both only if they collects antique clocks.
Everyone in the room who composes and performs experimental electronic music and hosts regular game nights featuring complex strategy games knows morse code.
Everyone in the room who knows morse code collects antique clocks.
Everyone in the room who is a certified scuba diver with advanced underwater photography skills is a Linux enthusiast, is a certified scuba diver with advanced underwater photography skills and does not know morse code.
Everyone in the room who does not collect antique clocks either enjoys stargazing or is a wine connoisseur with a private cellar of vintage wines but not both.
Everyone in the room who composes and performs experimental electronic music hosts regular game nights featuring complex strategy games. | Everyone in the room is not a skilled home brewer experimenting with craft beer recipes or practices digital art. | neutral | (there_is_a_room)&
((![X]:(room(X)=>(((owns_an_Android_phone(X))|(does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))))))=>(![X]:(room(X)=>(((collects_vintage_vinyl_records(X))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X)))))))&
((![X]:(room(X)=>(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))|(does_not_practice_digital_art(X))))))=>(![X]:(room(X)=>(((does_not_practice_digital_art(X))=>(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))))))&
((?[X,Y]:(room(X)&room(Y)&(is_a_Linux_enthusiast(X)&is_a_Linux_enthusiast(Y))&(X!=Y))))&
(![X]:(room(X)=>(((((does_not_enjoy_stargazing(X))|(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))|(uses_a_Windows_laptop(X))))=>(composes_and_performs_experimental_electronic_music(X))))))&
(~![X]:(anywhere(X)=>(((composes_and_performs_experimental_electronic_music(X))=>(plays_the_drums(X))))))&
(![X]:(room(X)=>(((plays_the_drums(X))=>(owns_an_Android_phone(X))))))&
(?[X]:(~room(X)&(enjoys_wildlife_photography(X))))&
((![X]:((knows_morse_code(X))=>(uses_a_Windows_laptop(X)))))&
((?[X,Y]:(room(X)&room(Y)&(((hosts_regular_game_nights_featuring_complex_strategy_games(X))|(enjoys_wildlife_photography(X)))&((hosts_regular_game_nights_featuring_complex_strategy_games(Y))|(enjoys_wildlife_photography(Y))))&(X!=Y))))&
(![X]:(room(X)=>(((((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))&(creates_YouTube_content(X))&(is_not_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))=>(plays_the_drums(X))))))&
(~![X]:(room(X)=>(((((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))&(does_not_write_poetry(X))&(hosts_a_popular_podcast_about_emerging_technologies(X))))<=(is_not_an_active_member_of_a_local_robotics_club(X))))))&
(![X]:(~room(X)=>(((collects_antique_clocks(X))<=(((practices_digital_art(X))|(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))))&
(![X]:(room(X)=>(((((composes_and_performs_experimental_electronic_music(X))&(hosts_regular_game_nights_featuring_complex_strategy_games(X))))=>(knows_morse_code(X))))))&
(![X]:(room(X)=>(((knows_morse_code(X))=>(collects_antique_clocks(X))))))&
(![X]:(room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))=>(((is_a_Linux_enthusiast(X))&(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))&(does_not_know_morse_code(X))))))))&
(![X]:(room(X)=>(((does_not_collect_antique_clocks(X))=>(((enjoys_stargazing(X))<~>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))))))))&
(![X]:(room(X)=>(((composes_and_performs_experimental_electronic_music(X))=>(hosts_regular_game_nights_featuring_complex_strategy_games(X))))))&
(![X]:(room(X)=>(((owns_a_smartwatch(X))=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))&
(![X]:(room(X)=>(((is_a_Linux_enthusiast(X))=>(enjoys_stargazing(X))))))&
(![X]:(room(X)=>(((enjoys_stargazing(X))=>(composes_and_performs_experimental_electronic_music(X))))))&
(![X]:(room(X)=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))&
((![X]:((((collects_antique_clocks(X))&(uses_a_Windows_laptop(X))))=>(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))) | (there_is_a_room)&
![X]:(room(X)=>(((practices_digital_art(X))|(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))))) | [] | null | 0.067341 |
Jerry, Joseph, Marcus, Maria, Jennifer are the only persons in the room.
Someone in the room enjoys kayaking.
Jerry has lived in exactly three countries.
At least one person in the room collects action figures.
Everyone in the room who neither does not collect action figures nor hosts a YouTube channel dedicated to art tutorials enjoys wildlife photography or owns an extensive assortment of vintage comic book memorabilia or both.
Joseph is a night owl.
Jerry collects action figures.
Jerry who enjoys kayaking collects action figures.
Jerry is a night owl.
Joseph either has lived in exactly three countries or has a pet dog but not both.
Joseph collects action figures.
Someone in the room has lived in exactly three countries.
Everyone in the room is a night owl or enjoys kayaking or both. | Not everyone in the room enjoys wildlife photography. | neutral | room(jerry)&room(joseph)&room(marcus)&room(maria)&room(jennifer)&(![X]:(room(X)=>(X='jerry'|X='joseph'|X='marcus'|X='maria'|X='jennifer')))&
(?[X]:(room(X)&(enjoys_kayaking(X))))&
(has_lived_in_exactly_three_countries(jerry))&
(((?[X]:(room(X)&collects_action_figures(X)))))&
(![X]:(room(X)=>(((~((does_not_collect_action_figures(X))|(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))=>(((enjoys_wildlife_photography(X))|(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))))))&
(is_a_night_owl(joseph))&
(collects_action_figures(jerry))&
((enjoys_kayaking(jerry))&(collects_action_figures(jerry)))&
(is_a_night_owl(jerry))&
(((has_lived_in_exactly_three_countries(joseph))<~>(has_a_pet_dog(joseph))))&
(collects_action_figures(joseph))&
(?[X]:(room(X)&(has_lived_in_exactly_three_countries(X))))&
(![X]:(room(X)=>(((is_a_night_owl(X))|(enjoys_kayaking(X))))))&
(collects_antique_jewelry(joseph))&
(?[X]:(room(X)&(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))&
(![X]:(~room(X)=>(((enjoys_wildlife_photography(X))=>(~((has_lived_in_exactly_three_countries(X))|(knows_morse_code(X)))))))) | room(jerry)&room(joseph)&room(marcus)&room(maria)&room(jennifer)&(![X]:(room(X)=>(X='jerry'|X='joseph'|X='marcus'|X='maria'|X='jennifer')))&
~![X]:(room(X)=>(enjoys_wildlife_photography(X))) | [] | null | 0 |
Oscar, Maria are the only persons in the room. If “someone outside the room plays the drums” then “Oscar either uses an ios phone or bakes bread at home but not both”. If “Oscar bakes bread at home” then “everyone in the room enjoys kayaking and exploring remote waterways”. | Oscar bakes bread at home. | neutral | room(oscar)&room(maria)&(![X]:(room(X)=>(X='oscar'|X='maria')))&
((?[X]:(~room(X)&(plays_the_drums(X))))=>(((uses_an_ios_phone(oscar))<~>(bakes_bread_at_home(oscar)))))&
((bakes_bread_at_home(oscar))=>(![X]:(room(X)=>(enjoys_kayaking_and_exploring_remote_waterways(X)))))&
(((is_a_tea_enthusiast(oscar))=>(~?[X]:(room(X)=>(((does_not_enjoy_logic_puzzles(X))|(does_not_bake_bread_at_home(X)))))))&((~(is_a_tea_enthusiast(oscar)))=>(has_a_piercing(oscar))))&
(~(![X]:(room(X)=>(((has_a_piercing(X))|(does_not_use_an_ios_phone(X))))))=>(![X]:(room(X)=>(((practices_digital_art(X))=>(((practices_and_performs_acrobatic_dance_routines(X))<~>(practices_digital_art(X)))))))))&
(![X]:(room(X)=>(((does_not_use_an_ios_phone(X))<=>(enjoys_kayaking_and_exploring_remote_waterways(X))))))&
(![X]:(room(X)=>(((has_a_piercing(X))|(does_not_use_an_ios_phone(X))))))&
(does_not_practice_zumba(maria))&
(can_play_the_piano(maria))&
(![X]:(~room(X)=>(((does_not_use_an_ios_phone(X))|(practices_digital_art(X))))))&
(![X]:(room(X)=>(((practices_digital_art(X))=>(can_play_the_piano(X))))))&
(((plays_the_drums(maria))&(does_not_practice_zumba(maria))))&
((practices_and_performs_acrobatic_dance_routines(oscar))&(enjoys_kayaking_and_exploring_remote_waterways(oscar)))&
(enjoys_logic_puzzles(maria))&
((?[X,Y]:(room(X)&room(Y)&(enjoys_logic_puzzles(X)&enjoys_logic_puzzles(Y))&(X!=Y))))&
(![X]:(room(X)=>(((can_play_the_piano(X))<=(((uses_an_ios_phone(X))|(can_play_the_piano(X))|(bakes_bread_at_home(X)))))))) | room(oscar)&room(maria)&(![X]:(room(X)=>(X='oscar'|X='maria')))&
bakes_bread_at_home(oscar) | [] | null | 0.045409 |
Bridget, Thomas are the only persons in the room.
Everyone in the room does not use contact lenses, does not have a curated collection of mid-century modern furniture or is not an avid collector of autographed memorabilia from famous musicians.
Everyone in the room does not work on fridays.
Everyone outside the room is not an enthusiastic bird watcher who travels for rare sightings.
Everyone in the room does not collect vintage stamps.
Everyone in the room does not create bespoke furniture pieces from reclaimed wood.
Everyone in the room does not have a curated collection of mid-century modern furniture.
Everyone in the room does not enjoy fishing.
Bridget is not a client of Meta, does not practice urban gardening or is not passionate about collecting and restoring classic cars.
Everyone in the room does not use contact lenses.
Bridget does not have a curated collection of mid-century modern furniture.
Not everyone in the room neither does not use contact lenses nor does not practice urban gardening.
Everyone in the room is not dedicated to sustainable living and zero-waste practices and is passionate about collecting and restoring classic cars.
Everyone in the room is not an enthusiastic bird watcher who travels for rare sightings or does not use a Windows laptop or both. | Thomas either does not use a Windows laptop or is not passionate about collecting and restoring classic cars but not both. | neutral | room(bridget)&room(thomas)&(![X]:(room(X)=>(X='bridget'|X='thomas')))&
(![X]:(room(X)=>(((does_not_use_contact_lenses(X))|(does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))|(is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))&
(![X]:(room(X)=>(does_not_work_on_fridays(X))))&
(![X]:(~room(X)=>(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))&
(![X]:(room(X)=>(does_not_collect_vintage_stamps(X))))&
(![X]:(room(X)=>(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))))&
(![X]:(room(X)=>(does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))))&
(![X]:(room(X)=>(does_not_enjoy_fishing(X))))&
(((is_not_a_client_of_Meta(bridget))|(does_not_practice_urban_gardening(bridget))|(is_not_passionate_about_collecting_and_restoring_classic_cars(bridget))))&
(![X]:(room(X)=>(does_not_use_contact_lenses(X))))&
(does_not_have_a_curated_collection_of_mid-century_modern_furniture(bridget))&
(~![X]:(room(X)=>(~((does_not_use_contact_lenses(X))|(does_not_practice_urban_gardening(X))))))&
(![X]:(room(X)=>(((is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))&(is_passionate_about_collecting_and_restoring_classic_cars(X))))))&
(![X]:(room(X)=>(((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(does_not_use_a_Windows_laptop(X)))))) | room(bridget)&room(thomas)&(![X]:(room(X)=>(X='bridget'|X='thomas')))&
((does_not_use_a_Windows_laptop(thomas))<~>(is_not_passionate_about_collecting_and_restoring_classic_cars(thomas))) | [] | null | 0.377472 |
Todd, Francis are the only persons in the room.
Either “Todd neither enjoys kayaking nor regularly goes on multi-day backpacking trips in national parks” or “everyone anywhere enjoys camping and organizing outdoor survival workshops or does not practice and performs acrobatic dance routines” but not both.
“Everyone anywhere hosts regular workshops on creative writing if they has a curated collection of mid-century modern furniture” if “not everyone in the room has a curated collection of mid-century modern furniture or does not enjoy camping and organizing outdoor survival workshops”.
“Everyone in the room who enjoys fishing enjoys origami” if “everyone in the room enjoys fishing or does not own a smartwatch”.
If “no one in the room enjoys logic puzzles or is not a member of a local theater group specializing in improv” then “everyone in the room enjoys logic puzzles only if they owns a smartwatch”.
Either “everyone in the room enjoys fishing or does not practice archery” or “everyone in the room is a member of a local theater group specializing in improv or does not own a smartwatch” but not both.
Todd regularly goes on multi-day backpacking trips in national parks.
Everyone outside the room is a drone photographer if they watches fantasy movies.
Todd does not practice and performs acrobatic dance routines.
Everyone in the room who either has a piercing or writes a travel blog but not both participates in citizen science projects related to wildlife monitoring.
Everyone in the room who participates in citizen science projects related to wildlife monitoring develops open-source software projects in their free time.
Everyone in the room hosts regular workshops on creative writing only if they has a curated collection of mid-century modern furniture.
Everyone in the room who has a curated collection of mid-century modern furniture owns a smartwatch.
Everyone in the room who owns a smartwatch neither enjoys fishing nor develops open-source software projects in their free time.
Everyone in the room practices archery if they neither enjoys fishing nor develops open-source software projects in their free time.
Francis does not enjoy logic puzzles.
Everyone in the room who does not enjoy fishing enjoys origami.
Everyone in the room collects classic novels if they has a curated collection of mid-century modern furniture.
If someone does not own a significant collection of rare gemstones and minerals then he/she enjoys camping and organizing outdoor survival workshops and vice versa.
Todd has a curated collection of mid-century modern furniture. | Todd is a member of a local theater group specializing in improv. | entailment | room(todd)&room(francis)&(![X]:(room(X)=>(X='todd'|X='francis')))&
((~((enjoys_kayaking(todd))|(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(todd))))<~>(![X]:(anywhere(X)=>(((does_not_practice_and_performs_acrobatic_dance_routines(X))|(enjoys_camping_and_organizing_outdoor_survival_workshops(X)))))))&
((~![X]:(room(X)=>(((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))|(has_a_curated_collection_of_mid-century_modern_furniture(X))))))=>(![X]:(anywhere(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(hosts_regular_workshops_on_creative_writing(X)))))))&
((![X]:(room(X)=>(((does_not_own_a_smartwatch(X))|(enjoys_fishing(X))))))=>(![X]:(room(X)=>(((enjoys_fishing(X))=>(enjoys_origami(X)))))))&
((~?[X]:(room(X)=>(((is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))|(enjoys_logic_puzzles(X))))))=>(![X]:(room(X)=>(((owns_a_smartwatch(X))<=(enjoys_logic_puzzles(X)))))))&
((![X]:(room(X)=>(((does_not_practice_archery(X))|(enjoys_fishing(X))))))<~>(![X]:(room(X)=>(((does_not_own_a_smartwatch(X))|(is_a_member_of_a_local_theater_group_specializing_in_improv(X)))))))&
(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(todd))&
(![X]:(~room(X)=>(((watches_fantasy_movies(X))=>(is_a_drone_photographer(X))))))&
(does_not_practice_and_performs_acrobatic_dance_routines(todd))&
(![X]:(room(X)=>(((((has_a_piercing(X))<~>(writes_a_travel_blog(X))))=>(participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))))))&
(![X]:(room(X)=>(((participates_in_citizen_science_projects_related_to_wildlife_monitoring(X))=>(develops_open-source_software_projects_in_their_free_time(X))))))&
(![X]:(room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))<=(hosts_regular_workshops_on_creative_writing(X))))))&
(![X]:(room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(owns_a_smartwatch(X))))))&
(![X]:(room(X)=>(((owns_a_smartwatch(X))=>(~((enjoys_fishing(X))|(develops_open-source_software_projects_in_their_free_time(X))))))))&
(![X]:(room(X)=>(((~((enjoys_fishing(X))|(develops_open-source_software_projects_in_their_free_time(X))))=>(practices_archery(X))))))&
(does_not_enjoy_logic_puzzles(francis))&
(![X]:(room(X)=>(((does_not_enjoy_fishing(X))=>(enjoys_origami(X))))))&
(![X]:(room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(collects_classic_novels(X))))))&
((![X]:((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))<=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X)))))&
(has_a_curated_collection_of_mid-century_modern_furniture(todd))&
(![X]:(room(X)=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))=>(collects_classic_novels(X))))))&
(writes_a_travel_blog(todd)) | room(todd)&room(francis)&(![X]:(room(X)=>(X='todd'|X='francis')))&
is_a_member_of_a_local_theater_group_specializing_in_improv(todd) | [
"p0",
"p5",
"p12",
"p13",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 445884653870776648668108
% SZS output start Proof for 445884653870776648668108
44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0]
49. ! [X0] : (room(X0) => (predw(X0) | ~predn(X0))) <~> ! [X0] : (room(X0) => (predj(X0) | ~predo(X0))) [input p5]
56. ! [X0] : (room(X0) => (predb(X0) => predo(X0))) [input p12]
57. ! [X0] : (room(X0) => (predo(X0) => ~(preda(X0) | predw(X0)))) [input p13]
58. ! [X0] : (room(X0) => (~(preda(X0) | predw(X0)) => predn(X0))) [input p14]
63. predb(mary) [input p19]
66. ~(predj(mary) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary)) [input hypothesis]
70. ! [X0] : (room(X0) => (predw(X0) | ~predn(X0))) <~> ! [X1] : (room(X1) => (predj(X1) | ~predo(X1))) [rectify 49]
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]
155. ! [X0] : ((predw(X0) | ~predn(X0)) | ~room(X0)) <~> ! [X1] : ((predj(X1) | ~predo(X1)) | ~room(X1)) [ennf transformation 70]
156. ! [X0] : (predw(X0) | ~predn(X0) | ~room(X0)) <~> ! [X1] : (predj(X1) | ~predo(X1) | ~room(X1)) [flattening 155]
163. ! [X0] : ((predo(X0) | ~predb(X0)) | ~room(X0)) [ennf transformation 56]
164. ! [X0] : (predo(X0) | ~predb(X0) | ~room(X0)) [flattening 163]
165. ! [X0] : (((~preda(X0) & ~predw(X0)) | ~predo(X0)) | ~room(X0)) [ennf transformation 57]
166. ! [X0] : ((~preda(X0) & ~predw(X0)) | ~predo(X0) | ~room(X0)) [flattening 165]
167. ! [X0] : ((predn(X0) | (preda(X0) | predw(X0))) | ~room(X0)) [ennf transformation 58]
168. ! [X0] : (predn(X0) | preda(X0) | predw(X0) | ~room(X0)) [flattening 167]
169. ~predj(mary) | ? [X0] : ((paul != X0 & mary != X0) & room(X0)) | ~room(paul) | ~room(mary) [ennf transformation 66]
170. ~predj(mary) | ? [X0] : (paul != X0 & mary != X0 & room(X0)) | ~room(paul) | ~room(mary) [flattening 169]
181. (? [X1] : (~predj(X1) & predo(X1) & room(X1)) | ? [X0] : (~predw(X0) & predn(X0) & room(X0))) & (! [X1] : (predj(X1) | ~predo(X1) | ~room(X1)) | ! [X0] : (predw(X0) | ~predn(X0) | ~room(X0))) [nnf transformation 156]
182. (? [X0] : (~predj(X0) & predo(X0) & room(X0)) | ? [X1] : (~predw(X1) & predn(X1) & room(X1))) & (! [X2] : (predj(X2) | ~predo(X2) | ~room(X2)) | ! [X3] : (predw(X3) | ~predn(X3) | ~room(X3))) [rectify 181]
183. ? [X0] : (~predj(X0) & predo(X0) & room(X0)) => (~predj(sK2) & predo(sK2) & room(sK2)) [choice axiom]
184. ? [X1] : (~predw(X1) & predn(X1) & room(X1)) => (~predw(sK3) & predn(sK3) & room(sK3)) [choice axiom]
185. ((~predj(sK2) & predo(sK2) & room(sK2)) | (~predw(sK3) & predn(sK3) & room(sK3))) & (! [X2] : (predj(X2) | ~predo(X2) | ~room(X2)) | ! [X3] : (predw(X3) | ~predn(X3) | ~room(X3))) [skolemisation 182,184,183]
187. ? [X0] : (paul != X0 & mary != X0 & room(X0)) => (paul != sK4 & mary != sK4 & room(sK4)) [choice axiom]
188. ~predj(mary) | (paul != sK4 & mary != sK4 & room(sK4)) | ~room(paul) | ~room(mary) [skolemisation 170,187]
270. room(mary) [cnf transformation 148]
271. room(paul) [cnf transformation 148]
272. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 148]
280. predj(X2) | ~predo(X2) | ~room(X2) | predw(X3) | ~predn(X3) | ~room(X3) [cnf transformation 185]
296. ~predb(X0) | predo(X0) | ~room(X0) [cnf transformation 164]
297. ~predw(X0) | ~predo(X0) | ~room(X0) [cnf transformation 166]
298. ~preda(X0) | ~predo(X0) | ~room(X0) [cnf transformation 166]
299. ~room(X0) | preda(X0) | predw(X0) | predn(X0) [cnf transformation 168]
301. predb(mary) [cnf transformation 63]
303. ~predj(mary) | room(sK4) | ~room(paul) | ~room(mary) [cnf transformation 188]
304. ~predj(mary) | mary != sK4 | ~room(paul) | ~room(mary) [cnf transformation 188]
305. ~predj(mary) | paul != sK4 | ~room(paul) | ~room(mary) [cnf transformation 188]
389. 18 <=> ! [X3] : (predw(X3) | ~room(X3) | ~predn(X3)) [avatar definition]
390. ~predn(X3) | ~room(X3) | predw(X3) <- (18) [avatar component clause 389]
392. 19 <=> ! [X2] : (predj(X2) | ~room(X2) | ~predo(X2)) [avatar definition]
393. ~predo(X2) | ~room(X2) | predj(X2) <- (19) [avatar component clause 392]
394. 18 | 19 [avatar split clause 280,392,389]
396. ~predj(mary) | paul != sK4 | ~room(mary) [subsumption resolution 305,271]
397. ~predj(mary) | paul != sK4 [subsumption resolution 396,270]
399. 20 <=> paul = sK4 [avatar definition]
401. paul != sK4 <- (~20) [avatar component clause 399]
403. 21 <=> predj(mary) [avatar definition]
406. ~20 | ~21 [avatar split clause 397,403,399]
407. ~predj(mary) | mary != sK4 | ~room(mary) [subsumption resolution 304,271]
408. ~predj(mary) | mary != sK4 [subsumption resolution 407,270]
410. 22 <=> mary = sK4 [avatar definition]
412. mary != sK4 <- (~22) [avatar component clause 410]
413. ~22 | ~21 [avatar split clause 408,403,410]
414. ~predj(mary) | room(sK4) | ~room(mary) [subsumption resolution 303,271]
415. ~predj(mary) | room(sK4) [subsumption resolution 414,270]
417. 23 <=> room(sK4) [avatar definition]
419. room(sK4) <- (23) [avatar component clause 417]
420. 23 | ~21 [avatar split clause 415,403,417]
421. predo(mary) | ~room(mary) [resolution 296,301]
422. predo(mary) [subsumption resolution 421,270]
491. preda(mary) | predw(mary) | predn(mary) [resolution 299,270]
498. 30 <=> predn(mary) [avatar definition]
500. predn(mary) <- (30) [avatar component clause 498]
502. 31 <=> predw(mary) [avatar definition]
503. ~predw(mary) <- (~31) [avatar component clause 502]
504. predw(mary) <- (31) [avatar component clause 502]
506. 32 <=> preda(mary) [avatar definition]
508. preda(mary) <- (32) [avatar component clause 506]
509. 30 | 31 | 32 [avatar split clause 491,506,502,498]
511. ~predo(mary) | ~room(mary) <- (31) [resolution 504,297]
512. ~room(mary) <- (31) [subsumption resolution 511,422]
513. $false <- (31) [subsumption resolution 512,270]
514. ~31 [avatar contradiction clause 513]
515. ~predo(mary) | ~room(mary) <- (32) [resolution 508,298]
516. ~room(mary) <- (32) [subsumption resolution 515,422]
517. $false <- (32) [subsumption resolution 516,270]
518. ~32 [avatar contradiction clause 517]
519. ~room(mary) | predw(mary) <- (18, 30) [resolution 500,390]
520. predw(mary) <- (18, 30) [subsumption resolution 519,270]
521. $false <- (18, 30, ~31) [subsumption resolution 520,503]
522. ~18 | ~30 | 31 [avatar contradiction clause 521]
523. ~room(mary) | predj(mary) <- (19) [resolution 393,422]
524. predj(mary) <- (19) [subsumption resolution 523,270]
527. 21 | ~19 [avatar split clause 524,392,403]
552. mary = sK4 | paul = sK4 <- (23) [resolution 419,272]
566. paul = sK4 <- (~22, 23) [subsumption resolution 552,412]
567. $false <- (~20, ~22, 23) [subsumption resolution 566,401]
568. 20 | 22 | ~23 [avatar contradiction clause 567]
569. $false [avatar sat refutation 394,406,413,420,509,514,518,522,527,568]
% SZS output end Proof for 445884653870776648668108
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.041 s
% ------------------------------
% ------------------------------
| 0.386132 |
There is a room. If someone maintains a large, organic vegetable garden year-round then he/she does not collect limited-edition art prints from contemporary artists and vice versa. Someone anywhere streams on Twitch. Everyone in the room collects limited-edition art prints from contemporary artists if they does not maintain a large, organic vegetable garden year-round. Not everyone in the room does not stream on Twitch and streams on Twitch if they streams on Twitch. Everyone outside the room enjoys cross-country skiing if they does not stream on Twitch and streams on Twitch. Everyone in the room who does not enjoy cross-country skiing maintains a large, organic vegetable garden year-round. If someone maintains a large, organic vegetable garden year-round then he/she streams on Twitch, does not enjoy cross-country skiing and maintains a large, organic vegetable garden year-round. Someone in the room neither streams on Twitch nor does not enjoy cross-country skiing. | Everyone in the room enjoys cross-country skiing. | neutral | (there_is_a_room)&
((![X]:((maintains_a_large,_organic_vegetable_garden_year-round(X))<=>(does_not_collect_limited-edition_art_prints_from_contemporary_artists(X)))))&
(?[X]:(anywhere(X)&(streams_on_Twitch(X))))&
(![X]:(room(X)=>(((does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))=>(collects_limited-edition_art_prints_from_contemporary_artists(X))))))&
(~![X]:(room(X)=>(((streams_on_Twitch(X))=>(((does_not_stream_on_Twitch(X))&(streams_on_Twitch(X))))))))&
(![X]:(~room(X)=>(((((does_not_stream_on_Twitch(X))&(streams_on_Twitch(X))))=>(enjoys_cross-country_skiing(X))))))&
(![X]:(room(X)=>(((does_not_enjoy_cross-country_skiing(X))=>(maintains_a_large,_organic_vegetable_garden_year-round(X))))))&
((![X]:((maintains_a_large,_organic_vegetable_garden_year-round(X))=>(((streams_on_Twitch(X))&(does_not_enjoy_cross-country_skiing(X))&(maintains_a_large,_organic_vegetable_garden_year-round(X)))))))&
(?[X]:(room(X)&(~((streams_on_Twitch(X))|(does_not_enjoy_cross-country_skiing(X))))))&
(![X]:(~room(X)=>(((enjoys_cross-country_skiing(X))=>(((collects_limited-edition_art_prints_from_contemporary_artists(X))&(streams_on_Twitch(X))))))))&
(~![X]:(anywhere(X)=>(((((collects_limited-edition_art_prints_from_contemporary_artists(X))&(streams_on_Twitch(X))))=>(enjoys_cross-country_skiing(X)))))) | (there_is_a_room)&
![X]:(room(X)=>(enjoys_cross-country_skiing(X))) | [] | null | 0.248222 |
“It is not the case that “Joseph enjoys macrame or enjoys wildlife photography or both”” only if “Joseph is an avid hiker”. “Joseph creates augmented reality experiences for mobile applications” only if “Joseph enjoys macrame”. Joseph has a vast collection of first-edition science fiction novels. Joseph enjoys wildlife photography. Joseph practices digital art. Joseph is an avid hiker. | Joseph enjoys macrame. | neutral | room(joseph)&room(elizabeth)&room(jay)&(![X]:(room(X)=>(X='joseph'|X='elizabeth'|X='jay')))&
((~(((enjoys_macrame(joseph))|(enjoys_wildlife_photography(joseph)))))=>(is_an_avid_hiker(joseph)))&
((creates_augmented_reality_experiences_for_mobile_applications(joseph))=>(enjoys_macrame(joseph)))&
(has_a_vast_collection_of_first-edition_science_fiction_novels(joseph))&
(enjoys_wildlife_photography(joseph))&
(practices_digital_art(joseph))&
(is_an_avid_hiker(joseph)) | room(joseph)&room(elizabeth)&room(jay)&(![X]:(room(X)=>(X='joseph'|X='elizabeth'|X='jay')))&
enjoys_macrame(joseph) | [] | null | 0.610566 |
Elizabeth, Virgil, Kenneth, Robert, Scott are the only persons in the room. If 'at least one person in the room does not create large-scale murals for public art installations and enjoys making ceramics' then 'Virgil enjoys fishing'. Either 'Virgil creates large-scale murals for public art installations and enjoys making ceramics' or 'everyone in the room does not enjoy fishing or enjoys making ceramics' but not both. If 'everyone in the room creates large-scale murals for public art installations or does not enjoy fishing' then 'Robert enjoys making ceramics'. It is true that 'if someone enjoys making ceramics then he/she enjoys making ceramics and does not create large-scale murals for public art installations and vice versa'. Everyone in the room who creates large-scale murals for public art installations and enjoys making ceramics enjoys fishing. It is not the case that 'Robert creates large-scale murals for public art installations'. Everyone in the room who neither does not enjoy logic puzzles nor enjoys making ceramics enjoys logic puzzles. Only one person anywhere enjoys logic puzzles. | Virgil enjoys making ceramics. | entailment | room(elizabeth)&room(virgil)&room(kenneth)&room(robert)&room(scott)&(![X]:(room(X)=>(X='elizabeth'|X='virgil'|X='kenneth'|X='robert'|X='scott')))&
((((?[X]:(room(X)&((does_not_create_large-scale_murals_for_public_art_installations(X))&(enjoys_making_ceramics(X)))))))=>(enjoys_fishing(virgil)))&
((((creates_large-scale_murals_for_public_art_installations(virgil))&(enjoys_making_ceramics(virgil))))<~>(![X]:(room(X)=>(((enjoys_making_ceramics(X))|(does_not_enjoy_fishing(X)))))))&
((![X]:(room(X)=>(((does_not_enjoy_fishing(X))|(creates_large-scale_murals_for_public_art_installations(X))))))=>(enjoys_making_ceramics(robert)))&
((![X]:((enjoys_making_ceramics(X))<=>(((enjoys_making_ceramics(X))&(does_not_create_large-scale_murals_for_public_art_installations(X)))))))&
(![X]:(room(X)=>(((((creates_large-scale_murals_for_public_art_installations(X))&(enjoys_making_ceramics(X))))=>(enjoys_fishing(X))))))&
(~(creates_large-scale_murals_for_public_art_installations(robert)))&
(![X]:(room(X)=>(((~((does_not_enjoy_logic_puzzles(X))|(enjoys_making_ceramics(X))))=>(enjoys_logic_puzzles(X))))))&
(((?[X]:(anywhere(X)&enjoys_logic_puzzles(X)))&(![X,Y]:((anywhere(X)&anywhere(Y)&(enjoys_logic_puzzles(X))&(enjoys_logic_puzzles(Y)))=>(X=Y))))) | room(elizabeth)&room(virgil)&room(kenneth)&room(robert)&room(scott)&(![X]:(room(X)=>(X='elizabeth'|X='virgil'|X='kenneth'|X='robert'|X='scott')))&
enjoys_making_ceramics(virgil) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 686500088250602495471671
% SZS output start Proof for 686500088250602495471671
44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
45. ? [X0] : (preda(X0) & ~predd(X0) & room(X0)) => predb(paul) [input p1]
46. (preda(paul) & predd(paul)) <~> ! [X0] : (room(X0) => (~predb(X0) | preda(X0))) [input p2]
47. ! [X0] : (room(X0) => (predd(X0) | ~predb(X0))) => preda(alice) [input p3]
48. ! [X0] : (preda(X0) <=> (~predd(X0) & preda(X0))) [input p4]
53. ~(preda(paul) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis]
126. ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
127. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 126]
128. predb(paul) | ! [X0] : (~preda(X0) | predd(X0) | ~room(X0)) [ennf transformation 45]
129. (preda(paul) & predd(paul)) <~> ! [X0] : ((~predb(X0) | preda(X0)) | ~room(X0)) [ennf transformation 46]
130. (preda(paul) & predd(paul)) <~> ! [X0] : (~predb(X0) | preda(X0) | ~room(X0)) [flattening 129]
131. preda(alice) | ? [X0] : ((~predd(X0) & predb(X0)) & room(X0)) [ennf transformation 47]
132. preda(alice) | ? [X0] : (~predd(X0) & predb(X0) & room(X0)) [flattening 131]
139. ~preda(paul) | ? [X0] : ((john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 53]
140. ~preda(paul) | ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 139]
142. (? [X0] : (predb(X0) & ~preda(X0) & room(X0)) | (~preda(paul) | ~predd(paul))) & (! [X0] : (~predb(X0) | preda(X0) | ~room(X0)) | (preda(paul) & predd(paul))) [nnf transformation 130]
143. (? [X0] : (predb(X0) & ~preda(X0) & room(X0)) | ~preda(paul) | ~predd(paul)) & (! [X0] : (~predb(X0) | preda(X0) | ~room(X0)) | (preda(paul) & predd(paul))) [flattening 142]
144. (? [X0] : (predb(X0) & ~preda(X0) & room(X0)) | ~preda(paul) | ~predd(paul)) & (! [X1] : (~predb(X1) | preda(X1) | ~room(X1)) | (preda(paul) & predd(paul))) [rectify 143]
145. ? [X0] : (predb(X0) & ~preda(X0) & room(X0)) => (predb(sK0) & ~preda(sK0) & room(sK0)) [choice axiom]
146. ((predb(sK0) & ~preda(sK0) & room(sK0)) | ~preda(paul) | ~predd(paul)) & (! [X1] : (~predb(X1) | preda(X1) | ~room(X1)) | (preda(paul) & predd(paul))) [skolemisation 144,145]
147. ? [X0] : (~predd(X0) & predb(X0) & room(X0)) => (~predd(sK1) & predb(sK1) & room(sK1)) [choice axiom]
148. preda(alice) | (~predd(sK1) & predb(sK1) & room(sK1)) [skolemisation 132,147]
149. ! [X0] : ((preda(X0) | (predd(X0) | ~preda(X0))) & ((~predd(X0) & preda(X0)) | ~preda(X0))) [nnf transformation 48]
150. ! [X0] : ((preda(X0) | predd(X0) | ~preda(X0)) & ((~predd(X0) & preda(X0)) | ~preda(X0))) [flattening 149]
153. ? [X0] : (john != X0 & alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (john != sK3 & alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) [choice axiom]
154. ~preda(paul) | (john != sK3 & alice != sK3 & fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 140,153]
236. room(mary) [cnf transformation 127]
237. room(paul) [cnf transformation 127]
238. room(fred) [cnf transformation 127]
239. room(alice) [cnf transformation 127]
240. room(john) [cnf transformation 127]
241. ~room(X0) | alice = X0 | fred = X0 | paul = X0 | mary = X0 | john = X0 [cnf transformation 127]
242. predb(paul) | ~preda(X0) | predd(X0) | ~room(X0) [cnf transformation 128]
244. ~predb(X1) | preda(X1) | ~room(X1) | preda(paul) [cnf transformation 146]
248. preda(alice) | room(sK1) [cnf transformation 148]
249. preda(alice) | predb(sK1) [cnf transformation 148]
252. ~preda(X0) | ~predd(X0) [cnf transformation 150]
260. ~preda(paul) | room(sK3) | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 154]
261. ~preda(paul) | mary != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 154]
262. ~preda(paul) | paul != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 154]
263. ~preda(paul) | fred != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 154]
264. ~preda(paul) | alice != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 154]
265. ~preda(paul) | john != sK3 | ~room(john) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 154]
267. 1 <=> ! [X0] : (~preda(X0) | ~room(X0) | predd(X0)) [avatar definition]
268. ~preda(X0) | ~room(X0) | predd(X0) <- (1) [avatar component clause 267]
270. 2 <=> predb(paul) [avatar definition]
271. ~predb(paul) <- (~2) [avatar component clause 270]
272. predb(paul) <- (2) [avatar component clause 270]
273. 1 | 2 [avatar split clause 242,270,267]
279. 4 <=> preda(paul) [avatar definition]
298. 8 <=> ! [X1] : (~predb(X1) | ~room(X1) | preda(X1)) [avatar definition]
299. ~predb(X1) | ~room(X1) | preda(X1) <- (8) [avatar component clause 298]
300. 4 | 8 [avatar split clause 244,298,279]
307. 10 <=> preda(alice) [avatar definition]
308. ~preda(alice) <- (~10) [avatar component clause 307]
309. preda(alice) <- (10) [avatar component clause 307]
312. 11 <=> predb(sK1) [avatar definition]
314. predb(sK1) <- (11) [avatar component clause 312]
315. 11 | 10 [avatar split clause 249,307,312]
317. 12 <=> room(sK1) [avatar definition]
319. room(sK1) <- (12) [avatar component clause 317]
320. 12 | 10 [avatar split clause 248,307,317]
323. ~preda(paul) | john != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 265,240]
324. ~preda(paul) | john != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 323,239]
325. ~preda(paul) | john != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 324,238]
326. ~preda(paul) | john != sK3 | ~room(mary) [subsumption resolution 325,237]
327. ~preda(paul) | john != sK3 [subsumption resolution 326,236]
329. 13 <=> john = sK3 [avatar definition]
331. john != sK3 <- (~13) [avatar component clause 329]
332. ~13 | ~4 [avatar split clause 327,279,329]
333. ~preda(paul) | alice != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 264,240]
334. ~preda(paul) | alice != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 333,239]
335. ~preda(paul) | alice != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 334,238]
336. ~preda(paul) | alice != sK3 | ~room(mary) [subsumption resolution 335,237]
337. ~preda(paul) | alice != sK3 [subsumption resolution 336,236]
339. 14 <=> alice = sK3 [avatar definition]
341. alice != sK3 <- (~14) [avatar component clause 339]
342. ~14 | ~4 [avatar split clause 337,279,339]
343. ~preda(paul) | fred != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 263,240]
344. ~preda(paul) | fred != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 343,239]
345. ~preda(paul) | fred != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 344,238]
346. ~preda(paul) | fred != sK3 | ~room(mary) [subsumption resolution 345,237]
347. ~preda(paul) | fred != sK3 [subsumption resolution 346,236]
349. 15 <=> fred = sK3 [avatar definition]
351. fred != sK3 <- (~15) [avatar component clause 349]
352. ~15 | ~4 [avatar split clause 347,279,349]
353. ~preda(paul) | paul != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 262,240]
354. ~preda(paul) | paul != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 353,239]
355. ~preda(paul) | paul != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 354,238]
356. ~preda(paul) | paul != sK3 | ~room(mary) [subsumption resolution 355,237]
357. ~preda(paul) | paul != sK3 [subsumption resolution 356,236]
359. 16 <=> paul = sK3 [avatar definition]
361. paul != sK3 <- (~16) [avatar component clause 359]
362. ~16 | ~4 [avatar split clause 357,279,359]
363. ~preda(paul) | mary != sK3 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 261,240]
364. ~preda(paul) | mary != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 363,239]
365. ~preda(paul) | mary != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 364,238]
366. ~preda(paul) | mary != sK3 | ~room(mary) [subsumption resolution 365,237]
367. ~preda(paul) | mary != sK3 [subsumption resolution 366,236]
369. 17 <=> mary = sK3 [avatar definition]
371. mary != sK3 <- (~17) [avatar component clause 369]
372. ~17 | ~4 [avatar split clause 367,279,369]
373. ~preda(paul) | room(sK3) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 260,240]
374. ~preda(paul) | room(sK3) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 373,239]
375. ~preda(paul) | room(sK3) | ~room(paul) | ~room(mary) [subsumption resolution 374,238]
376. ~preda(paul) | room(sK3) | ~room(mary) [subsumption resolution 375,237]
377. ~preda(paul) | room(sK3) [subsumption resolution 376,236]
379. 18 <=> room(sK3) [avatar definition]
381. room(sK3) <- (18) [avatar component clause 379]
382. 18 | ~4 [avatar split clause 377,279,379]
384. ~room(paul) | preda(paul) <- (2, 8) [resolution 299,272]
385. preda(paul) <- (2, 8) [subsumption resolution 384,237]
388. 4 | ~2 | ~8 [avatar split clause 385,298,270,279]
439. alice = sK3 | fred = sK3 | paul = sK3 | mary = sK3 | john = sK3 <- (18) [resolution 241,381]
440. fred = sK3 | paul = sK3 | mary = sK3 | john = sK3 <- (~14, 18) [subsumption resolution 439,341]
441. paul = sK3 | mary = sK3 | john = sK3 <- (~14, ~15, 18) [subsumption resolution 440,351]
442. mary = sK3 | john = sK3 <- (~14, ~15, ~16, 18) [subsumption resolution 441,361]
443. john = sK3 <- (~14, ~15, ~16, ~17, 18) [subsumption resolution 442,371]
444. $false <- (~13, ~14, ~15, ~16, ~17, 18) [subsumption resolution 443,331]
445. 13 | 14 | 15 | 16 | 17 | ~18 [avatar contradiction clause 444]
446. ~preda(X0) | ~room(X0) <- (1) [subsumption resolution 268,252]
447. ~room(alice) <- (1, 10) [resolution 446,309]
448. $false <- (1, 10) [subsumption resolution 447,239]
449. ~1 | ~10 [avatar contradiction clause 448]
450. ~room(sK1) | preda(sK1) <- (8, 11) [resolution 314,299]
451. preda(sK1) <- (8, 11, 12) [subsumption resolution 450,319]
452. alice = sK1 | fred = sK1 | paul = sK1 | mary = sK1 | john = sK1 <- (12) [resolution 319,241]
454. 19 <=> john = sK1 [avatar definition]
456. john = sK1 <- (19) [avatar component clause 454]
458. 20 <=> mary = sK1 [avatar definition]
460. mary = sK1 <- (20) [avatar component clause 458]
462. 21 <=> paul = sK1 [avatar definition]
464. paul = sK1 <- (21) [avatar component clause 462]
466. 22 <=> fred = sK1 [avatar definition]
468. fred = sK1 <- (22) [avatar component clause 466]
470. 23 <=> alice = sK1 [avatar definition]
472. alice = sK1 <- (23) [avatar component clause 470]
473. 19 | 20 | 21 | 22 | 23 | ~12 [avatar split clause 452,317,470,466,462,458,454]
476. predb(paul) <- (11, 21) [backward demodulation 314,464]
480. $false <- (~2, 11, 21) [subsumption resolution 476,271]
481. 2 | ~11 | ~21 [avatar contradiction clause 480]
483. preda(mary) <- (8, 11, 12, 20) [backward demodulation 451,460]
488. ~room(mary) <- (1, 8, 11, 12, 20) [resolution 483,446]
490. $false <- (1, 8, 11, 12, 20) [subsumption resolution 488,236]
491. ~1 | ~8 | ~11 | ~12 | ~20 [avatar contradiction clause 490]
492. preda(john) <- (8, 11, 12, 19) [backward demodulation 451,456]
499. ~room(john) <- (1, 8, 11, 12, 19) [resolution 492,446]
501. $false <- (1, 8, 11, 12, 19) [subsumption resolution 499,240]
502. ~1 | ~8 | ~11 | ~12 | ~19 [avatar contradiction clause 501]
503. preda(alice) <- (8, 11, 12, 23) [backward demodulation 451,472]
507. $false <- (8, ~10, 11, 12, 23) [subsumption resolution 503,308]
508. ~8 | 10 | ~11 | ~12 | ~23 [avatar contradiction clause 507]
513. preda(fred) <- (8, 11, 12, 22) [backward demodulation 451,468]
519. ~room(fred) <- (1, 8, 11, 12, 22) [resolution 513,446]
521. $false <- (1, 8, 11, 12, 22) [subsumption resolution 519,238]
522. ~1 | ~8 | ~11 | ~12 | ~22 [avatar contradiction clause 521]
523. $false [avatar sat refutation 273,300,315,320,332,342,352,362,372,382,388,445,449,473,481,491,502,508,522]
% SZS output end Proof for 686500088250602495471671
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0.191383 |
Janice, Lauri are the only persons in the room.
Not everyone in the room is a Linux enthusiast if they makes intricate hand-cut paper art for exhibitions if Janice enjoys fishing.
If no one in the room enjoys rooftop gardening or is not a member of a local theater group specializing in improv then Janice is not a member of a local theater group specializing in improv.
Lauri enjoys rooftop gardening only if Janice has a vast collection of first-edition science fiction novels.
If Lauri neither is a Linux enthusiast nor is not a dedicated volunteer for local community service projects then everyone in the room enjoys virtual reality gaming if they does enjoy trail running.
Lauri enjoys rooftop gardening and enjoys windsurfing.
Lauri enjoys salsa dancing.
Janice collects modern art.
Janice is a wine connoisseur.
Janice does enjoy trail running.
Janice is a Linux enthusiast.
Everyone in the room who enjoys salsa dancing and makes intricate hand-cut paper art for exhibitions enjoys fishing.
Everyone in the room creates YouTube content if they enjoys fishing.
Janice enjoys salsa dancing.
Janice makes intricate hand-cut paper art for exhibitions.
Lauri is a dedicated volunteer for local community service projects.
Everyone outside the room who is a dedicated volunteer for local community service projects creates YouTube content. | Lauri either does not enjoy rooftop gardening or is not a wine connoisseur but not both. | neutral | room(janice)&room(lauri)&(![X]:(room(X)=>(X='janice'|X='lauri')))&
((enjoys_fishing(janice))=>(~![X]:(room(X)=>(((makes_intricate_hand-cut_paper_art_for_exhibitions(X))=>(is_a_Linux_enthusiast(X)))))))&
((~?[X]:(room(X)=>(((is_not_a_member_of_a_local_theater_group_specializing_in_improv(X))|(enjoys_rooftop_gardening(X))))))=>(is_not_a_member_of_a_local_theater_group_specializing_in_improv(janice)))&
((enjoys_rooftop_gardening(lauri))=>(has_a_vast_collection_of_first-edition_science_fiction_novels(janice)))&
((~((is_a_Linux_enthusiast(lauri))|(is_not_a_dedicated_volunteer_for_local_community_service_projects(lauri))))=>(![X]:(room(X)=>(((does_enjoy_trail_running(X))=>(enjoys_virtual_reality_gaming(X)))))))&
(((enjoys_rooftop_gardening(lauri))&(enjoys_windsurfing(lauri))))&
(enjoys_salsa_dancing(lauri))&
(collects_modern_art(janice))&
(is_a_wine_connoisseur(janice))&
(does_enjoy_trail_running(janice))&
(is_a_Linux_enthusiast(janice))&
(![X]:(room(X)=>(((((enjoys_salsa_dancing(X))&(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))=>(enjoys_fishing(X))))))&
(![X]:(room(X)=>(((enjoys_fishing(X))=>(creates_YouTube_content(X))))))&
(enjoys_salsa_dancing(janice))&
(makes_intricate_hand-cut_paper_art_for_exhibitions(janice))&
(is_a_dedicated_volunteer_for_local_community_service_projects(lauri))&
(![X]:(~room(X)=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))=>(creates_YouTube_content(X))))))&
(![X]:(anywhere(X)=>(((creates_YouTube_content(X))=>(collects_modern_art(X))))))&
(((?[X]:(anywhere(X)&is_a_Linux_enthusiast(X)))))&
(![X]:(room(X)=>(((((enjoys_rooftop_gardening(X))&(creates_YouTube_content(X))))<=(owns_a_smart_tv(X)))))) | room(janice)&room(lauri)&(![X]:(room(X)=>(X='janice'|X='lauri')))&
((does_not_enjoy_rooftop_gardening(lauri))<~>(is_not_a_wine_connoisseur(lauri))) | [] | null | 0.000549 |
Bonnie, Donald, Yvonne, Alvin, Nicole are the only persons in the room. If someone does not maintain a large, organic vegetable garden year-round then he/she is an enthusiastic bird watcher who travels for rare sightings and vice versa. Everyone in the room maintains a large, organic vegetable garden year-round. | Nicole is an enthusiastic bird watcher who travels for rare sightings. | contradiction | room(bonnie)&room(donald)&room(yvonne)&room(alvin)&room(nicole)&(![X]:(room(X)=>(X='bonnie'|X='donald'|X='yvonne'|X='alvin'|X='nicole')))&
(![X]:(room(X)=>(collects_classic_novels(X))))&
(![X]:(anywhere(X)=>(((does_not_collect_comic_books(X))<=>(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))))))&
(![X]:(room(X)=>(((does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X))<=>(maintains_a_large,_organic_vegetable_garden_year-round(X))))))&
(~![X]:(room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))<=>(((does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))&(is_not_a_client_of_LVMH(X))&(is_an_active_member_of_a_local_robotics_club(X))))))))&
((![X]:((does_not_maintain_a_large,_organic_vegetable_garden_year-round(X))<=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X)))))&
((((collects_historical_artifacts_related_to_ancient_civilizations(alvin))&(can_play_the_flute(alvin))))&(does_not_write_a_travel_blog(alvin)))&
(![X]:(room(X)=>(((((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))<~>(owns_a_smartwatch(X))))<=>(is_an_active_member_of_a_local_robotics_club(X))))))&
(![X]:(room(X)=>(maintains_a_large,_organic_vegetable_garden_year-round(X))))&
(![X]:(room(X)=>(((maintains_a_large,_organic_vegetable_garden_year-round(X))<=(maintains_a_personal_blog_focused_on_cybersecurity_tips(X))))))&
(![X]:(~room(X)=>(((((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(writes_a_travel_blog(X))))<=(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))&(creates_augmented_reality_experiences_for_mobile_applications(X))&(enjoys_cross-country_skiing(X))))))))&
(~![X]:(room(X)=>(((owns_a_smartwatch(X))<=(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(writes_a_travel_blog(X)))))))) | room(bonnie)&room(donald)&room(yvonne)&room(alvin)&room(nicole)&(![X]:(room(X)=>(X='bonnie'|X='donald'|X='yvonne'|X='alvin'|X='nicole')))&
is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(nicole) | [
"p0",
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 467285453505020380444399
% SZS output start Proof for 467285453505020380444399
44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
49. ! [X0] : (~prede(X0) <=> predc(X0)) [input p5]
52. ! [X0] : (room(X0) => prede(X0)) [input p8]
56. predc(john) & ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input hypothesis]
132. ! [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]
133. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 132]
138. ! [X0] : (prede(X0) | ~room(X0)) [ennf transformation 52]
141. predc(john) & ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 56]
142. predc(john) & ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 141]
150. ! [X0] : ((~prede(X0) | ~predc(X0)) & (predc(X0) | prede(X0))) [nnf transformation 49]
239. room(john) [cnf transformation 133]
251. ~predc(X0) | ~prede(X0) [cnf transformation 150]
258. ~room(X0) | prede(X0) [cnf transformation 138]
268. predc(john) [cnf transformation 142]
300. ~prede(john) [resolution 251,268]
307. prede(john) [resolution 258,239]
310. $false [subsumption resolution 307,300]
% SZS output end Proof for 467285453505020380444399
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.208852 |
Victor, Thomas are the only persons in the room. Either “Victor owns a telescope” or “everyone in the room does not have a piercing or can play the flute” but not both. “If someone cannot play the flute then he/she is a night owl” unless “everyone in the room cannot play the flute or enjoys origami”. “Victor can play the harmonica” only if “someone in the room is an avid hiker”. If “someone outside the room is a scotch connoisseur” then “Thomas has a specialized collection of handmade artisan pottery” otherwise “Victor is a night owl and enjoys deep-sea diving and exploring underwater caves”. “Everyone in the room cannot play the harmonica or is a wine connoisseur with a private cellar of vintage wines” if “everyone outside the room does not use contact lenses or does not have a piercing” and vice versa. Victor regularly contributes to tech forums and online communities. Thomas owns a telescope. Everyone in the room is a client of LVMH. If someone practices urban gardening then he/she does not make homemade pastries and vice versa. Thomas collects rare and antique scientific instruments. More than one person in the room enjoys origami. Victor hosts themed dinner parties featuring gourmet home-cooked meals. If someone cannot play the flute then he/she is a night owl. Everyone outside the room who is a scotch connoisseur either regularly goes on multi-day backpacking trips in national parks or uses contact lenses but not both. Everyone in the room who either regularly goes on multi-day backpacking trips in national parks or uses contact lenses but not both is a scotch connoisseur. If someone does not have lived in exactly three countries then he/she regularly contributes to tech forums and online communities and vice versa. Everyone in the room is not an avid hiker if they mentors a youth basketball team on weekends. Victor has a specialized collection of handmade artisan pottery. Everyone outside the room does not create large-scale murals for public art installations only if they neither is an avid hiker nor can play the flute. Thomas can play the flute. If someone is not an avid hiker and does not use contact lenses then he/she makes homemade pastries and vice versa. Thomas who has a specialized collection of handmade artisan pottery is an active member of a local robotics club. Victor enjoys origami. | Victor owns a telescope. | neutral | room(victor)&room(thomas)&(![X]:(room(X)=>(X='victor'|X='thomas')))&
((owns_a_telescope(victor))<~>(![X]:(room(X)=>(((can_play_the_flute(X))|(does_not_have_a_piercing(X)))))))&
(~(![X]:(room(X)=>(((enjoys_origami(X))|(cannot_play_the_flute(X))))))=>((![X]:((cannot_play_the_flute(X))=>(is_a_night_owl(X))))))&
((can_play_the_harmonica(victor))=>(?[X]:(room(X)&(is_an_avid_hiker(X)))))&
(((?[X]:(~room(X)&(is_a_scotch_connoisseur(X))))=>(has_a_specialized_collection_of_handmade_artisan_pottery(thomas)))&((~(?[X]:(~room(X)&(is_a_scotch_connoisseur(X)))))=>(((is_a_night_owl(victor))&(enjoys_deep-sea_diving_and_exploring_underwater_caves(victor))))))&
((![X]:(~room(X)=>(((does_not_have_a_piercing(X))|(does_not_use_contact_lenses(X))))))<=>(![X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))|(cannot_play_the_harmonica(X)))))))&
(regularly_contributes_to_tech_forums_and_online_communities(victor))&
(owns_a_telescope(thomas))&
(![X]:(room(X)=>(is_a_client_of_LVMH(X))))&
((![X]:((practices_urban_gardening(X))<=>(does_not_make_homemade_pastries(X)))))&
(collects_rare_and_antique_scientific_instruments(thomas))&
((?[X,Y]:(room(X)&room(Y)&(enjoys_origami(X)&enjoys_origami(Y))&(X!=Y))))&
(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(victor))&
((![X]:((cannot_play_the_flute(X))=>(is_a_night_owl(X)))))&
(![X]:(~room(X)=>(((is_a_scotch_connoisseur(X))=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))<~>(uses_contact_lenses(X))))))))&
(![X]:(room(X)=>(((((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))<~>(uses_contact_lenses(X))))=>(is_a_scotch_connoisseur(X))))))&
((![X]:((does_not_have_lived_in_exactly_three_countries(X))<=>(regularly_contributes_to_tech_forums_and_online_communities(X)))))&
(![X]:(room(X)=>(((mentors_a_youth_basketball_team_on_weekends(X))=>(is_not_an_avid_hiker(X))))))&
(has_a_specialized_collection_of_handmade_artisan_pottery(victor))&
(![X]:(~room(X)=>(((~((is_an_avid_hiker(X))|(can_play_the_flute(X))))<=(does_not_create_large-scale_murals_for_public_art_installations(X))))))&
(can_play_the_flute(thomas))&
((![X]:((((is_not_an_avid_hiker(X))&(does_not_use_contact_lenses(X))))<=>(makes_homemade_pastries(X)))))&
((has_a_specialized_collection_of_handmade_artisan_pottery(thomas))&(is_an_active_member_of_a_local_robotics_club(thomas)))&
(enjoys_origami(victor)) | room(victor)&room(thomas)&(![X]:(room(X)=>(X='victor'|X='thomas')))&
owns_a_telescope(victor) | [] | null | 0 |
Jeanne, Thomas are the only persons in the room. Jeanne does not practice calligraphy. Jeanne practices tai chi. Not everyone in the room who is a skilled home brewer experimenting with craft beer recipes owns an Android phone. Jeanne is not a skilled home brewer experimenting with craft beer recipes. | Thomas owns an Android phone. | contradiction | room(jeanne)&room(thomas)&(![X]:(room(X)=>(X='jeanne'|X='thomas')))&
(does_not_practice_calligraphy(jeanne))&
(practices_tai_chi(jeanne))&
(![X]:(room(X)=>(((((collects_luxury_watches(X))&(does_not_enjoy_stargazing(X))&(does_practice_yoga(X))))<=>(collects_modern_art(X))))))&
(![X]:(anywhere(X)=>(((collects_modern_art(X))=>(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))))&
((![X]:((is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X))<=>(~((develops_open-source_software_projects_in_their_free_time(X))|(is_a_tea_enthusiast(X)))))))&
((![X]:((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))<=>(practices_calligraphy(X)))))&
(is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(jeanne))&
(is_not_a_tea_enthusiast(jeanne))&
(is_an_expert_in_identifying_and_foraging_wild_edible_plants(thomas))&
(((?[X]:(room(X)&has_a_piercing(X)))))&
(![X]:(room(X)=>(((does_not_practice_yoga(X))|(does_practice_yoga(X))))))&
(![X]:(room(X)=>(((does_practice_yoga(X))=>(has_a_specialized_collection_of_handmade_artisan_pottery(X))))))&
((![X]:((practices_calligraphy(X))=>(is_not_allergic_to_anything(X)))))&
(has_a_piercing(thomas))&
(![X]:(room(X)=>(((does_practice_yoga(X))<=>(practices_calligraphy(X))))))&
(collects_luxury_watches(thomas))&
(~![X]:(room(X)=>(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))=>(owns_an_Android_phone(X))))))&
(![X]:(room(X)=>(((collects_luxury_watches(X))=>(develops_open-source_software_projects_in_their_free_time(X))))))&
(does_practice_yoga(thomas))&
(is_not_a_member_of_a_local_theater_group_specializing_in_improv(jeanne))&
(collects_first_edition_books(jeanne))&
(is_not_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(jeanne))&
(![X]:(room(X)=>(((is_an_expert_in_identifying_and_foraging_wild_edible_plants(X))=>(does_not_watche_fantasy_movies(X)))))) | room(jeanne)&room(thomas)&(![X]:(room(X)=>(X='jeanne'|X='thomas')))&
owns_an_Android_phone(thomas) | [
"p0",
"p17",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 310588155400545328667313
% SZS output start Proof for 310588155400545328667313
44. ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input p0]
61. ~! [X0] : (room(X0) => (predn(X0) => predv(X0))) [input p17]
66. ~predn(mary) [input p22]
68. predv(paul) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis]
152. ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 44]
153. ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 152]
158. ? [X0] : ((~predv(X0) & predn(X0)) & room(X0)) [ennf transformation 61]
159. ? [X0] : (~predv(X0) & predn(X0) & room(X0)) [flattening 158]
160. predv(paul) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 68]
161. predv(paul) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 160]
169. ? [X0] : (~predv(X0) & predn(X0) & room(X0)) => (~predv(sK1) & predn(sK1) & room(sK1)) [choice axiom]
170. ~predv(sK1) & predn(sK1) & room(sK1) [skolemisation 159,169]
253. ~room(X0) | mary = X0 | paul = X0 [cnf transformation 153]
268. room(sK1) [cnf transformation 170]
269. predn(sK1) [cnf transformation 170]
270. ~predv(sK1) [cnf transformation 170]
272. ~predn(mary) [cnf transformation 66]
276. predv(paul) [cnf transformation 161]
289. mary = sK1 | paul = sK1 [resolution 253,268]
300. 3 <=> paul = sK1 [avatar definition]
302. paul = sK1 <- (3) [avatar component clause 300]
304. 4 <=> mary = sK1 [avatar definition]
306. mary = sK1 <- (4) [avatar component clause 304]
307. 3 | 4 [avatar split clause 289,304,300]
312. ~predv(paul) <- (3) [backward demodulation 270,302]
313. $false <- (3) [subsumption resolution 312,276]
314. ~3 [avatar contradiction clause 313]
319. predn(mary) <- (4) [backward demodulation 269,306]
323. $false <- (4) [subsumption resolution 319,272]
324. ~4 [avatar contradiction clause 323]
326. $false [avatar sat refutation 307,314,324]
% SZS output end Proof for 310588155400545328667313
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.349249 |
Gladys, Joseph are the only persons in the room. "Joseph does not collect vintage vinyl records or mentors a youth basketball team on weekends or both" only if "Joseph builds model airplanes". Gladys collects vintage vinyl records. Gladys mentors a youth basketball team on weekends. Joseph does not collect vintage vinyl records or mentors a youth basketball team on weekends or both. Joseph builds model airplanes. More than one person in the room collects vintage vinyl records. | Gladys builds model airplanes. | neutral | room(gladys)&room(joseph)&(![X]:(room(X)=>(X='gladys'|X='joseph')))&
((((does_not_collect_vintage_vinyl_records(joseph))|(mentors_a_youth_basketball_team_on_weekends(joseph))))=>(builds_model_airplanes(joseph)))&
(collects_vintage_vinyl_records(gladys))&
(mentors_a_youth_basketball_team_on_weekends(gladys))&
(((does_not_collect_vintage_vinyl_records(joseph))|(mentors_a_youth_basketball_team_on_weekends(joseph))))&
(builds_model_airplanes(joseph))&
((?[X,Y]:(room(X)&room(Y)&(collects_vintage_vinyl_records(X)&collects_vintage_vinyl_records(Y))&(X!=Y))))&
(is_a_drone_photographer(joseph))&
(collects_vintage_vinyl_records(joseph))&
(mentors_a_youth_basketball_team_on_weekends(joseph))&
((?[X,Y]:(room(X)&room(Y)&(mentors_a_youth_basketball_team_on_weekends(X)&mentors_a_youth_basketball_team_on_weekends(Y))&(X!=Y))))&
(?[X]:(room(X)&(builds_model_airplanes(X))))&
((![X]:((is_a_drone_photographer(X))=>(mentors_a_youth_basketball_team_on_weekends(X))))) | room(gladys)&room(joseph)&(![X]:(room(X)=>(X='gladys'|X='joseph')))&
builds_model_airplanes(gladys) | [] | null | 0.05805 |
Barbara, Elizabeth, Marina are the only persons in the room.
Elizabeth practices tai chi.
Elizabeth who own a television, is allergic to anything or collects classic novels does not enjoy coding in Python.
Everyone in the room who practices urban gardening plays video games.
Elizabeth can play the piano.
Everyone in the room who collects classic novels neither collects foreign coins nor is a Linux enthusiast.
Barbara practices kickboxing.
Everyone in the room who practices kickboxing is not an amateur astronomer who builds and uses custom telescopes.
Everyone in the room is not a Linux enthusiast. | Barbara neither is a Linux enthusiast nor is an amateur astronomer who builds and uses custom telescopes. | entailment | room(barbara)&room(elizabeth)&room(marina)&(![X]:(room(X)=>(X='barbara'|X='elizabeth'|X='marina')))&
(practices_tai_chi(elizabeth))&
((((own_a_television(elizabeth))|(is_allergic_to_anything(elizabeth))|(collects_classic_novels(elizabeth))))&(does_not_enjoy_coding_in_Python(elizabeth)))&
(![X]:(room(X)=>(((practices_urban_gardening(X))=>(plays_video_games(X))))))&
(can_play_the_piano(elizabeth))&
(![X]:(room(X)=>(((collects_classic_novels(X))=>(~((collects_foreign_coins(X))|(is_a_Linux_enthusiast(X))))))))&
((collects_classic_novels(barbara))&(plays_video_games(barbara)))&
(![X]:(room(X)=>(((((own_a_television(X))|(does_not_enjoy_skydiving(X))|(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))=>(enjoys_virtual_reality_gaming(X))))))&
(practices_kickboxing(barbara))&
(![X]:(room(X)=>(((practices_kickboxing(X))=>(is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))&
(((?[X]:(room(X)&practices_urban_gardening(X)))))&
(![X]:(~room(X)=>(((((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))&(practices_kickboxing(X))&(does_not_collect_foreign_coins(X))))=>(frequently_participates_in_hackathons_and_coding_competitions(X))))))&
(![X]:(room(X)=>(is_not_a_Linux_enthusiast(X))))&
(![X]:(room(X)=>(((is_allergic_to_anything(X))=>(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X)))))) | room(barbara)&room(elizabeth)&room(marina)&(![X]:(room(X)=>(X='barbara'|X='elizabeth'|X='marina')))&
~((is_a_Linux_enthusiast(barbara))|(is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(barbara))) | [
"p0",
"p8",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6554379984280753226263025
% SZS output start Proof for 6554379984280753226263025
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
52. predn(mary) [input p8]
53. ! [X0] : (room(X0) => (predn(X0) => ~predb(X0))) [input p9]
56. ! [X0] : (room(X0) => ~preda(X0)) [input p12]
58. ~(~(predb(mary) | preda(mary)) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis]
142. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
143. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 142]
146. ! [X0] : ((~predb(X0) | ~predn(X0)) | ~room(X0)) [ennf transformation 53]
147. ! [X0] : (~predb(X0) | ~predn(X0) | ~room(X0)) [flattening 146]
148. ! [X0] : (~preda(X0) | ~room(X0)) [ennf transformation 56]
149. (predb(mary) | preda(mary)) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 58]
150. predb(mary) | preda(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 149]
154. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) [choice axiom]
155. predb(mary) | preda(mary) | (fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 150,154]
236. room(mary) [cnf transformation 143]
237. room(paul) [cnf transformation 143]
238. room(fred) [cnf transformation 143]
239. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 143]
242. predn(mary) [cnf transformation 52]
243. ~predb(X0) | ~predn(X0) | ~room(X0) [cnf transformation 147]
245. ~preda(X0) | ~room(X0) [cnf transformation 148]
246. predb(mary) | preda(mary) | room(sK1) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 155]
247. predb(mary) | preda(mary) | mary != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 155]
248. predb(mary) | preda(mary) | paul != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 155]
249. predb(mary) | preda(mary) | fred != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 155]
250. predb(mary) | preda(mary) | fred != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 249,238]
251. predb(mary) | preda(mary) | fred != sK1 | ~room(mary) [subsumption resolution 250,237]
252. predb(mary) | preda(mary) | fred != sK1 [subsumption resolution 251,236]
254. 1 <=> fred = sK1 [avatar definition]
256. fred != sK1 <- (~1) [avatar component clause 254]
258. 2 <=> preda(mary) [avatar definition]
260. preda(mary) <- (2) [avatar component clause 258]
262. 3 <=> predb(mary) [avatar definition]
264. predb(mary) <- (3) [avatar component clause 262]
265. ~1 | 2 | 3 [avatar split clause 252,262,258,254]
266. predb(mary) | preda(mary) | paul != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 248,238]
267. predb(mary) | preda(mary) | paul != sK1 | ~room(mary) [subsumption resolution 266,237]
268. predb(mary) | preda(mary) | paul != sK1 [subsumption resolution 267,236]
270. 4 <=> paul = sK1 [avatar definition]
272. paul != sK1 <- (~4) [avatar component clause 270]
273. ~4 | 2 | 3 [avatar split clause 268,262,258,270]
274. predb(mary) | preda(mary) | mary != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 247,238]
275. predb(mary) | preda(mary) | mary != sK1 | ~room(mary) [subsumption resolution 274,237]
276. predb(mary) | preda(mary) | mary != sK1 [subsumption resolution 275,236]
278. 5 <=> mary = sK1 [avatar definition]
280. mary != sK1 <- (~5) [avatar component clause 278]
281. ~5 | 2 | 3 [avatar split clause 276,262,258,278]
282. predb(mary) | preda(mary) | room(sK1) | ~room(paul) | ~room(mary) [subsumption resolution 246,238]
283. predb(mary) | preda(mary) | room(sK1) | ~room(mary) [subsumption resolution 282,237]
284. predb(mary) | preda(mary) | room(sK1) [subsumption resolution 283,236]
286. 6 <=> room(sK1) [avatar definition]
288. room(sK1) <- (6) [avatar component clause 286]
289. 6 | 2 | 3 [avatar split clause 284,262,258,286]
290. ~room(mary) <- (2) [resolution 245,260]
291. $false <- (2) [subsumption resolution 290,236]
292. ~2 [avatar contradiction clause 291]
293. ~predn(mary) | ~room(mary) <- (3) [resolution 243,264]
294. ~room(mary) <- (3) [subsumption resolution 293,242]
295. $false <- (3) [subsumption resolution 294,236]
296. ~3 [avatar contradiction clause 295]
343. paul = sK1 | mary = sK1 | fred = sK1 <- (6) [resolution 239,288]
357. mary = sK1 | fred = sK1 <- (~4, 6) [subsumption resolution 343,272]
358. fred = sK1 <- (~4, ~5, 6) [subsumption resolution 357,280]
359. $false <- (~1, ~4, ~5, 6) [subsumption resolution 358,256]
360. 1 | 4 | 5 | ~6 [avatar contradiction clause 359]
361. $false [avatar sat refutation 265,273,281,289,292,296,360]
% SZS output end Proof for 6554379984280753226263025
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0.064423 |
Sean is the only person in the room.
If 'everyone in the room is richer than Jeanne' then 'everyone anywhere is kind if and only if they is a tall person'.
Sean is not a tall quiet person.
Sean is the richest outside the room.
Sean is a kind person. | Sean is quiet. | contradiction | room(sean)&(![X]:(room(X)=>(X='sean')))&
((?[X]:(~room(X)&(kind(X))))=>(![X]:((~room(X)&(X!=sean))=>older(X,sean))))&
((![X]:(room(X)=>(richer(jeanne,X))))=>(![X]:(anywhere(X)=>(((kind(X))<=>(tall(X)&person(X)))))))&
((~(~(quiet(sean)&kind(sean)&person(sean))))=>(![X]:((~room(X)&(X!=sean))=>richer(X,sean))))&
((![X]:((quieter(jeanne,X))=>(~(tall(X)&person(X))))))&
(![X]:((~room(X)&(X!=sean))=>older(X,sean)))&
(~(tall(sean)&quiet(sean)&person(sean)))&
(![X]:((~room(X)&(X!=sean))=>richer(X,sean)))&
(kind(sean)&person(sean))&
(?[X]:(room(X)&(older(amy,X))))&
(?[X]:(~room(X)&(kind(X))))&
(![X]:((room(X)&(X!=sean))=>older(X,sean))) | room(sean)&(![X]:(room(X)=>(X='sean')))&
quiet(sean) | [
"b4",
"b42",
"p0",
"p2",
"p6",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 6868144602794151005170315
% SZS output start Proof for 6868144602794151005170315
5. ! [X0] : anywhere(X0) [input b4]
43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42]
44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
46. ! [X0] : (room(X0) => richer(fred,X0)) => ! [X0] : (anywhere(X0) => (kind(X0) <=> (person(X0) & tall(X0)))) [input p2]
50. ~(person(mary) & quiet(mary) & tall(mary)) [input p6]
51. ! [X0] : ((mary != X0 & ~room(X0)) => richer(X0,mary)) [input p7]
52. person(mary) & kind(mary) [input p8]
56. quiet(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis]
58. ! [X0] : (room(X0) => richer(fred,X0)) => ! [X1] : (anywhere(X1) => (kind(X1) <=> (person(X1) & tall(X1)))) [rectify 46]
131. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
134. ! [X1] : ((kind(X1) <=> (person(X1) & tall(X1))) | ~anywhere(X1)) | ? [X0] : (~richer(fred,X0) & room(X0)) [ennf transformation 58]
141. ~person(mary) | ~quiet(mary) | ~tall(mary) [ennf transformation 50]
142. ! [X0] : (richer(X0,mary) | (mary = X0 | room(X0))) [ennf transformation 51]
143. ! [X0] : (richer(X0,mary) | mary = X0 | room(X0)) [flattening 142]
146. quiet(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 56]
149. ! [X1] : (((kind(X1) | (~person(X1) | ~tall(X1))) & ((person(X1) & tall(X1)) | ~kind(X1))) | ~anywhere(X1)) | ? [X0] : (~richer(fred,X0) & room(X0)) [nnf transformation 134]
150. ! [X1] : (((kind(X1) | ~person(X1) | ~tall(X1)) & ((person(X1) & tall(X1)) | ~kind(X1))) | ~anywhere(X1)) | ? [X0] : (~richer(fred,X0) & room(X0)) [flattening 149]
151. ! [X0] : (((kind(X0) | ~person(X0) | ~tall(X0)) & ((person(X0) & tall(X0)) | ~kind(X0))) | ~anywhere(X0)) | ? [X1] : (~richer(fred,X1) & room(X1)) [rectify 150]
152. ? [X1] : (~richer(fred,X1) & room(X1)) => (~richer(fred,sK0) & room(sK0)) [choice axiom]
153. ! [X0] : (((kind(X0) | ~person(X0) | ~tall(X0)) & ((person(X0) & tall(X0)) | ~kind(X0))) | ~anywhere(X0)) | (~richer(fred,sK0) & room(sK0)) [skolemisation 151,152]
158. anywhere(X0) [cnf transformation 5]
209. mary != fred [cnf transformation 43]
240. ~room(X0) | mary = X0 [cnf transformation 131]
242. tall(X0) | ~kind(X0) | ~anywhere(X0) | room(sK0) [cnf transformation 153]
243. tall(X0) | ~kind(X0) | ~anywhere(X0) | ~richer(fred,sK0) [cnf transformation 153]
251. ~person(mary) | ~quiet(mary) | ~tall(mary) [cnf transformation 141]
252. richer(X0,mary) | mary = X0 | room(X0) [cnf transformation 143]
253. kind(mary) [cnf transformation 52]
254. person(mary) [cnf transformation 52]
262. quiet(mary) [cnf transformation 146]
273. 3 <=> richer(fred,sK0) [avatar definition]
275. ~richer(fred,sK0) <- (~3) [avatar component clause 273]
282. 5 <=> room(sK0) [avatar definition]
284. room(sK0) <- (5) [avatar component clause 282]
293. tall(X0) | ~kind(X0) | ~richer(fred,sK0) [subsumption resolution 243,158]
295. 7 <=> ! [X0] : (tall(X0) | ~kind(X0)) [avatar definition]
296. ~kind(X0) | tall(X0) <- (7) [avatar component clause 295]
297. ~3 | 7 [avatar split clause 293,295,273]
298. tall(X0) | ~kind(X0) | room(sK0) [subsumption resolution 242,158]
299. 5 | 7 [avatar split clause 298,295,282]
302. 8 <=> quiet(mary) [avatar definition]
306. 9 <=> kind(mary) [avatar definition]
307. kind(mary) <- (9) [avatar component clause 306]
310. 10 <=> person(mary) [avatar definition]
314. 11 <=> ! [X0] : (richer(X0,mary) | mary = X0) [avatar definition]
315. richer(X0,mary) | mary = X0 <- (11) [avatar component clause 314]
320. 12 <=> tall(mary) [avatar definition]
322. ~tall(mary) <- (~12) [avatar component clause 320]
323. ~12 | ~8 | ~10 [avatar split clause 251,310,302,320]
324. richer(X0,mary) | mary = X0 [subsumption resolution 252,240]
325. 11 [avatar split clause 324,314]
326. 10 [avatar split clause 254,310]
327. 9 [avatar split clause 253,306]
328. 8 [avatar split clause 262,302]
331. mary = sK0 <- (5) [resolution 240,284]
334. ~richer(fred,mary) <- (~3, 5) [backward demodulation 275,331]
336. mary = fred <- (~3, 5, 11) [resolution 315,334]
337. $false <- (~3, 5, 11) [subsumption resolution 336,209]
338. 3 | ~5 | ~11 [avatar contradiction clause 337]
343. tall(mary) <- (7, 9) [resolution 296,307]
344. $false <- (7, 9, ~12) [subsumption resolution 343,322]
345. ~7 | ~9 | 12 [avatar contradiction clause 344]
346. $false [avatar sat refutation 297,299,323,325,326,327,328,338,345]
% SZS output end Proof for 6868144602794151005170315
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.04437 |
Dolores, Gayle, Roger are the only persons in the room.
Either “Gayle either does not practice digital art or enjoys logic puzzles but not both” or “everyone in the room does not write and illustrates their own graphic novels or enjoys windsurfing” but not both.
If “it is not the case that “someone outside the room does not design and sews custom cosplay costumes for conventions”” then “Gayle who enjoys windsurfing collects comic books”.
Dolores participates in long-distance cycling events across the country.
Not everyone anywhere writes and illustrates their own graphic novels if they is not a coffee connoisseur.
Gayle enjoys windsurfing.
Everyone in the room hosts a YouTube channel dedicated to art tutorials if they hosts a popular podcast about emerging technologies.
Gayle does not host a popular podcast about emerging technologies.
Dolores is an enthusiastic bird watcher who travels for rare sightings.
Everyone in the room enjoys logic puzzles.
Everyone anywhere builds model airplanes if they participates in long-distance cycling events across the country.
Dolores is an expert in identifying and foraging wild edible plants.
Gayle does not have a specialized collection of handmade artisan pottery.
Dolores is not a coffee connoisseur.
Dolores has a specialized collection of handmade artisan pottery.
Dolores owns an extensive assortment of vintage comic book memorabilia.
Everyone outside the room writes and illustrates their own graphic novels if they enjoys logic puzzles.
Everyone in the room does not participate in long-distance cycling events across the country if they hosts a popular podcast about emerging technologies.
It is not the case that “Gayle is an avid collector of autographed memorabilia from famous musicians”.
Dolores either hosts a YouTube channel dedicated to art tutorials or practices digital art but not both.
Dolores enjoys windsurfing. | Dolores builds model airplanes. | entailment | room(dolores)&room(gayle)&room(roger)&(![X]:(room(X)=>(X='dolores'|X='gayle'|X='roger')))&
((((does_not_practice_digital_art(gayle))<~>(enjoys_logic_puzzles(gayle))))<~>(![X]:(room(X)=>(((enjoys_windsurfing(X))|(does_not_write_and_illustrates_their_own_graphic_novels(X)))))))&
((~(?[X]:(~room(X)&(does_not_design_and_sews_custom_cosplay_costumes_for_conventions(X)))))=>((enjoys_windsurfing(gayle))&(collects_comic_books(gayle))))&
(participates_in_long-distance_cycling_events_across_the_country(dolores))&
(~![X]:(anywhere(X)=>(((is_not_a_coffee_connoisseur(X))=>(writes_and_illustrates_their_own_graphic_novels(X))))))&
(enjoys_windsurfing(gayle))&
(![X]:(room(X)=>(((hosts_a_popular_podcast_about_emerging_technologies(X))=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(X))))))&
(does_not_host_a_popular_podcast_about_emerging_technologies(gayle))&
(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(dolores))&
(![X]:(room(X)=>(enjoys_logic_puzzles(X))))&
(![X]:(anywhere(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))=>(builds_model_airplanes(X))))))&
(is_an_expert_in_identifying_and_foraging_wild_edible_plants(dolores))&
(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(gayle))&
(is_not_a_coffee_connoisseur(dolores))&
(has_a_specialized_collection_of_handmade_artisan_pottery(dolores))&
(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(dolores))&
(![X]:(~room(X)=>(((enjoys_logic_puzzles(X))=>(writes_and_illustrates_their_own_graphic_novels(X))))))&
(![X]:(room(X)=>(((hosts_a_popular_podcast_about_emerging_technologies(X))=>(does_not_participate_in_long-distance_cycling_events_across_the_country(X))))))&
(~(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(gayle)))&
(((hosts_a_YouTube_channel_dedicated_to_art_tutorials(dolores))<~>(practices_digital_art(dolores))))&
(enjoys_windsurfing(dolores)) | room(dolores)&room(gayle)&room(roger)&(![X]:(room(X)=>(X='dolores'|X='gayle'|X='roger')))&
builds_model_airplanes(dolores) | [
"b4",
"p0",
"p3",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8607663532184802072639167
% SZS output start Proof for 8607663532184802072639167
5. ! [X0] : anywhere(X0) [input b4]
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
47. predh(mary) [input p3]
54. ! [X0] : (anywhere(X0) => (predh(X0) => predi(X0))) [input p10]
65. ~(predi(mary) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis]
148. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
149. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 148]
155. ! [X0] : ((predi(X0) | ~predh(X0)) | ~anywhere(X0)) [ennf transformation 54]
156. ! [X0] : (predi(X0) | ~predh(X0) | ~anywhere(X0)) [flattening 155]
159. ~predi(mary) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 65]
160. ~predi(mary) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 159]
171. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) [choice axiom]
172. ~predi(mary) | (fred != sK3 & paul != sK3 & mary != sK3 & room(sK3)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 160,171]
173. anywhere(X0) [cnf transformation 5]
254. room(mary) [cnf transformation 149]
255. room(paul) [cnf transformation 149]
256. room(fred) [cnf transformation 149]
257. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 149]
267. predh(mary) [cnf transformation 47]
272. predi(X0) | ~predh(X0) | ~anywhere(X0) [cnf transformation 156]
279. ~predi(mary) | room(sK3) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 172]
280. ~predi(mary) | mary != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 172]
281. ~predi(mary) | paul != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 172]
282. ~predi(mary) | fred != sK3 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 172]
324. ~predh(X0) | predi(X0) [subsumption resolution 272,173]
335. ~predi(mary) | fred != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 282,256]
336. ~predi(mary) | fred != sK3 | ~room(mary) [subsumption resolution 335,255]
337. ~predi(mary) | fred != sK3 [subsumption resolution 336,254]
339. 11 <=> fred = sK3 [avatar definition]
341. fred != sK3 <- (~11) [avatar component clause 339]
343. 12 <=> predi(mary) [avatar definition]
346. ~11 | ~12 [avatar split clause 337,343,339]
347. ~predi(mary) | paul != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 281,256]
348. ~predi(mary) | paul != sK3 | ~room(mary) [subsumption resolution 347,255]
349. ~predi(mary) | paul != sK3 [subsumption resolution 348,254]
351. 13 <=> paul = sK3 [avatar definition]
353. paul != sK3 <- (~13) [avatar component clause 351]
354. ~13 | ~12 [avatar split clause 349,343,351]
355. ~predi(mary) | mary != sK3 | ~room(paul) | ~room(mary) [subsumption resolution 280,256]
356. ~predi(mary) | mary != sK3 | ~room(mary) [subsumption resolution 355,255]
357. ~predi(mary) | mary != sK3 [subsumption resolution 356,254]
359. 14 <=> mary = sK3 [avatar definition]
361. mary != sK3 <- (~14) [avatar component clause 359]
362. ~14 | ~12 [avatar split clause 357,343,359]
363. ~predi(mary) | room(sK3) | ~room(paul) | ~room(mary) [subsumption resolution 279,256]
364. ~predi(mary) | room(sK3) | ~room(mary) [subsumption resolution 363,255]
365. ~predi(mary) | room(sK3) [subsumption resolution 364,254]
367. 15 <=> room(sK3) [avatar definition]
369. room(sK3) <- (15) [avatar component clause 367]
370. 15 | ~12 [avatar split clause 365,343,367]
378. predi(mary) [resolution 324,267]
381. 12 [avatar split clause 378,343]
428. paul = sK3 | mary = sK3 | fred = sK3 <- (15) [resolution 257,369]
442. mary = sK3 | fred = sK3 <- (~13, 15) [subsumption resolution 428,353]
443. fred = sK3 <- (~13, ~14, 15) [subsumption resolution 442,361]
444. $false <- (~11, ~13, ~14, 15) [subsumption resolution 443,341]
445. 11 | 13 | 14 | ~15 [avatar contradiction clause 444]
446. $false [avatar sat refutation 346,354,362,370,381,445]
% SZS output end Proof for 8607663532184802072639167
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.530717 |
Laura, Roberto, Anna, Helen are the only persons in the room.
Everyone in the room is not a scotch connoisseur, enjoys camping and organizing outdoor survival workshops and is not a coffee connoisseur only if they enjoys coding in Python or is an avid collector of autographed memorabilia from famous musicians or both.
More than one person in the room is not a scotch connoisseur, enjoys camping and organizing outdoor survival workshops and is not a coffee connoisseur.
If someone is not a scotch connoisseur or travels domestically frequently or both then he/she makes homemade pastries.
Laura who is not an avid collector of autographed memorabilia from famous musicians travels domestically frequently.
Roberto who does not develop open-source software projects in their free time either enjoys fishing or is a coffee connoisseur but not both.
Everyone in the room does not enjoy fishing.
Everyone in the room enjoys coding in Python or does not own a television or both if they neither enjoys coding in Python nor writes a travel blog and vice versa. | Anna makes homemade pastries. | entailment | room(laura)&room(roberto)&room(anna)&room(helen)&(![X]:(room(X)=>(X='laura'|X='roberto'|X='anna'|X='helen')))&
(~(![X]:(~room(X)=>(((collects_rare_and_antique_scientific_instruments(X))|(does_not_make_homemade_pastries(X))))))=>((((does_not_play_the_drums(laura))|(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(laura))))&(((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(laura))&(does_not_host_regular_game_nights_featuring_complex_strategy_games(laura))&(does_not_develop_open-source_software_projects_in_their_free_time(laura))))))&
((![X]:(room(X)=>(((does_not_watche_fantasy_movies(X))&(does_not_play_video_games(X))&(collects_rare_and_antique_scientific_instruments(X))))))=>((![X]:((does_not_collect_antique_jewelry(X))=>(does_not_watche_fantasy_movies(X))))))&
((~![X]:(room(X)=>(((does_not_write_a_travel_blog(X))|(owns_a_significant_collection_of_rare_gemstones_and_minerals(X))))))=>(~![X]:(room(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))=>(does_not_play_the_drums(X)))))))&
((![X]:((((does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))&(does_not_own_a_television(X))&(is_not_a_scotch_connoisseur(X))))=>(((is_an_avid_hiker(X))|(does_not_collect_rare_and_antique_scientific_instruments(X)))))))&
(![X]:(room(X)=>(((((enjoys_coding_in_Python(X))|(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))<=(((is_not_a_scotch_connoisseur(X))&(enjoys_camping_and_organizing_outdoor_survival_workshops(X))&(is_not_a_coffee_connoisseur(X))))))))&
(~![X]:(room(X)=>(((owns_a_significant_collection_of_rare_gemstones_and_minerals(X))=>(does_not_play_the_drums(X))))))&
((![X]:((((does_not_develop_open-source_software_projects_in_their_free_time(X))|(enjoys_coding_in_Python(X))))=>(((does_not_own_an_Android_phone(X))|(collects_rare_and_antique_scientific_instruments(X)))))))&
((?[X,Y]:(room(X)&room(Y)&(((is_not_a_scotch_connoisseur(X))&(enjoys_camping_and_organizing_outdoor_survival_workshops(X))&(is_not_a_coffee_connoisseur(X)))&((is_not_a_scotch_connoisseur(Y))&(enjoys_camping_and_organizing_outdoor_survival_workshops(Y))&(is_not_a_coffee_connoisseur(Y))))&(X!=Y))))&
(~![X]:(room(X)=>(((((is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))|(does_not_collect_antique_jewelry(X))))=>(((does_not_host_regular_game_nights_featuring_complex_strategy_games(X))<~>(does_not_own_a_significant_collection_of_rare_gemstones_and_minerals(X))))))))&
((![X]:((((is_not_a_scotch_connoisseur(X))|(travels_domestically_frequently(X))))=>(makes_homemade_pastries(X)))))&
(![X]:(room(X)=>(((((is_a_scotch_connoisseur(X))|(does_not_collect_foreign_coins(X))))=>(((does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))<~>(collects_foreign_coins(X))))))))&
(?[X]:(room(X)&(((is_a_professional_photographer_specializing_in_portrait_photography(X))&(is_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))))))&
(~![X]:(room(X)=>(is_a_coffee_connoisseur(X))))&
((laura_dream=>(~![X]:(room(X)=>(does_not_collect_rare_and_antique_scientific_instruments(X))))))&
(![X]:(room(X)=>(((((does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))|(does_not_collect_foreign_coins(X))))<=(((is_a_professional_photographer_specializing_in_portrait_photography(X))|(is_not_a_professional_photographer_specializing_in_portrait_photography(X))))))))&
(![X]:(room(X)=>(((((does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))|(does_not_collect_foreign_coins(X))))=>(((is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(X))|(owns_an_Android_phone(X))))))))&
((is_not_an_avid_collector_of_autographed_memorabilia_from_famous_musicians(laura))&(travels_domestically_frequently(laura)))&
((does_not_develop_open-source_software_projects_in_their_free_time(roberto))&(((enjoys_fishing(roberto))<~>(is_a_coffee_connoisseur(roberto)))))&
(![X]:(room(X)=>(((((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))|(does_not_enjoy_coding_in_Python(X))))<=(((does_not_enjoy_fishing(X))&(drives_a_hybrid_car(X))))))))&
(![X]:(~room(X)=>(does_not_travel_domestically_frequently(X))))&
(![X]:(room(X)=>(does_not_enjoy_fishing(X))))&
(![X]:(room(X)=>(((((enjoys_coding_in_Python(X))|(does_not_own_a_television(X))))<=>(~((enjoys_coding_in_Python(X))|(writes_a_travel_blog(X)))))))) | room(laura)&room(roberto)&room(anna)&room(helen)&(![X]:(room(X)=>(X='laura'|X='roberto'|X='anna'|X='helen')))&
makes_homemade_pastries(anna) | [
"p0",
"p5",
"p8",
"p10",
"p17",
"p18",
"p21",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2936954282098030653797365
% SZS output start Proof for 2936954282098030653797365
44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
49. ! [X0] : (room(X0) => ((~predh(X0) & predc(X0) & ~predu(X0)) => (prede(X0) | predw(X0)))) [input p5]
52. ? [X0,X1] : (X0 != X1 & ~predh(X1) & predc(X1) & ~predu(X1) & ~predh(X0) & predc(X0) & ~predu(X0) & room(X1) & room(X0)) [input p8]
54. ! [X0] : ((predf(X0) | ~predu(X0)) => preda(X0)) [input p10]
61. predf(mary) & ~prede(mary) [input p17]
62. (predk(paul) <~> predh(paul)) & ~predt(paul) [input p18]
65. ! [X0] : (room(X0) => ~predk(X0)) [input p21]
66. ! [X0] : (room(X0) => ((~predn(X0) | predw(X0)) <=> ~(predz(X0) | predw(X0)))) [input p22]
67. ~(preda(fred) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis]
79. predk(paul) <~> predh(paul) [pure predicate removal 62]
154. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
155. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 154]
158. ! [X0] : (((prede(X0) | predw(X0)) | (predh(X0) | ~predc(X0) | predu(X0))) | ~room(X0)) [ennf transformation 49]
159. ! [X0] : (prede(X0) | predw(X0) | predh(X0) | ~predc(X0) | predu(X0) | ~room(X0)) [flattening 158]
162. ! [X0] : (preda(X0) | (~predf(X0) & predu(X0))) [ennf transformation 54]
169. ! [X0] : (~predk(X0) | ~room(X0)) [ennf transformation 65]
170. ! [X0] : (((~predn(X0) | predw(X0)) <=> (~predz(X0) & ~predw(X0))) | ~room(X0)) [ennf transformation 66]
171. ~preda(fred) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 67]
172. ~preda(fred) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 171]
179. ? [X0,X1] : (X0 != X1 & ~predh(X1) & predc(X1) & ~predu(X1) & ~predh(X0) & predc(X0) & ~predu(X0) & room(X1) & room(X0)) => (sK2 != sK3 & ~predh(sK3) & predc(sK3) & ~predu(sK3) & ~predh(sK2) & predc(sK2) & ~predu(sK2) & room(sK3) & room(sK2)) [choice axiom]
180. sK2 != sK3 & ~predh(sK3) & predc(sK3) & ~predu(sK3) & ~predh(sK2) & predc(sK2) & ~predu(sK2) & room(sK3) & room(sK2) [skolemisation 52,179]
190. (~predh(paul) | ~predk(paul)) & (predh(paul) | predk(paul)) [nnf transformation 79]
191. ! [X0] : ((((~predn(X0) | predw(X0)) | (predz(X0) | predw(X0))) & ((~predz(X0) & ~predw(X0)) | (predn(X0) & ~predw(X0)))) | ~room(X0)) [nnf transformation 170]
192. ! [X0] : (((~predn(X0) | predw(X0) | predz(X0) | predw(X0)) & ((~predz(X0) & ~predw(X0)) | (predn(X0) & ~predw(X0)))) | ~room(X0)) [flattening 191]
193. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK7 & fred != sK7 & paul != sK7 & mary != sK7 & room(sK7)) [choice axiom]
194. ~preda(fred) | (alice != sK7 & fred != sK7 & paul != sK7 & mary != sK7 & room(sK7)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 172,193]
275. room(mary) [cnf transformation 155]
276. room(paul) [cnf transformation 155]
277. room(fred) [cnf transformation 155]
278. room(alice) [cnf transformation 155]
279. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 155]
282. ~predc(X0) | predw(X0) | predh(X0) | prede(X0) | predu(X0) | ~room(X0) [cnf transformation 159]
285. room(sK2) [cnf transformation 180]
286. room(sK3) [cnf transformation 180]
287. ~predu(sK2) [cnf transformation 180]
288. predc(sK2) [cnf transformation 180]
289. ~predh(sK2) [cnf transformation 180]
290. ~predu(sK3) [cnf transformation 180]
291. predc(sK3) [cnf transformation 180]
292. ~predh(sK3) [cnf transformation 180]
293. sK2 != sK3 [cnf transformation 180]
297. predu(X0) | preda(X0) [cnf transformation 162]
310. ~prede(mary) [cnf transformation 61]
312. predh(paul) | predk(paul) [cnf transformation 190]
315. ~predk(X0) | ~room(X0) [cnf transformation 169]
316. ~predw(X0) | ~predw(X0) | ~room(X0) [cnf transformation 192]
321. ~preda(fred) | room(sK7) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 194]
322. ~preda(fred) | mary != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 194]
323. ~preda(fred) | paul != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 194]
324. ~preda(fred) | fred != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 194]
325. ~preda(fred) | alice != sK7 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 194]
326. ~predw(X0) | ~room(X0) [duplicate literal removal 316]
356. 6 <=> predk(paul) [avatar definition]
357. predk(paul) <- (6) [avatar component clause 356]
360. 7 <=> predh(paul) [avatar definition]
361. predh(paul) <- (7) [avatar component clause 360]
364. 6 | 7 [avatar split clause 312,360,356]
365. ~preda(fred) | alice != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 325,278]
366. ~preda(fred) | alice != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 365,277]
367. ~preda(fred) | alice != sK7 | ~room(mary) [subsumption resolution 366,276]
368. ~preda(fred) | alice != sK7 [subsumption resolution 367,275]
370. 8 <=> alice = sK7 [avatar definition]
372. alice != sK7 <- (~8) [avatar component clause 370]
374. 9 <=> preda(fred) [avatar definition]
376. ~preda(fred) <- (~9) [avatar component clause 374]
377. ~8 | ~9 [avatar split clause 368,374,370]
378. ~preda(fred) | fred != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 324,278]
379. ~preda(fred) | fred != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 378,277]
380. ~preda(fred) | fred != sK7 | ~room(mary) [subsumption resolution 379,276]
381. ~preda(fred) | fred != sK7 [subsumption resolution 380,275]
383. 10 <=> fred = sK7 [avatar definition]
385. fred != sK7 <- (~10) [avatar component clause 383]
386. ~10 | ~9 [avatar split clause 381,374,383]
387. ~preda(fred) | paul != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 323,278]
388. ~preda(fred) | paul != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 387,277]
389. ~preda(fred) | paul != sK7 | ~room(mary) [subsumption resolution 388,276]
390. ~preda(fred) | paul != sK7 [subsumption resolution 389,275]
392. 11 <=> paul = sK7 [avatar definition]
394. paul != sK7 <- (~11) [avatar component clause 392]
395. ~11 | ~9 [avatar split clause 390,374,392]
396. ~preda(fred) | mary != sK7 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 322,278]
397. ~preda(fred) | mary != sK7 | ~room(paul) | ~room(mary) [subsumption resolution 396,277]
398. ~preda(fred) | mary != sK7 | ~room(mary) [subsumption resolution 397,276]
399. ~preda(fred) | mary != sK7 [subsumption resolution 398,275]
401. 12 <=> mary = sK7 [avatar definition]
403. mary != sK7 <- (~12) [avatar component clause 401]
404. ~12 | ~9 [avatar split clause 399,374,401]
405. ~preda(fred) | room(sK7) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 321,278]
406. ~preda(fred) | room(sK7) | ~room(paul) | ~room(mary) [subsumption resolution 405,277]
407. ~preda(fred) | room(sK7) | ~room(mary) [subsumption resolution 406,276]
408. ~preda(fred) | room(sK7) [subsumption resolution 407,275]
410. 13 <=> room(sK7) [avatar definition]
412. room(sK7) <- (13) [avatar component clause 410]
413. 13 | ~9 [avatar split clause 408,374,410]
414. preda(sK2) [resolution 297,287]
415. preda(sK3) [resolution 297,290]
418. ~room(paul) <- (6) [resolution 315,357]
419. $false <- (6) [subsumption resolution 418,276]
420. ~6 [avatar contradiction clause 419]
457. predw(sK2) | predh(sK2) | prede(sK2) | predu(sK2) | ~room(sK2) [resolution 282,288]
458. predw(sK3) | predh(sK3) | prede(sK3) | predu(sK3) | ~room(sK3) [resolution 282,291]
459. predw(sK2) | prede(sK2) | predu(sK2) | ~room(sK2) [subsumption resolution 457,289]
460. predw(sK2) | prede(sK2) | ~room(sK2) [subsumption resolution 459,287]
461. predw(sK2) | prede(sK2) [subsumption resolution 460,285]
463. 14 <=> prede(sK2) [avatar definition]
465. prede(sK2) <- (14) [avatar component clause 463]
467. 15 <=> predw(sK2) [avatar definition]
469. predw(sK2) <- (15) [avatar component clause 467]
470. 14 | 15 [avatar split clause 461,467,463]
471. predw(sK3) | prede(sK3) | predu(sK3) | ~room(sK3) [subsumption resolution 458,292]
472. predw(sK3) | prede(sK3) | ~room(sK3) [subsumption resolution 471,290]
473. predw(sK3) | prede(sK3) [subsumption resolution 472,286]
475. 16 <=> prede(sK3) [avatar definition]
477. prede(sK3) <- (16) [avatar component clause 475]
479. 17 <=> predw(sK3) [avatar definition]
481. predw(sK3) <- (17) [avatar component clause 479]
482. 16 | 17 [avatar split clause 473,479,475]
489. fred = sK2 | paul = sK2 | mary = sK2 | alice = sK2 [resolution 279,285]
490. fred = sK3 | paul = sK3 | mary = sK3 | alice = sK3 [resolution 279,286]
529. 26 <=> alice = sK2 [avatar definition]
533. 27 <=> mary = sK2 [avatar definition]
535. mary = sK2 <- (27) [avatar component clause 533]
537. 28 <=> paul = sK2 [avatar definition]
539. paul = sK2 <- (28) [avatar component clause 537]
541. 29 <=> fred = sK2 [avatar definition]
543. fred = sK2 <- (29) [avatar component clause 541]
544. 26 | 27 | 28 | 29 [avatar split clause 489,541,537,533,529]
546. 30 <=> alice = sK3 [avatar definition]
548. alice = sK3 <- (30) [avatar component clause 546]
550. 31 <=> mary = sK3 [avatar definition]
552. mary = sK3 <- (31) [avatar component clause 550]
554. 32 <=> paul = sK3 [avatar definition]
556. paul = sK3 <- (32) [avatar component clause 554]
558. 33 <=> fred = sK3 [avatar definition]
560. fred = sK3 <- (33) [avatar component clause 558]
561. 30 | 31 | 32 | 33 [avatar split clause 490,558,554,550,546]
625. alice != sK2 <- (30) [backward demodulation 293,548]
628. ~26 | ~30 [avatar split clause 625,546,529]
644. prede(mary) <- (14, 27) [backward demodulation 465,535]
645. $false <- (14, 27) [subsumption resolution 644,310]
646. ~14 | ~27 [avatar contradiction clause 645]
651. predw(mary) <- (15, 27) [forward demodulation 469,535]
659. ~room(mary) <- (15, 27) [resolution 651,326]
662. $false <- (15, 27) [subsumption resolution 659,275]
663. ~15 | ~27 [avatar contradiction clause 662]
667. ~predh(paul) <- (28) [backward demodulation 289,539]
672. $false <- (7, 28) [subsumption resolution 667,361]
673. ~7 | ~28 [avatar contradiction clause 672]
678. preda(fred) <- (29) [backward demodulation 414,543]
684. 9 | ~29 [avatar split clause 678,541,374]
685. fred = sK7 | paul = sK7 | mary = sK7 | alice = sK7 <- (13) [resolution 412,279]
686. paul = sK7 | mary = sK7 | alice = sK7 <- (~10, 13) [subsumption resolution 685,385]
687. mary = sK7 | alice = sK7 <- (~10, ~11, 13) [subsumption resolution 686,394]
688. alice = sK7 <- (~10, ~11, ~12, 13) [subsumption resolution 687,403]
689. $false <- (~8, ~10, ~11, ~12, 13) [subsumption resolution 688,372]
690. 8 | 10 | 11 | 12 | ~13 [avatar contradiction clause 689]
697. prede(mary) <- (16, 31) [backward demodulation 477,552]
698. $false <- (16, 31) [subsumption resolution 697,310]
699. ~16 | ~31 [avatar contradiction clause 698]
720. ~predh(paul) <- (32) [backward demodulation 292,556]
724. $false <- (7, 32) [subsumption resolution 720,361]
725. ~7 | ~32 [avatar contradiction clause 724]
737. predw(mary) <- (17, 31) [forward demodulation 481,552]
768. ~room(mary) <- (17, 31) [resolution 737,326]
771. $false <- (17, 31) [subsumption resolution 768,275]
772. ~17 | ~31 [avatar contradiction clause 771]
777. preda(fred) <- (33) [backward demodulation 415,560]
781. $false <- (~9, 33) [subsumption resolution 777,376]
782. 9 | ~33 [avatar contradiction clause 781]
783. $false [avatar sat refutation 364,377,386,395,404,413,420,470,482,544,561,628,646,663,673,684,690,699,725,772,782]
% SZS output end Proof for 2936954282098030653797365
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.043 s
% ------------------------------
% ------------------------------
| 0.582775 |
Marlyn is the only person in the room.
Either “everyone in the room is not a client of Costco or does not enjoy making ceramics” or “Marlyn enjoys making ceramics” but not both.
If “Marlyn is a client of Costco” then “everyone in the room does not mentor a youth basketball team on weekends or is not allergic to anything”. | Marlyn enjoys stargazing. | neutral | room(marlyn)&(![X]:(room(X)=>(X='marlyn')))&
((![X]:(room(X)=>(((does_not_enjoy_making_ceramics(X))|(is_not_a_client_of_Costco(X))))))<~>(enjoys_making_ceramics(marlyn)))&
((is_a_client_of_Costco(marlyn))=>(![X]:(room(X)=>(((is_not_allergic_to_anything(X))|(does_not_mentor_a_youth_basketball_team_on_weekends(X)))))))&
((![X]:(room(X)=>(((mentors_a_youth_basketball_team_on_weekends(X))|(is_not_allergic_to_anything(X))))))=>(![X]:(room(X)=>(((is_not_allergic_to_anything(X))=>(is_a_client_of_Costco(X)))))))&
((![X]:(room(X)=>(((does_not_collect_foreign_coins(X))|(practices_tai_chi(X))))))=>(is_a_client_of_Costco(marlyn)))&
(enjoys_making_ceramics(marlyn))&
(![X]:(room(X)=>(((regularly_contributes_to_tech_forums_and_online_communities(X))<=(is_passionate_about_collecting_and_restoring_classic_cars(X))))))&
(~(is_allergic_to_anything(marlyn)))&
(![X]:(room(X)=>(((practices_tai_chi(X))<=(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))&
(((enjoys_making_ceramics(marlyn))<~>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(marlyn))))&
(![X]:(room(X)=>(((is_a_drone_photographer(X))=>(((does_not_enjoy_stargazing(X))|(does_not_regularly_contributes_to_tech_forums_and_online_communities(X))))))))&
(does_not_collect_foreign_coins(marlyn))&
(is_a_client_of_Costco(marlyn))&
(![X]:(room(X)=>(((is_a_client_of_Costco(X))<=(((is_not_a_client_of_Costco(X))<~>(is_a_client_of_Costco(X)))))))) | room(marlyn)&(![X]:(room(X)=>(X='marlyn')))&
enjoys_stargazing(marlyn) | [] | null | 0.649691 |
Greg, Sarah, Lawrence, Doris are the only persons in the room.
“Lawrence collects foreign coins” if “everyone in the room uses contact lenses or does not host themed dinner parties featuring gourmet home-cooked meals” and vice versa.
“More than one person in the room is passionate about collecting and restoring classic cars” unless “everyone in the room enjoys kayaking or does not practice digital art”.
“Doris is not passionate about collecting and restoring classic cars” only if “no one in the room who hosts themed dinner parties featuring gourmet home-cooked meals or collects foreign coins or both collects foreign coins”.
“Everyone anywhere hosts themed dinner parties featuring gourmet home-cooked meals or does not practice digital art” unless “everyone in the room does not compete in national level swimming championships or enjoys macrame”.
“Everyone in the room practices pilates if they neither enjoys macrame nor does not compete in national level swimming championships and vice versa” if “Sarah enjoys macrame”. | Lawrence collects foreign coins. | neutral | room(greg)&room(sarah)&room(lawrence)&room(doris)&(![X]:(room(X)=>(X='greg'|X='sarah'|X='lawrence'|X='doris')))&
((![X]:(room(X)=>(((does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))|(uses_contact_lenses(X))))))<=>(collects_foreign_coins(lawrence)))&
(~(![X]:(room(X)=>(((does_not_practice_digital_art(X))|(enjoys_kayaking(X))))))=>((?[X,Y]:(room(X)&room(Y)&(is_passionate_about_collecting_and_restoring_classic_cars(X)&is_passionate_about_collecting_and_restoring_classic_cars(Y))&(X!=Y)))))&
((is_not_passionate_about_collecting_and_restoring_classic_cars(doris))=>(~?[X]:(room(X)=>(((((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))|(collects_foreign_coins(X))))=>(collects_foreign_coins(X)))))))&
(~(![X]:(room(X)=>(((enjoys_macrame(X))|(does_not_compete_in_national_level_swimming_championships(X))))))=>(![X]:(anywhere(X)=>(((does_not_practice_digital_art(X))|(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))))))&
((enjoys_macrame(sarah))=>(![X]:(room(X)=>(((practices_pilates(X))<=>(~((enjoys_macrame(X))|(does_not_compete_in_national_level_swimming_championships(X)))))))))&
(![X]:(room(X)=>(~((does_not_enjoy_kayaking(X))|(does_not_enjoy_macrame(X))))))&
(practices_digital_art(doris))&
(![X]:(anywhere(X)=>(((competes_in_national_level_swimming_championships(X))=>(does_not_enjoy_kayaking(X))))))&
(~![X]:(room(X)=>(((does_not_practice_pilates(X))<=>(practices_digital_art(X))))))&
(uses_contact_lenses(greg))&
(?[X]:(room(X)&(((enjoys_macrame(X))|(competes_in_national_level_swimming_championships(X))))))&
(![X]:(room(X)=>(((does_not_enjoy_macrame(X))=>(uses_contact_lenses(X))))))&
(does_not_practice_digital_art(greg)) | room(greg)&room(sarah)&room(lawrence)&room(doris)&(![X]:(room(X)=>(X='greg'|X='sarah'|X='lawrence'|X='doris')))&
collects_foreign_coins(lawrence) | [] | null | 0 |
There is a room.
“At least one person in the room can play the flute or writes and illustrates their own graphic novels or both” if “no one in the room does not collect limited-edition art prints from contemporary artists or does not have a pet dog” and vice versa.
At least one person outside the room does not have a pet dog.
Everyone in the room does not practice pilates if they creates bespoke furniture pieces from reclaimed wood.
Everyone in the room does not collect rare and antique scientific instruments if they does not practice pilates.
More than one person in the room creates bespoke furniture pieces from reclaimed wood.
Someone in the room practices pilates.
Everyone in the room is not an amateur astronomer who builds and uses custom telescopes if they collects first edition books.
Everyone in the room who is not an amateur astronomer who builds and uses custom telescopes does not collect first edition books.
Not everyone outside the room cannot play the flute if they does not collect first edition books.
Everyone anywhere writes and illustrates their own graphic novels if they does not enjoy camping and organizing outdoor survival workshops.
No one anywhere collects first edition books if they has a pet dog and vice versa.
If someone does not collect rare and antique scientific instruments then he/she collects limited-edition art prints from contemporary artists.
Everyone outside the room has a pet dog if they collects rare and antique scientific instruments.
Everyone anywhere enjoys camping and organizing outdoor survival workshops if they collects rare and antique scientific instruments. | Everyone in the room does not enjoy camping and organizing outdoor survival workshops or creates bespoke furniture pieces from reclaimed wood. | contradiction | (there_is_a_room)&
((~?[X]:(room(X)=>(((does_not_have_a_pet_dog(X))|(does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))))))<=>(((?[X]:(room(X)&((can_play_the_flute(X))|(writes_and_illustrates_their_own_graphic_novels(X))))))))&
(((?[X]:(~room(X)&does_not_have_a_pet_dog(X)))))&
(![X]:(room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))=>(does_not_practice_pilates(X))))))&
(![X]:(room(X)=>(((does_not_practice_pilates(X))=>(does_not_collect_rare_and_antique_scientific_instruments(X))))))&
((?[X,Y]:(room(X)&room(Y)&(creates_bespoke_furniture_pieces_from_reclaimed_wood(X)&creates_bespoke_furniture_pieces_from_reclaimed_wood(Y))&(X!=Y))))&
(?[X]:(room(X)&(practices_pilates(X))))&
(![X]:(room(X)=>(((collects_first_edition_books(X))=>(is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))))))&
(![X]:(room(X)=>(((is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))=>(does_not_collect_first_edition_books(X))))))&
(~![X]:(~room(X)=>(((does_not_collect_first_edition_books(X))=>(cannot_play_the_flute(X))))))&
(![X]:(anywhere(X)=>(((does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))=>(writes_and_illustrates_their_own_graphic_novels(X))))))&
(~?[X]:(anywhere(X)=>(((collects_first_edition_books(X))<=>(has_a_pet_dog(X))))))&
((![X]:((does_not_collect_rare_and_antique_scientific_instruments(X))=>(collects_limited-edition_art_prints_from_contemporary_artists(X)))))&
(![X]:(~room(X)=>(((collects_rare_and_antique_scientific_instruments(X))=>(has_a_pet_dog(X))))))&
(![X]:(anywhere(X)=>(((collects_rare_and_antique_scientific_instruments(X))=>(enjoys_camping_and_organizing_outdoor_survival_workshops(X)))))) | (there_is_a_room)&
![X]:(room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))|(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))))) | [
"b4",
"p1",
"p2",
"p3",
"p6",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1803669137612222182936643
% SZS output start Proof for 1803669137612222182936643
5. ! [X0] : anywhere(X0) [input b4]
45. ~? [X0] : (room(X0) => (~predi(X0) | ~predb(X0))) <=> ? [X0] : ((prede(X0) | predc(X0)) & room(X0)) [input p1]
46. ? [X0] : (~predb(X0) & ~room(X0)) [input p2]
47. ! [X0] : (room(X0) => (predj(X0) => ~predf(X0))) [input p3]
50. ? [X0] : (predf(X0) & room(X0)) [input p6]
54. ! [X0] : (anywhere(X0) => (~predd(X0) => prede(X0))) [input p10]
59. ! [X0] : (room(X0) => (~predd(X0) | predj(X0))) & there_is_a_room [input hypothesis]
60. ~? [X0] : (room(X0) => (~predi(X0) | ~predb(X0))) <=> ? [X1] : ((prede(X1) | predc(X1)) & room(X1)) [rectify 45]
61. ! [X0] : (room(X0) => (~predd(X0) | predj(X0))) [pure predicate removal 59]
134. ! [X0] : ((predi(X0) & predb(X0)) & room(X0)) <=> ? [X1] : ((prede(X1) | predc(X1)) & room(X1)) [ennf transformation 60]
135. ! [X0] : (predi(X0) & predb(X0) & room(X0)) <=> ? [X1] : ((prede(X1) | predc(X1)) & room(X1)) [flattening 134]
136. ! [X0] : ((~predf(X0) | ~predj(X0)) | ~room(X0)) [ennf transformation 47]
137. ! [X0] : (~predf(X0) | ~predj(X0) | ~room(X0)) [flattening 136]
146. ! [X0] : ((prede(X0) | predd(X0)) | ~anywhere(X0)) [ennf transformation 54]
147. ! [X0] : (prede(X0) | predd(X0) | ~anywhere(X0)) [flattening 146]
154. ! [X0] : ((~predd(X0) | predj(X0)) | ~room(X0)) [ennf transformation 61]
155. ! [X0] : (~predd(X0) | predj(X0) | ~room(X0)) [flattening 154]
157. (! [X0] : (predi(X0) & predb(X0) & room(X0)) | ! [X1] : ((~prede(X1) & ~predc(X1)) | ~room(X1))) & (? [X1] : ((prede(X1) | predc(X1)) & room(X1)) | ? [X0] : (~predi(X0) | ~predb(X0) | ~room(X0))) [nnf transformation 135]
158. (! [X0] : (predi(X0) & predb(X0) & room(X0)) | ! [X1] : ((~prede(X1) & ~predc(X1)) | ~room(X1))) & (? [X2] : ((prede(X2) | predc(X2)) & room(X2)) | ? [X3] : (~predi(X3) | ~predb(X3) | ~room(X3))) [rectify 157]
159. ? [X2] : ((prede(X2) | predc(X2)) & room(X2)) => ((prede(sK0) | predc(sK0)) & room(sK0)) [choice axiom]
160. ? [X3] : (~predi(X3) | ~predb(X3) | ~room(X3)) => (~predi(sK1) | ~predb(sK1) | ~room(sK1)) [choice axiom]
161. (! [X0] : (predi(X0) & predb(X0) & room(X0)) | ! [X1] : ((~prede(X1) & ~predc(X1)) | ~room(X1))) & (((prede(sK0) | predc(sK0)) & room(sK0)) | (~predi(sK1) | ~predb(sK1) | ~room(sK1))) [skolemisation 158,160,159]
162. ? [X0] : (~predb(X0) & ~room(X0)) => (~predb(sK2) & ~room(sK2)) [choice axiom]
163. ~predb(sK2) & ~room(sK2) [skolemisation 46,162]
166. ? [X0] : (predf(X0) & room(X0)) => (predf(sK5) & room(sK5)) [choice axiom]
167. predf(sK5) & room(sK5) [skolemisation 50,166]
172. anywhere(X0) [cnf transformation 5]
256. room(X0) | ~prede(X1) | ~room(X1) [cnf transformation 161]
261. ~room(sK2) [cnf transformation 163]
263. ~predf(X0) | ~predj(X0) | ~room(X0) [cnf transformation 137]
270. room(sK5) [cnf transformation 167]
271. predf(sK5) [cnf transformation 167]
277. prede(X0) | predd(X0) | ~anywhere(X0) [cnf transformation 147]
284. ~predd(X0) | predj(X0) | ~room(X0) [cnf transformation 155]
286. 1 <=> ! [X1] : (~prede(X1) | ~room(X1)) [avatar definition]
287. ~prede(X1) | ~room(X1) <- (1) [avatar component clause 286]
302. 5 <=> ! [X0] : room(X0) [avatar definition]
303. room(X0) <- (5) [avatar component clause 302]
304. 1 | 5 [avatar split clause 256,302,286]
333. predd(X0) | prede(X0) [subsumption resolution 277,172]
339. $false <- (5) [resolution 303,261]
342. ~5 [avatar contradiction clause 339]
350. ~predj(sK5) | ~room(sK5) [resolution 263,271]
351. ~predj(sK5) [subsumption resolution 350,270]
357. predj(X0) | ~room(X0) | prede(X0) [resolution 284,333]
358. ~room(X0) | predj(X0) <- (1) [subsumption resolution 357,287]
361. predj(sK5) <- (1) [resolution 358,270]
362. $false <- (1) [subsumption resolution 361,351]
363. ~1 [avatar contradiction clause 362]
364. $false [avatar sat refutation 304,342,363]
% SZS output end Proof for 1803669137612222182936643
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.409937 |
Christine is the only person in the room.
If everyone in the room enjoys writing detailed reviews of new and classic board games or does not watche fantasy movies then no one in the room who enjoys writing detailed reviews of new and classic board games has a saltwater aquarium.
If everyone anywhere frequently participates in hackathons and coding competitions or does not own a high-end gaming PC with custom-built components then everyone outside the room hosts themed dinner parties featuring gourmet home-cooked meals, practices digital art or practices zumba if they frequently participates in hackathons and coding competitions.
Everyone in the room maintains a personal blog focused on cybersecurity tips or does not collect vintage stamps if everyone anywhere can play the flute or does not maintain a personal blog focused on cybersecurity tips and vice versa.
If everyone in the room is a certified yoga instructor teaching classes weekly or is not an enthusiastic bird watcher who travels for rare sightings then not everyone in the room who is a certified yoga instructor teaching classes weekly owns a high-end gaming PC with custom-built components.
If everyone in the room does not drive a hybrid car or has a tattoo then if someone hosts themed dinner parties featuring gourmet home-cooked meals then he/she practices zumba.
If everyone in the room has a tattoo or does not drive a hybrid car then everyone in the room who has a tattoo is a certified yoga instructor teaching classes weekly, is not an enthusiastic bird watcher who travels for rare sightings or frequently participates in hackathons and coding competitions otherwise everyone in the room owns a high-end gaming PC with custom-built components and collects vintage stamps if they is a cybersecurity expert.
If everyone in the room creates bespoke furniture pieces from reclaimed wood or does not maintain a personal blog focused on cybersecurity tips then everyone in the room practices digital art or does not own a television.
Everyone in the room is an avid hiker or does not watche fantasy movies.
Everyone in the room owns a high-end gaming PC with custom-built components if they has a tattoo.
Everyone in the room who has lived in exactly three countries is an enthusiastic bird watcher who travels for rare sightings. | Christine is an avid hiker. | entailment | room(christine)&(![X]:(room(X)=>(X='christine')))&
((![X]:(room(X)=>(((does_not_watche_fantasy_movies(X))|(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))))=>(~?[X]:(room(X)=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))=>(has_a_saltwater_aquarium(X)))))))&
((![X]:(anywhere(X)=>(((does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))|(frequently_participates_in_hackathons_and_coding_competitions(X))))))=>(![X]:(~room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))|(practices_digital_art(X))|(practices_zumba(X)))))))))&
((![X]:(anywhere(X)=>(((does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))|(can_play_the_flute(X))))))<=>(![X]:(room(X)=>(((does_not_collect_vintage_stamps(X))|(maintains_a_personal_blog_focused_on_cybersecurity_tips(X)))))))&
((![X]:(room(X)=>(((is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))=>(~![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(owns_a_high-end_gaming_PC_with_custom-built_components(X)))))))&
((![X]:(room(X)=>(((has_a_tattoo(X))|(does_not_drive_a_hybrid_car(X))))))=>((![X]:((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))=>(practices_zumba(X))))))&
(((![X]:(room(X)=>(((does_not_drive_a_hybrid_car(X))|(has_a_tattoo(X))))))=>(![X]:(room(X)=>(((has_a_tattoo(X))=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))|(is_not_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))|(frequently_participates_in_hackathons_and_coding_competitions(X)))))))))&((~(![X]:(room(X)=>(((does_not_drive_a_hybrid_car(X))|(has_a_tattoo(X)))))))=>(![X]:(room(X)=>(((is_a_cybersecurity_expert(X))=>(((owns_a_high-end_gaming_PC_with_custom-built_components(X))&(collects_vintage_stamps(X))))))))))&
((![X]:(room(X)=>(((does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))|(creates_bespoke_furniture_pieces_from_reclaimed_wood(X))))))=>(![X]:(room(X)=>(((does_not_own_a_television(X))|(practices_digital_art(X)))))))&
(![X]:(room(X)=>(((does_not_watche_fantasy_movies(X))|(is_an_avid_hiker(X))))))&
(![X]:(room(X)=>(((has_a_tattoo(X))=>(owns_a_high-end_gaming_PC_with_custom-built_components(X))))))&
(![X]:(room(X)=>(((has_lived_in_exactly_three_countries(X))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))&
(![X]:(room(X)=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(practices_digital_art(X))))))&
(![X]:(room(X)=>(((practices_digital_art(X))|(does_not_watche_fantasy_movies(X))))))&
(![X]:(room(X)=>(((~((can_play_the_flute(X))|(is_an_avid_hiker(X))))=>(is_a_certified_yoga_instructor_teaching_classes_weekly(X))))))&
(![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(can_play_the_flute(X)))))) | room(christine)&(![X]:(room(X)=>(X='christine')))&
is_an_avid_hiker(christine) | [
"b42",
"p0",
"p1",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 3253146131201692411826980
% SZS output start Proof for 3253146131201692411826980
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]
45. ! [X0] : (room(X0) => (predm(X0) | ~predc(X0))) => ~? [X0] : (room(X0) => (predm(X0) => predi(X0))) [input p1]
52. ! [X0] : (room(X0) => (predq(X0) | ~predc(X0))) [input p8]
59. ~(predq(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis]
60. ! [X0] : (room(X0) => (predm(X0) | ~predc(X0))) => ~? [X1] : (room(X1) => (predm(X1) => predi(X1))) [rectify 45]
79. ! [X0] : (room(X0) => (predm(X0) | ~predc(X0))) => ~? [X1] : (room(X1) => ~predm(X1)) [pure predicate removal 60]
151. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
152. ! [X1] : (predm(X1) & room(X1)) | ? [X0] : ((~predm(X0) & predc(X0)) & room(X0)) [ennf transformation 79]
153. ! [X1] : (predm(X1) & room(X1)) | ? [X0] : (~predm(X0) & predc(X0) & room(X0)) [flattening 152]
157. ! [X0] : ((predq(X0) | ~predc(X0)) | ~room(X0)) [ennf transformation 52]
158. ! [X0] : (predq(X0) | ~predc(X0) | ~room(X0)) [flattening 157]
163. ~predq(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 59]
165. ! [X0] : (predm(X0) & room(X0)) | ? [X1] : (~predm(X1) & predc(X1) & room(X1)) [rectify 153]
166. ? [X1] : (~predm(X1) & predc(X1) & room(X1)) => (~predm(sK0) & predc(sK0) & room(sK0)) [choice axiom]
167. ! [X0] : (predm(X0) & room(X0)) | (~predm(sK0) & predc(sK0) & room(sK0)) [skolemisation 165,166]
177. ? [X0] : (mary != X0 & room(X0)) => (mary != sK5 & room(sK5)) [choice axiom]
178. ~predq(mary) | (mary != sK5 & room(sK5)) | ~room(mary) [skolemisation 163,177]
224. mary != paul [cnf transformation 43]
260. room(mary) [cnf transformation 151]
261. ~room(X0) | mary = X0 [cnf transformation 151]
262. room(X0) | room(sK0) [cnf transformation 167]
263. room(X0) | predc(sK0) [cnf transformation 167]
278. ~predc(X0) | predq(X0) | ~room(X0) [cnf transformation 158]
281. ~predq(mary) | room(sK5) | ~room(mary) [cnf transformation 178]
282. ~predq(mary) | mary != sK5 | ~room(mary) [cnf transformation 178]
292. 3 <=> predc(sK0) [avatar definition]
294. predc(sK0) <- (3) [avatar component clause 292]
297. 4 <=> room(sK0) [avatar definition]
299. room(sK0) <- (4) [avatar component clause 297]
302. 5 <=> ! [X0] : room(X0) [avatar definition]
303. room(X0) <- (5) [avatar component clause 302]
305. 3 | 5 [avatar split clause 263,302,292]
306. 4 | 5 [avatar split clause 262,302,297]
361. ~predq(mary) | mary != sK5 [subsumption resolution 282,260]
363. 17 <=> mary = sK5 [avatar definition]
365. mary != sK5 <- (~17) [avatar component clause 363]
367. 18 <=> predq(mary) [avatar definition]
370. ~17 | ~18 [avatar split clause 361,367,363]
371. ~predq(mary) | room(sK5) [subsumption resolution 281,260]
373. 19 <=> room(sK5) [avatar definition]
375. room(sK5) <- (19) [avatar component clause 373]
376. 19 | ~18 [avatar split clause 371,367,373]
378. mary = sK0 <- (4) [resolution 261,299]
381. predc(mary) <- (3, 4) [backward demodulation 294,378]
385. predq(mary) | ~room(mary) <- (3, 4) [resolution 278,381]
389. predq(mary) <- (3, 4) [subsumption resolution 385,260]
390. 18 | ~3 | ~4 [avatar split clause 389,297,292,367]
391. mary = sK5 <- (19) [resolution 375,261]
392. $false <- (~17, 19) [subsumption resolution 391,365]
393. 17 | ~19 [avatar contradiction clause 392]
397. mary = X0 <- (5) [resolution 303,261]
421. mary != mary <- (5) [superposition 224,397]
437. $false <- (5) [trivial inequality removal 421]
438. ~5 [avatar contradiction clause 437]
439. $false [avatar sat refutation 305,306,370,376,390,393,438]
% SZS output end Proof for 3253146131201692411826980
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0.66621 |
Elizabeth, Irene, Jennifer are the only persons in the room.
'Everyone in the room bakes bread at home or does not watche fantasy movies' if 'no one in the room is not a craft beer aficionado or is a wine connoisseur with a private cellar of vintage wines' and vice versa.
If 'everyone in the room has a curated collection of mid-century modern furniture or does not enjoy deep-sea diving and exploring underwater caves' then 'at least one person outside the room is a chess master who participates in national tournaments' otherwise 'only one person in the room watches fantasy movies'.
If 'everyone in the room is not a client of Meta or is an amateur astronomer who builds and uses custom telescopes' then 'everyone in the room who is not a tea enthusiast has a curated collection of mid-century modern furniture'.
Everyone in the room who is a client of Meta works on fridays or is a client of Costco or both.
Irene is a client of Meta.
Everyone in the room does not regularly contributes to tech forums and online communities, is not a craft beer aficionado and is a client of Costco only if they regularly contributes to tech forums and online communities.
It is not the case that 'Elizabeth bakes bread at home, is a client of Costco and owns an Android phone'.
Everyone in the room works on fridays if they enjoys origami.
It is not the case that 'Jennifer enjoys virtual reality gaming'.
Jennifer is a client of Costco.
Someone in the room practices archery.
Everyone in the room does enjoy mountain biking if they enjoys virtual reality gaming. | Irene is a client of Meta. | entailment | room(elizabeth)&room(irene)&room(jennifer)&(![X]:(room(X)=>(X='elizabeth'|X='irene'|X='jennifer')))&
((~?[X]:(room(X)=>(((is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X))|(is_not_a_craft_beer_aficionado(X))))))<=>(![X]:(room(X)=>(((does_not_watche_fantasy_movies(X))|(bakes_bread_at_home(X)))))))&
(((![X]:(room(X)=>(((does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))|(has_a_curated_collection_of_mid-century_modern_furniture(X))))))=>(((?[X]:(~room(X)&is_a_chess_master_who_participates_in_national_tournaments(X))))))&((~(![X]:(room(X)=>(((does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))|(has_a_curated_collection_of_mid-century_modern_furniture(X)))))))=>(((?[X]:(room(X)&watches_fantasy_movies(X)))&(![X,Y]:((room(X)&room(Y)&(watches_fantasy_movies(X))&(watches_fantasy_movies(Y)))=>(X=Y)))))))&
((![X]:(room(X)=>(((is_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))|(is_not_a_client_of_Meta(X))))))=>(![X]:(room(X)=>(((is_not_a_tea_enthusiast(X))=>(has_a_curated_collection_of_mid-century_modern_furniture(X)))))))&
(![X]:(room(X)=>(((is_a_client_of_Meta(X))=>(((works_on_fridays(X))|(is_a_client_of_Costco(X))))))))&
(is_a_client_of_Meta(irene))&
(![X]:(room(X)=>(((regularly_contributes_to_tech_forums_and_online_communities(X))<=(((does_not_regularly_contributes_to_tech_forums_and_online_communities(X))&(is_not_a_craft_beer_aficionado(X))&(is_a_client_of_Costco(X))))))))&
(~(((bakes_bread_at_home(elizabeth))&(is_a_client_of_Costco(elizabeth))&(owns_an_Android_phone(elizabeth)))))&
(![X]:(room(X)=>(((enjoys_origami(X))=>(works_on_fridays(X))))))&
(~(enjoys_virtual_reality_gaming(jennifer)))&
(is_a_client_of_Costco(jennifer))&
(?[X]:(room(X)&(practices_archery(X))))&
(![X]:(room(X)=>(((enjoys_virtual_reality_gaming(X))=>(does_enjoy_mountain_biking(X))))))&
(?[X]:(room(X)&(knows_morse_code(X))))&
(![X]:(room(X)=>(((is_not_a_chess_master_who_participates_in_national_tournaments(X))|(owns_an_Android_phone(X))))))&
(collects_comic_books(irene))&
(![X]:(room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(plays_video_games(X))))))&
(((does_not_enjoy_virtual_reality_gaming(irene))|(collects_modern_art(irene))|(bakes_bread_at_home(irene)))) | room(elizabeth)&room(irene)&room(jennifer)&(![X]:(room(X)=>(X='elizabeth'|X='irene'|X='jennifer')))&
is_a_client_of_Meta(irene) | [
"p0",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 7781353340207441751132945
% SZS output start Proof for 7781353340207441751132945
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
49. predj(paul) [input p5]
62. ~(predj(paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis]
149. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
150. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 149]
158. ~predj(paul) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 62]
159. ~predj(paul) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 158]
180. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK8 & paul != sK8 & mary != sK8 & room(sK8)) [choice axiom]
181. ~predj(paul) | (fred != sK8 & paul != sK8 & mary != sK8 & room(sK8)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 159,180]
262. room(mary) [cnf transformation 150]
263. room(paul) [cnf transformation 150]
264. room(fred) [cnf transformation 150]
265. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 150]
283. predj(paul) [cnf transformation 49]
289. ~predj(paul) | room(sK8) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181]
290. ~predj(paul) | mary != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181]
291. ~predj(paul) | paul != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181]
292. ~predj(paul) | fred != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 181]
397. fred != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 292,283]
398. fred != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 397,264]
399. fred != sK8 | ~room(mary) [subsumption resolution 398,263]
400. fred != sK8 [subsumption resolution 399,262]
401. paul != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 291,283]
402. paul != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 401,264]
403. paul != sK8 | ~room(mary) [subsumption resolution 402,263]
404. paul != sK8 [subsumption resolution 403,262]
405. mary != sK8 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 290,283]
406. mary != sK8 | ~room(paul) | ~room(mary) [subsumption resolution 405,264]
407. mary != sK8 | ~room(mary) [subsumption resolution 406,263]
408. mary != sK8 [subsumption resolution 407,262]
409. room(sK8) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 289,283]
410. room(sK8) | ~room(paul) | ~room(mary) [subsumption resolution 409,264]
411. room(sK8) | ~room(mary) [subsumption resolution 410,263]
412. room(sK8) [subsumption resolution 411,262]
462. paul = sK8 | mary = sK8 | fred = sK8 [resolution 265,412]
502. mary = sK8 | fred = sK8 [subsumption resolution 462,404]
503. fred = sK8 [subsumption resolution 502,408]
504. $false [subsumption resolution 503,400]
% SZS output end Proof for 7781353340207441751132945
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Jane, Stanley are the only persons in the room.
If “Jane bakes bread at home” then “everyone in the room enjoys coding in Python if they enjoys writing detailed reviews of new and classic board games”.
If “someone in the room owns an Android phone and enjoys coding in Python” then “everyone in the room enjoys writing detailed reviews of new and classic board games or does not own an Android phone”.
If “everyone in the room enjoys writing detailed reviews of new and classic board games or does not own an Android phone” then “more than one person in the room owns a 3D printer”. | More than one person in the room owns an Android phone. | neutral | room(jane)&room(stanley)&(![X]:(room(X)=>(X='jane'|X='stanley')))&
((bakes_bread_at_home(jane))=>(![X]:(room(X)=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))=>(enjoys_coding_in_Python(X)))))))&
(((?[X]:(room(X)&(((owns_an_Android_phone(X))&(enjoys_coding_in_Python(X))))))=>(![X]:(room(X)=>(((does_not_own_an_Android_phone(X))|(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X)))))))&
((![X]:(room(X)=>(((does_not_own_an_Android_phone(X))|(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))))=>((?[X,Y]:(room(X)&room(Y)&(owns_a_3D_printer(X)&owns_a_3D_printer(Y))&(X!=Y))))))&
(((?[X]:(room(X)&writes_a_travel_blog(X)))&(![X,Y]:((room(X)&room(Y)&(writes_a_travel_blog(X))&(writes_a_travel_blog(Y)))=>(X=Y)))))&
(![X]:(room(X)=>(collects_historical_artifacts_related_to_ancient_civilizations(X))))&
((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(jane))&(enjoys_stargazing(jane)))&
(![X]:(~room(X)=>(((does_not_enjoy_stargazing(X))=>(bakes_bread_at_home(X))))))&
(?[X]:(room(X)&(((owns_an_Android_phone(X))&(enjoys_coding_in_Python(X))))))&
(~![X]:(room(X)=>(((does_not_collect_action_figures(X))<=(owns_a_telescope(X))))))&
((?[X,Y]:(room(X)&room(Y)&(enjoys_stargazing(X)&enjoys_stargazing(Y))&(X!=Y))))&
(![X]:(room(X)=>(((owns_an_Android_phone(X))=>(collects_first_edition_books(X))))))&
(![X]:(anywhere(X)=>(((enjoys_stargazing(X))=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))|(owns_a_telescope(X))|(does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))))))))&
(![X]:(room(X)=>(((((collects_historical_artifacts_related_to_ancient_civilizations(X))|(owns_a_telescope(X))|(does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))))=>(enjoys_stargazing(X))))))&
((collects_first_edition_books(jane))&(collects_historical_artifacts_related_to_ancient_civilizations(jane)))&
((?[X,Y]:(room(X)&room(Y)&(owns_a_3D_printer(X)&owns_a_3D_printer(Y))&(X!=Y))))&
(![X]:(~room(X)=>(((bakes_bread_at_home(X))<=(collects_action_figures(X)))))) | room(jane)&room(stanley)&(![X]:(room(X)=>(X='jane'|X='stanley')))&
(?[X,Y]:(room(X)&room(Y)&(owns_an_Android_phone(X)&owns_an_Android_phone(Y))&(X!=Y))) | [] | null | 0 |
Chris, Jean, Martin, William are the only persons in the room.
If “Chris works as a freelance web developer specializing in e-commerce sites or creates large-scale murals for public art installations or both” then “only one person in the room is a client of Costco”.
“Someone in the room creates large-scale murals for public art installations” unless “Chris owns a microscope”.
“No one in the room is a client of Costco or cannot play the flute” only if “someone in the room does not practice calligraphy”.
If “everyone in the room can play the flute or does not enjoy salsa dancing” then “not everyone in the room enjoys writing detailed reviews of new and classic board games if they does not compete in national level swimming championships”.
If “everyone anywhere is a client of Costco or cannot play the flute” then “Jean who cannot play the flute enjoys salsa dancing”.
Everyone in the room practices calligraphy.
If someone does not own a microscope then he/she owns a microscope.
Chris collects vintage stamps.
Everyone in the room either enjoys writing detailed reviews of new and classic board games or is a client of Costco but not both if they owns a microscope.
Everyone in the room owns a microscope or does not host themed dinner parties featuring gourmet home-cooked meals.
Chris owns a microscope. | Chris competes in national level swimming championships. | neutral | room(chris)&room(jean)&room(martin)&room(william)&(![X]:(room(X)=>(X='chris'|X='jean'|X='martin'|X='william')))&
((((works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(chris))|(creates_large-scale_murals_for_public_art_installations(chris))))=>(((?[X]:(room(X)&is_a_client_of_Costco(X)))&(![X,Y]:((room(X)&room(Y)&(is_a_client_of_Costco(X))&(is_a_client_of_Costco(Y)))=>(X=Y))))))&
(~(owns_a_microscope(chris))=>(?[X]:(room(X)&(creates_large-scale_murals_for_public_art_installations(X)))))&
((~?[X]:(room(X)=>(((cannot_play_the_flute(X))|(is_a_client_of_Costco(X))))))=>(?[X]:(room(X)&(does_not_practice_calligraphy(X)))))&
((![X]:(room(X)=>(((does_not_enjoy_salsa_dancing(X))|(can_play_the_flute(X))))))=>(~![X]:(room(X)=>(((does_not_compete_in_national_level_swimming_championships(X))=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X)))))))&
((![X]:(anywhere(X)=>(((cannot_play_the_flute(X))|(is_a_client_of_Costco(X))))))=>((cannot_play_the_flute(jean))&(enjoys_salsa_dancing(jean))))&
(![X]:(room(X)=>(practices_calligraphy(X))))&
((![X]:((does_not_own_a_microscope(X))=>(owns_a_microscope(X)))))&
(collects_vintage_stamps(chris))&
(![X]:(room(X)=>(((owns_a_microscope(X))=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))<~>(is_a_client_of_Costco(X))))))))&
(![X]:(room(X)=>(((does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))|(owns_a_microscope(X))))))&
(owns_a_microscope(chris))&
(((competes_in_national_level_swimming_championships(chris))|(is_a_client_of_Costco(chris))|(works_as_a_freelance_web_developer_specializing_in_e-commerce_sites(chris))))&
((![X]:((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))=>(owns_a_microscope(X)))))&
(![X]:(~room(X)=>(((enjoys_salsa_dancing(X))=>(collects_vintage_stamps(X)))))) | room(chris)&room(jean)&room(martin)&room(william)&(![X]:(room(X)=>(X='chris'|X='jean'|X='martin'|X='william')))&
competes_in_national_level_swimming_championships(chris) | [] | null | 0.128727 |
Charlotte, Monica are the only persons in the room.
If 'Jessie is a sibling of Charlotte' then 'if someone is a sibling of Jennifer then he/she is a patient tourist and vice versa'.
'Monica does not practice archery' if 'Charlotte and Jennifer hate each other' and vice versa.
If 'at least one person in the room does not host themed dinner parties featuring gourmet home-cooked meals' then 'if someone is a sibling of Carroll then he/she is a funny kind brave curious european'.
If 'it is not the case that 'Charlotte hates Carroll'' then 'at least one person outside the room can play the guitar' otherwise 'Monica is humble'.
Monica is a client of Mary.
Charlotte is not not old.
Everyone in the room is not a dedicated advocate for digital privacy and encryption if and only if they is a happy brave person.
Everyone in the room who is a wise happy funny brave european is not a kind happy wise curious european.
If someone is not liked by Carroll then he/she is a client of Mary.
Charlotte is a sibling of Jennifer.
Charlotte is a sibling of Jessie.
Everyone in the room who is younger than Jessie does not enjoy landscape photography and is a client of Jessie.
Charlotte and Mary like each other.
All creative persons are old.
Charlotte and Jennifer hate each other.
Jessie is a sibling of Charlotte.
Charlotte is a brave old wise kind quiet person.
Monica is humble.
Charlotte is a dedicated advocate for digital privacy and encryption.
Charlotte is a client of Tim.
Jessie and Monica like each other.
Charlotte is not a humble calm wise tourist. | Charlotte is liked by Jennifer. | contradiction | room(charlotte)&room(monica)&(![X]:(room(X)=>(X='charlotte'|X='monica')))&
((sibling(charlotte,jessie))=>((![X]:((sibling(jennifer,X))<=>(patient(X)&tourist(X))))))&
(((hate(charlotte,jennifer) & hate(jennifer,charlotte)))<=>(does_not_practice_archery(monica)))&
((((?[X]:(room(X)&does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))))=>((![X]:((sibling(carroll,X))=>(funny(X)&kind(X)&brave(X)&curious(X)&european(X))))))&
(((~(hate(carroll,charlotte)))=>(((?[X]:(~room(X)&can_play_the_guitar(X))))))&((~(~(hate(carroll,charlotte))))=>(humble(monica))))&
(client(mary,monica))&
(~~old(charlotte))&
(![X]:(room(X)=>(((is_not_a_dedicated_advocate_for_digital_privacy_and_encryption(X))<=>(happy(X)&brave(X)&person(X))))))&
(![X]:(room(X)=>(((wise(X)&happy(X)&funny(X)&brave(X)&european(X))=>(~(kind(X)&happy(X)&wise(X)&curious(X)&european(X)))))))&
((![X]:((~like(X,carroll))=>(client(mary,X)))))&
(sibling(jennifer,charlotte))&
(sibling(jessie,charlotte))&
(![X]:(room(X)=>(((younger(jessie,X))=>(((does_not_enjoy_landscape_photography(X))&(client(jessie,X))))))))&
((like(charlotte,mary) & like(mary,charlotte)))&
(![X]:(creative(X)=>old(X)))&
((hate(charlotte,jennifer) & hate(jennifer,charlotte)))&
(sibling(charlotte,jessie))&
(brave(charlotte)&old(charlotte)&wise(charlotte)&kind(charlotte)&quiet(charlotte)&person(charlotte))&
(humble(monica))&
(is_a_dedicated_advocate_for_digital_privacy_and_encryption(charlotte))&
(client(tim,charlotte))&
((like(jessie,monica) & like(monica,jessie)))&
(~(humble(charlotte)&calm(charlotte)&wise(charlotte)&tourist(charlotte))) | room(charlotte)&room(monica)&(![X]:(room(X)=>(X='charlotte'|X='monica')))&
like(charlotte,jennifer) | [
"b0",
"b42",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4301460382969218134210474
% SZS output start Proof for 4301460382969218134210474
1. ! [X0,X1] : (X0 != X1 => (like(X0,X1) => ~hate(X0,X1))) [input b0]
43. susan != lucy & john != lucy & alice != lucy & fred != lucy & paul != lucy & mary != lucy & susan != lucy & john != susan & alice != susan & fred != susan & paul != susan & mary != susan & john != lucy & john != susan & alice != john & fred != john & paul != john & mary != john & alice != lucy & alice != susan & alice != john & fred != alice & paul != alice & mary != alice & fred != lucy & fred != susan & fred != john & fred != alice & paul != fred & mary != fred & paul != lucy & paul != susan & paul != john & paul != alice & paul != fred & mary != paul & mary != lucy & mary != susan & mary != john & mary != alice & mary != fred & mary != paul [input b42]
59. hate(alice,mary) & hate(mary,alice) [input p15]
67. like(mary,alice) & ! [X0] : (room(X0) => (paul = X0 | mary = X0)) & room(paul) & room(mary) [input hypothesis]
85. ! [X0,X1] : ((~hate(X0,X1) | ~like(X0,X1)) | X0 = X1) [ennf transformation 1]
86. ! [X0,X1] : (~hate(X0,X1) | ~like(X0,X1) | X0 = X1) [flattening 85]
162. like(mary,alice) & ! [X0] : ((paul = X0 | mary = X0) | ~room(X0)) & room(paul) & room(mary) [ennf transformation 67]
163. like(mary,alice) & ! [X0] : (paul = X0 | mary = X0 | ~room(X0)) & room(paul) & room(mary) [flattening 162]
173. ~hate(X0,X1) | ~like(X0,X1) | X0 = X1 [cnf transformation 86]
232. mary != alice [cnf transformation 43]
275. hate(mary,alice) [cnf transformation 59]
288. like(mary,alice) [cnf transformation 163]
315. 7 <=> hate(mary,alice) [avatar definition]
317. hate(mary,alice) <- (7) [avatar component clause 315]
330. 7 [avatar split clause 275,315]
360. ~like(mary,alice) | mary = alice <- (7) [resolution 173,317]
362. mary = alice <- (7) [subsumption resolution 360,288]
363. $false <- (7) [subsumption resolution 362,232]
364. ~7 [avatar contradiction clause 363]
365. $false [avatar sat refutation 330,364]
% SZS output end Proof for 4301460382969218134210474
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0.209576 |
Aurelia is the only person in the room.
If “at least one person in the room is patient” then “Aurelia owns an extensive assortment of vintage comic book memorabilia”.
If “no one in the room does not like Patti or does not use contact lenses” then “everyone in the room does not have a specialized collection of handmade artisan pottery or owns a smartwatch”.
If someone is creative then he/she cannot play the flute.
Aurelia creates bespoke furniture pieces from reclaimed wood.
Aurelia uses contact lenses.
Patti is a client of Aurelia.
Aurelia is patient. | Aurelia can play the flute. | neutral | room(aurelia)&(![X]:(room(X)=>(X='aurelia')))&
((((?[X]:(room(X)&patient(X)))))=>(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(aurelia)))&
((~?[X]:(room(X)=>(((does_not_use_contact_lenses(X))|(~like(patti,X))))))=>(![X]:(room(X)=>(((owns_a_smartwatch(X))|(does_not_have_a_specialized_collection_of_handmade_artisan_pottery(X)))))))&
((![X]:((creative(X))=>(cannot_play_the_flute(X)))))&
(creates_bespoke_furniture_pieces_from_reclaimed_wood(aurelia))&
(uses_contact_lenses(aurelia))&
(client(aurelia,patti))&
(patient(aurelia))&
(sibling(bradley,aurelia))&
(can_play_the_guitar(aurelia))&
((![X]:((poorer(janeen,X))=>(sibling(michael,X)))))&
(has_completed_a_triathlon(aurelia))&
((is_dedicated_to_sustainable_living_and_zero-waste_practices(aurelia))&(does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(aurelia)))&
(![X]:(room(X)=>(((has_a_curated_collection_of_mid-century_modern_furniture(X))=>(humble(X))))))&
(![X]:(room(X)=>(((humble(X))=>(mentors_a_youth_basketball_team_on_weekends(X))))))&
(enjoys_kayaking_and_exploring_remote_waterways(aurelia))&
(is_right-handed(aurelia))&
(![X]:(old(X)=>quiet(X)))&
(![X]:(brave(X)=>tall(X)))&
((like(janeen,aurelia) & like(aurelia,janeen)))&
(![X]:(room(X)=>(((owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))=>(collects_antique_jewelry(X))))))&
(![X]:(quiet(X)=>calm(X)))&
(((creates_bespoke_furniture_pieces_from_reclaimed_wood(aurelia))&(~hate(michael,aurelia))&(richer(bradley,aurelia))))&
(![X]:(room(X)=>(((can_play_the_guitar(X))=>(sibling(elizabeth,X)))))) | room(aurelia)&(![X]:(room(X)=>(X='aurelia')))&
can_play_the_flute(aurelia) | [] | null | 0.290609 |
There is a room.
Everyone outside the room who neither creates augmented reality experiences for mobile applications nor enjoys writing detailed reviews of new and classic board games enjoys origami.
Everyone in the room neither does not enjoy deep-sea diving and exploring underwater caves nor designs and sews custom cosplay costumes for conventions if they is a dedicated volunteer for local community service projects.
No one anywhere who enjoys writing detailed reviews of new and classic board games owns a smartwatch.
No one anywhere who enjoys writing detailed reviews of new and classic board games is a client of Costco.
Everyone in the room who enjoys writing detailed reviews of new and classic board games designs and sews custom cosplay costumes for conventions and own a television.
Everyone in the room designs and sews custom cosplay costumes for conventions and own a television if and only if they collects first edition books.
Everyone anywhere who collects first edition books maintains a personal blog focused on cybersecurity tips, has lived in exactly three countries and is a client of Costco. | Everyone in the room does not enjoy writing detailed reviews of new and classic board games. | entailment | (there_is_a_room)&
(![X]:(~room(X)=>(((~((creates_augmented_reality_experiences_for_mobile_applications(X))|(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))=>(enjoys_origami(X))))))&
(![X]:(room(X)=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))=>(~((does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))|(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))))))&
(![X]:(room(X)=>(((~((does_not_enjoy_deep-sea_diving_and_exploring_underwater_caves(X))|(designs_and_sews_custom_cosplay_costumes_for_conventions(X))))=>(is_a_client_of_Meta(X))))))&
(![X]:(room(X)=>(((is_a_client_of_Meta(X))=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))))&
(~?[X]:(anywhere(X)=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))=>(owns_a_smartwatch(X))))))&
(![X]:(~room(X)=>(((frequently_participates_in_hackathons_and_coding_competitions(X))=>(has_lived_in_exactly_three_countries(X))))))&
(![X]:(room(X)=>(((is_a_certified_yoga_instructor_teaching_classes_weekly(X))=>(own_a_television(X))))))&
(![X]:(anywhere(X)=>(((practices_graffiti_art(X))=>(is_a_dedicated_volunteer_for_local_community_service_projects(X))))))&
(![X]:(anywhere(X)=>(((is_a_dedicated_volunteer_for_local_community_service_projects(X))=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))))&
(~?[X]:(anywhere(X)=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))=>(is_a_client_of_Costco(X))))))&
(![X]:(room(X)=>(((is_a_client_of_Costco(X))=>(enjoys_cross-country_skiing(X))))))&
(![X]:(anywhere(X)=>(((does_not_own_a_smartwatch(X))=>(enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))))))&
(![X]:(room(X)=>(((enjoys_writing_detailed_reviews_of_new_and_classic_board_games(X))=>(((designs_and_sews_custom_cosplay_costumes_for_conventions(X))&(own_a_television(X))))))))&
(![X]:(room(X)=>(((((designs_and_sews_custom_cosplay_costumes_for_conventions(X))&(own_a_television(X))))<=>(collects_first_edition_books(X))))))&
(![X]:(anywhere(X)=>(((collects_first_edition_books(X))=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))&(has_lived_in_exactly_three_countries(X))&(is_a_client_of_Costco(X))))))))&
(![X]:(~room(X)=>(((((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))&(has_lived_in_exactly_three_countries(X))&(is_a_client_of_Costco(X))))=>(has_lived_in_exactly_three_countries(X))))))&
(![X]:(room(X)=>(((has_lived_in_exactly_three_countries(X))|(does_not_enjoy_cross-country_skiing(X))))))&
(![X]:(room(X)=>(((~((does_not_own_a_smartwatch(X))|(frequently_participates_in_hackathons_and_coding_competitions(X))))=>(is_a_client_of_Costco(X))))))&
(![X]:(~room(X)=>(((is_a_client_of_Costco(X))=>(enjoys_making_ceramics(X))))))&
((![X]:((designs_and_sews_custom_cosplay_costumes_for_conventions(X))<=>(writes_and_illustrates_their_own_graphic_novels(X)))))&
(![X]:(room(X)=>(creates_augmented_reality_experiences_for_mobile_applications(X))))&
(![X]:(room(X)=>(((has_completed_a_triathlon(X))=>(enjoys_cross-country_skiing(X))))))&
(![X]:(room(X)=>(((enjoys_cross-country_skiing(X))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))&
(![X]:(room(X)=>(((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))=>(collects_first_edition_books(X)))))) | (there_is_a_room)&
![X]:(room(X)=>(does_not_enjoy_writing_detailed_reviews_of_new_and_classic_board_games(X))) | [
"b4",
"p0",
"p5",
"p10",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7443628469970641022894440
% SZS output start Proof for 7443628469970641022894440
5. ! [X0] : anywhere(X0) [input b4]
44. there_is_a_room [input p0]
49. ~? [X0] : (anywhere(X0) => (predm(X0) => prede(X0))) [input p5]
54. ~? [X0] : (anywhere(X0) => (predm(X0) => predw(X0))) [input p10]
57. ! [X0] : (room(X0) => (predm(X0) => (predk(X0) & preds(X0)))) [input p13]
58. ! [X0] : (room(X0) => ((predk(X0) & preds(X0)) <=> predf(X0))) [input p14]
59. ! [X0] : (anywhere(X0) => (predf(X0) => (predw(X0) & predo(X0) & predl(X0)))) [input p15]
69. ~(! [X0] : (room(X0) => ~predm(X0)) & there_is_a_room) [input hypothesis]
151. ! [X0] : ((~prede(X0) & predm(X0)) & anywhere(X0)) [ennf transformation 49]
152. ! [X0] : (~prede(X0) & predm(X0) & anywhere(X0)) [flattening 151]
155. ! [X0] : ((~predw(X0) & predm(X0)) & anywhere(X0)) [ennf transformation 54]
156. ! [X0] : (~predw(X0) & predm(X0) & anywhere(X0)) [flattening 155]
161. ! [X0] : (((predk(X0) & preds(X0)) | ~predm(X0)) | ~room(X0)) [ennf transformation 57]
162. ! [X0] : ((predk(X0) & preds(X0)) | ~predm(X0) | ~room(X0)) [flattening 161]
163. ! [X0] : (((predk(X0) & preds(X0)) <=> predf(X0)) | ~room(X0)) [ennf transformation 58]
164. ! [X0] : (((predw(X0) & predo(X0) & predl(X0)) | ~predf(X0)) | ~anywhere(X0)) [ennf transformation 59]
165. ! [X0] : ((predw(X0) & predo(X0) & predl(X0)) | ~predf(X0) | ~anywhere(X0)) [flattening 164]
176. ? [X0] : (predm(X0) & room(X0)) | ~there_is_a_room [ennf transformation 69]
178. ! [X0] : ((((predk(X0) & preds(X0)) | ~predf(X0)) & (predf(X0) | (~predk(X0) | ~preds(X0)))) | ~room(X0)) [nnf transformation 163]
179. ! [X0] : ((((predk(X0) & preds(X0)) | ~predf(X0)) & (predf(X0) | ~predk(X0) | ~preds(X0))) | ~room(X0)) [flattening 178]
181. ? [X0] : (predm(X0) & room(X0)) => (predm(sK0) & room(sK0)) [choice axiom]
182. (predm(sK0) & room(sK0)) | ~there_is_a_room [skolemisation 176,181]
183. anywhere(X0) [cnf transformation 5]
264. there_is_a_room [cnf transformation 44]
266. predm(X0) [cnf transformation 152]
271. ~predw(X0) [cnf transformation 156]
274. preds(X0) | ~predm(X0) | ~room(X0) [cnf transformation 162]
275. predk(X0) | ~predm(X0) | ~room(X0) [cnf transformation 162]
276. predf(X0) | ~predk(X0) | ~preds(X0) | ~room(X0) [cnf transformation 179]
281. predw(X0) | ~predf(X0) | ~anywhere(X0) [cnf transformation 165]
289. room(sK0) | ~there_is_a_room [cnf transformation 182]
291. ~room(X0) | predk(X0) [subsumption resolution 275,266]
292. ~room(X0) | preds(X0) [subsumption resolution 274,266]
293. predf(X0) | ~preds(X0) | ~room(X0) [subsumption resolution 276,291]
294. ~room(X0) | predf(X0) [subsumption resolution 293,292]
295. ~predf(X0) | ~anywhere(X0) [subsumption resolution 281,271]
296. ~predf(X0) [subsumption resolution 295,183]
297. room(sK0) [subsumption resolution 289,264]
301. predf(sK0) [resolution 294,297]
302. $false [subsumption resolution 301,296]
% SZS output end Proof for 7443628469970641022894440
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0.054057 |
Jane, Erica, David are the only persons in the room.
David who maintains a personal blog focused on cybersecurity tips owns a high-end gaming PC with custom-built components. | David maintains a personal blog focused on cybersecurity tips. | entailment | room(jane)&room(erica)&room(david)&(![X]:(room(X)=>(X='jane'|X='erica'|X='david')))&
((enjoys_stargazing(erica))&(enjoys_landscape_photography(erica)))&
(owns_a_high-end_gaming_PC_with_custom-built_components(erica))&
(((collects_vintage_vinyl_records(david))<~>(collects_historical_artifacts_related_to_ancient_civilizations(david))))&
(((watches_fantasy_movies(erica))&(collects_antique_jewelry(erica))&(maintains_a_personal_blog_focused_on_cybersecurity_tips(erica))))&
(((?[X]:(room(X)&is_a_wine_connoisseur(X)))&(![X,Y]:((room(X)&room(Y)&(is_a_wine_connoisseur(X))&(is_a_wine_connoisseur(Y)))=>(X=Y)))))&
(~(~(enjoys_stargazing(jane))))&
(hosts_regular_workshops_on_creative_writing(jane))&
(![X]:(room(X)=>(((watches_fantasy_movies(X))<=(has_a_vast_collection_of_first-edition_science_fiction_novels(X))))))&
(~(enjoys_salsa_dancing(erica)))&
((enjoys_landscape_photography(erica))&(((composes_and_performs_experimental_electronic_music(erica))<~>(owns_a_high-end_gaming_PC_with_custom-built_components(erica)))))&
(![X]:(room(X)=>(((owns_an_Android_phone(X))|(does_not_write_a_travel_blog(X))))))&
(is_passionate_about_collecting_and_restoring_classic_cars(jane))&
(maintains_a_personal_blog_focused_on_cybersecurity_tips(jane))&
(collects_vintage_vinyl_records(jane))&
((maintains_a_personal_blog_focused_on_cybersecurity_tips(david))&(owns_a_high-end_gaming_PC_with_custom-built_components(david)))&
(is_a_wine_connoisseur(david))&
((![X]:((creates_augmented_reality_experiences_for_mobile_applications(X))=>(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(X)))))&
(~(~(has_a_tattoo(jane))))&
(has_a_vast_collection_of_first-edition_science_fiction_novels(jane)) | room(jane)&room(erica)&room(david)&(![X]:(room(X)=>(X='jane'|X='erica'|X='david')))&
maintains_a_personal_blog_focused_on_cybersecurity_tips(david) | [
"p0",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7901004928902906977482401
% SZS output start Proof for 7901004928902906977482401
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
59. predi(fred) & predh(fred) [input p15]
64. ~(predh(fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis]
152. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
153. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 152]
156. ~predh(fred) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 64]
157. ~predh(fred) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 156]
163. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) [choice axiom]
164. ~predh(fred) | (fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 157,163]
245. room(mary) [cnf transformation 153]
246. room(paul) [cnf transformation 153]
247. room(fred) [cnf transformation 153]
248. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 153]
260. predh(fred) [cnf transformation 59]
263. ~predh(fred) | room(sK1) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 164]
264. ~predh(fred) | mary != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 164]
265. ~predh(fred) | paul != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 164]
266. ~predh(fred) | fred != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 164]
278. fred != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 266,260]
279. fred != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 278,247]
280. fred != sK1 | ~room(mary) [subsumption resolution 279,246]
281. fred != sK1 [subsumption resolution 280,245]
282. paul != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 265,260]
283. paul != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 282,247]
284. paul != sK1 | ~room(mary) [subsumption resolution 283,246]
285. paul != sK1 [subsumption resolution 284,245]
286. mary != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 264,260]
287. mary != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 286,247]
288. mary != sK1 | ~room(mary) [subsumption resolution 287,246]
289. mary != sK1 [subsumption resolution 288,245]
290. room(sK1) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 263,260]
291. room(sK1) | ~room(paul) | ~room(mary) [subsumption resolution 290,247]
292. room(sK1) | ~room(mary) [subsumption resolution 291,246]
293. room(sK1) [subsumption resolution 292,245]
340. paul = sK1 | mary = sK1 | fred = sK1 [resolution 248,293]
354. mary = sK1 | fred = sK1 [subsumption resolution 340,285]
355. fred = sK1 [subsumption resolution 354,289]
356. $false [subsumption resolution 355,281]
% SZS output end Proof for 7901004928902906977482401
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.145619 |
There is a room.
Either “everyone in the room is not an amateur astronomer who builds and uses custom telescopes, does not have a saltwater aquarium or is not an avid mountain climber who has scaled several peaks” or “everyone in the room does not write in-depth travel guides for off-the-beaten-path destinations, does not collect rare and antique scientific instruments or does not host regular game nights featuring complex strategy games” but not both.
Either “everyone in the room does not own an extensive assortment of vintage comic book memorabilia” or “everyone in the room does not play the violin or cannot play the harmonica or both” but not both.
Everyone in the room does not play the violin or cannot play the harmonica or both.
Everyone in the room does not play the violin, does not enjoy mountain biking or does not have a piercing.
Everyone in the room does not have a saltwater aquarium.
Everyone outside the room does not own an extensive assortment of vintage comic book memorabilia or does not write in-depth travel guides for off-the-beaten-path destinations or both.
Not everyone in the room does not regularly goes on multi-day backpacking trips in national parks or does not write poetry or both.
Everyone in the room does not write poetry or does not enjoy mountain biking or both.
Everyone outside the room does not enjoy mountain biking. | Everyone in the room has a saltwater aquarium. | contradiction | (there_is_a_room)&
((![X]:(room(X)=>(((is_not_an_amateur_astronomer_who_builds_and_uses_custom_telescopes(X))|(does_not_have_a_saltwater_aquarium(X))|(is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))<~>(![X]:(room(X)=>(((does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))|(does_not_collect_rare_and_antique_scientific_instruments(X))|(does_not_host_regular_game_nights_featuring_complex_strategy_games(X)))))))&
((![X]:(room(X)=>(does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))))<~>(![X]:(room(X)=>(((does_not_play_the_violin(X))|(cannot_play_the_harmonica(X)))))))&
(![X]:(room(X)=>(((does_not_play_the_violin(X))|(cannot_play_the_harmonica(X))))))&
(![X]:(room(X)=>(((does_not_play_the_violin(X))|(does_not_enjoy_mountain_biking(X))|(does_not_have_a_piercing(X))))))&
(![X]:(room(X)=>(does_not_have_a_saltwater_aquarium(X))))&
(![X]:(~room(X)=>(((does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))|(does_not_write_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))&
(~![X]:(room(X)=>(((does_not_regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))|(does_not_write_poetry(X))))))&
(![X]:(room(X)=>(((does_not_write_poetry(X))|(does_not_enjoy_mountain_biking(X))))))&
(![X]:(~room(X)=>(does_not_enjoy_mountain_biking(X)))) | (there_is_a_room)&
![X]:(room(X)=>(has_a_saltwater_aquarium(X))) | [
"p2",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 6615739232834342983335203
% SZS output start Proof for 6615739232834342983335203
46. ! [X0] : (room(X0) => ~predb(X0)) <~> ! [X0] : (room(X0) => (~predi(X0) | ~predq(X0))) [input p2]
49. ! [X0] : (room(X0) => ~predc(X0)) [input p5]
54. ! [X0] : (room(X0) => predc(X0)) & there_is_a_room [input hypothesis]
56. ! [X0] : (room(X0) => ~predb(X0)) <~> ! [X1] : (room(X1) => (~predi(X1) | ~predq(X1))) [rectify 46]
62. ! [X0] : (room(X0) => predc(X0)) [pure predicate removal 54]
138. ! [X0] : (~predb(X0) | ~room(X0)) <~> ! [X1] : ((~predi(X1) | ~predq(X1)) | ~room(X1)) [ennf transformation 56]
139. ! [X0] : (~predb(X0) | ~room(X0)) <~> ! [X1] : (~predi(X1) | ~predq(X1) | ~room(X1)) [flattening 138]
142. ! [X0] : (~predc(X0) | ~room(X0)) [ennf transformation 49]
146. ! [X0] : (predc(X0) | ~room(X0)) [ennf transformation 62]
153. (? [X1] : (predi(X1) & predq(X1) & room(X1)) | ? [X0] : (predb(X0) & room(X0))) & (! [X1] : (~predi(X1) | ~predq(X1) | ~room(X1)) | ! [X0] : (~predb(X0) | ~room(X0))) [nnf transformation 139]
154. (? [X0] : (predi(X0) & predq(X0) & room(X0)) | ? [X1] : (predb(X1) & room(X1))) & (! [X2] : (~predi(X2) | ~predq(X2) | ~room(X2)) | ! [X3] : (~predb(X3) | ~room(X3))) [rectify 153]
155. ? [X0] : (predi(X0) & predq(X0) & room(X0)) => (predi(sK2) & predq(sK2) & room(sK2)) [choice axiom]
156. ? [X1] : (predb(X1) & room(X1)) => (predb(sK3) & room(sK3)) [choice axiom]
157. ((predi(sK2) & predq(sK2) & room(sK2)) | (predb(sK3) & room(sK3))) & (! [X2] : (~predi(X2) | ~predq(X2) | ~room(X2)) | ! [X3] : (~predb(X3) | ~room(X3))) [skolemisation 154,156,155]
258. room(sK2) | room(sK3) [cnf transformation 157]
265. ~predc(X0) | ~room(X0) [cnf transformation 142]
268. predc(X0) | ~room(X0) [cnf transformation 146]
334. 13 <=> room(sK3) [avatar definition]
336. room(sK3) <- (13) [avatar component clause 334]
345. 15 <=> room(sK2) [avatar definition]
347. room(sK2) <- (15) [avatar component clause 345]
349. 13 | 15 [avatar split clause 258,345,334]
358. ~room(X0) [subsumption resolution 268,265]
359. $false <- (13) [subsumption resolution 336,358]
360. ~13 [avatar contradiction clause 359]
363. $false <- (15) [subsumption resolution 347,358]
364. ~15 [avatar contradiction clause 363]
367. $false [avatar sat refutation 349,360,364]
% SZS output end Proof for 6615739232834342983335203
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0.230264 |
Barbara, Amber, Douglas, Virgil are the only persons in the room. Amber is the richest in the room. It is true that “only one person in the room is not a old person”. Amber and Douglas are respectively quiet and old. Douglas and Amber are respectively old and quiet. Amber is the oldest in the room. Amber and Barbara are respectively old and quiet. If someone is not a quiet person then he/she is not a old quiet person and vice versa. Douglas and Barbara are respectively old and quiet. Barbara and Amber are respectively quiet and old. Amber and Douglas are respectively old and quiet. If someone is not quiet then he/she is not old or is not a quiet person or both and vice versa. If someone is not a quiet old person then he/she is not old, not quiet and vice versa. If someone is not a old quiet person then he/she is not a quiet person and vice versa. | Amber is a quiet old person. | entailment | room(barbara)&room(amber)&room(douglas)&room(virgil)&(![X]:(room(X)=>(X='barbara'|X='amber'|X='douglas'|X='virgil')))&
(![X]:((room(X)&(X!=amber))=>richer(X,amber)))&
(((?[X]:(room(X)&~(old(X)&person(X))))&(![X,Y]:((room(X)&room(Y)&(~(old(X)&person(X)))&(~(old(Y)&person(Y))))=>(X=Y)))))&
((quiet(amber))&(old(douglas)))&
((old(douglas))&(quiet(amber)))&
(![X]:((room(X)&(X!=amber))=>older(X,amber)))&
((old(amber))&(quiet(barbara)))&
((![X]:((~(quiet(X)&person(X)))<=>(~(old(X)&quiet(X)&person(X))))))&
((old(douglas))&(quiet(barbara)))&
((quiet(barbara))&(old(amber)))&
((old(amber))&(quiet(douglas)))&
((![X]:((~quiet(X))<=>(((~old(X))|(~(quiet(X)&person(X))))))))&
((![X]:((~(quiet(X)&old(X)&person(X)))<=>(~old(X)&~quiet(X)))))&
((![X]:((~(old(X)&quiet(X)&person(X)))<=>(~(quiet(X)&person(X)))))) | room(barbara)&room(amber)&room(douglas)&room(virgil)&(![X]:(room(X)=>(X='barbara'|X='amber'|X='douglas'|X='virgil')))&
quiet(amber)&old(amber)&person(amber) | [
"p0",
"p3",
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6414219340201890669520639
% SZS output start Proof for 6414219340201890669520639
44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
47. old(fred) & quiet(paul) [input p3]
50. quiet(mary) & old(paul) [input p6]
55. ! [X0] : (~quiet(X0) <=> (~(person(X0) & quiet(X0)) | ~old(X0))) [input p11]
58. ~(person(paul) & old(paul) & quiet(paul) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis]
132. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
133. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 132]
141. ! [X0] : (~quiet(X0) <=> ((~person(X0) | ~quiet(X0)) | ~old(X0))) [ennf transformation 55]
142. ! [X0] : (~quiet(X0) <=> (~person(X0) | ~quiet(X0) | ~old(X0))) [flattening 141]
145. ~person(paul) | ~old(paul) | ~quiet(paul) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 58]
146. ~person(paul) | ~old(paul) | ~quiet(paul) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 145]
152. ! [X0] : ((~quiet(X0) | (person(X0) & quiet(X0) & old(X0))) & ((~person(X0) | ~quiet(X0) | ~old(X0)) | quiet(X0))) [nnf transformation 142]
153. ! [X0] : ((~quiet(X0) | (person(X0) & quiet(X0) & old(X0))) & (~person(X0) | ~quiet(X0) | ~old(X0) | quiet(X0))) [flattening 152]
158. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK1 & fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) [choice axiom]
159. ~person(paul) | ~old(paul) | ~quiet(paul) | (alice != sK1 & fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 146,158]
240. room(mary) [cnf transformation 133]
241. room(paul) [cnf transformation 133]
242. room(fred) [cnf transformation 133]
243. room(alice) [cnf transformation 133]
244. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 133]
252. quiet(paul) [cnf transformation 47]
257. old(paul) [cnf transformation 50]
273. ~quiet(X0) | person(X0) [cnf transformation 153]
286. ~person(paul) | ~old(paul) | ~quiet(paul) | room(sK1) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 159]
287. ~person(paul) | ~old(paul) | ~quiet(paul) | mary != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 159]
288. ~person(paul) | ~old(paul) | ~quiet(paul) | paul != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 159]
289. ~person(paul) | ~old(paul) | ~quiet(paul) | fred != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 159]
290. ~person(paul) | ~old(paul) | ~quiet(paul) | alice != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 159]
300. ~person(paul) | ~quiet(paul) | alice != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 290,257]
301. ~person(paul) | alice != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 300,252]
302. ~person(paul) | alice != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 301,243]
303. ~person(paul) | alice != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 302,242]
304. ~person(paul) | alice != sK1 | ~room(mary) [subsumption resolution 303,241]
305. ~person(paul) | alice != sK1 [subsumption resolution 304,240]
307. 3 <=> alice = sK1 [avatar definition]
309. alice != sK1 <- (~3) [avatar component clause 307]
311. 4 <=> person(paul) [avatar definition]
314. ~3 | ~4 [avatar split clause 305,311,307]
315. ~person(paul) | ~quiet(paul) | fred != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 289,257]
316. ~person(paul) | fred != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 315,252]
317. ~person(paul) | fred != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 316,243]
318. ~person(paul) | fred != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 317,242]
319. ~person(paul) | fred != sK1 | ~room(mary) [subsumption resolution 318,241]
320. ~person(paul) | fred != sK1 [subsumption resolution 319,240]
322. 5 <=> fred = sK1 [avatar definition]
324. fred != sK1 <- (~5) [avatar component clause 322]
325. ~5 | ~4 [avatar split clause 320,311,322]
326. ~person(paul) | ~quiet(paul) | paul != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 288,257]
327. ~person(paul) | paul != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 326,252]
328. ~person(paul) | paul != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 327,243]
329. ~person(paul) | paul != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 328,242]
330. ~person(paul) | paul != sK1 | ~room(mary) [subsumption resolution 329,241]
331. ~person(paul) | paul != sK1 [subsumption resolution 330,240]
333. 6 <=> paul = sK1 [avatar definition]
335. paul != sK1 <- (~6) [avatar component clause 333]
336. ~6 | ~4 [avatar split clause 331,311,333]
337. ~person(paul) | ~quiet(paul) | mary != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 287,257]
338. ~person(paul) | mary != sK1 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 337,252]
339. ~person(paul) | mary != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 338,243]
340. ~person(paul) | mary != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 339,242]
341. ~person(paul) | mary != sK1 | ~room(mary) [subsumption resolution 340,241]
342. ~person(paul) | mary != sK1 [subsumption resolution 341,240]
344. 7 <=> mary = sK1 [avatar definition]
346. mary != sK1 <- (~7) [avatar component clause 344]
347. ~7 | ~4 [avatar split clause 342,311,344]
348. ~person(paul) | ~quiet(paul) | room(sK1) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 286,257]
349. ~person(paul) | room(sK1) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 348,252]
350. ~person(paul) | room(sK1) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 349,243]
351. ~person(paul) | room(sK1) | ~room(paul) | ~room(mary) [subsumption resolution 350,242]
352. ~person(paul) | room(sK1) | ~room(mary) [subsumption resolution 351,241]
353. ~person(paul) | room(sK1) [subsumption resolution 352,240]
355. 8 <=> room(sK1) [avatar definition]
357. room(sK1) <- (8) [avatar component clause 355]
358. 8 | ~4 [avatar split clause 353,311,355]
362. person(paul) [resolution 273,252]
367. 4 [avatar split clause 362,311]
563. fred = sK1 | paul = sK1 | mary = sK1 | alice = sK1 <- (8) [resolution 244,357]
581. paul = sK1 | mary = sK1 | alice = sK1 <- (~5, 8) [subsumption resolution 563,324]
582. mary = sK1 | alice = sK1 <- (~5, ~6, 8) [subsumption resolution 581,335]
583. alice = sK1 <- (~5, ~6, ~7, 8) [subsumption resolution 582,346]
584. $false <- (~3, ~5, ~6, ~7, 8) [subsumption resolution 583,309]
585. 3 | 5 | 6 | 7 | ~8 [avatar contradiction clause 584]
586. $false [avatar sat refutation 314,325,336,347,358,367,585]
% SZS output end Proof for 6414219340201890669520639
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.623521 |
Rosario, Mildred, David are the only persons in the room.
Everyone in the room does not collect first edition books if they does not collect action figures.
It is not the case that “David enjoys cross-country skiing”.
Everyone in the room enjoys watercolor painting if they is not a client of LVMH.
Everyone in the room plays eSports competitively if they enjoys watercolor painting.
Mildred writes in-depth travel guides for off-the-beaten-path destinations.
If someone collects action figures, is a client of LVMH or collects foreign coins then he/she builds model airplanes.
Mildred does not collect action figures.
David enjoys spelunking.
Everyone in the room enjoys watercolor painting if they enjoys stand-up paddleboarding.
Rosario does not build model airplanes.
Everyone in the room who is a client of LVMH writes in-depth travel guides for off-the-beaten-path destinations.
Mildred volunteers for local environmental conservation projects.
Everyone in the room neither is not a certified yoga instructor teaching classes weekly nor enjoys logic puzzles if and only if they neither does not frequently participates in hackathons and coding competitions nor does not collect foreign coins. | David enjoys spelunking. | entailment | room(rosario)&room(mildred)&room(david)&(![X]:(room(X)=>(X='rosario'|X='mildred'|X='david')))&
(![X]:(room(X)=>(((does_not_collect_action_figures(X))=>(does_not_collect_first_edition_books(X))))))&
(~(enjoys_cross-country_skiing(david)))&
(![X]:(room(X)=>(((is_not_a_client_of_LVMH(X))=>(enjoys_watercolor_painting(X))))))&
(![X]:(room(X)=>(((enjoys_watercolor_painting(X))=>(plays_eSports_competitively(X))))))&
(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(mildred))&
((![X]:((((collects_action_figures(X))|(is_a_client_of_LVMH(X))|(collects_foreign_coins(X))))=>(builds_model_airplanes(X)))))&
(does_not_collect_action_figures(mildred))&
(enjoys_spelunking(david))&
(![X]:(room(X)=>(((enjoys_stand-up_paddleboarding(X))=>(enjoys_watercolor_painting(X))))))&
(does_not_build_model_airplanes(rosario))&
(![X]:(room(X)=>(((is_a_client_of_LVMH(X))=>(writes_in-depth_travel_guides_for_off-the-beaten-path_destinations(X))))))&
(volunteers_for_local_environmental_conservation_projects(mildred))&
(![X]:(room(X)=>(((~((is_not_a_certified_yoga_instructor_teaching_classes_weekly(X))|(enjoys_logic_puzzles(X))))<=>(~((does_not_frequently_participates_in_hackathons_and_coding_competitions(X))|(does_not_collect_foreign_coins(X))))))))&
(![X]:(room(X)=>(((does_not_collect_first_edition_books(X))|(uses_contact_lenses(X))))))&
(enjoys_stand-up_paddleboarding(mildred))&
(![X]:(room(X)=>(bakes_bread_at_home(X))))&
(?[X]:(~room(X)&(((has_lived_in_exactly_three_countries(X))&(enjoys_logic_puzzles(X))&(plays_eSports_competitively(X))))))&
(?[X]:(room(X)&(makes_intricate_hand-cut_paper_art_for_exhibitions(X))))&
(![X]:(room(X)=>(((collect_rare_sneakers(X))<=>(plays_the_violin(X)))))) | room(rosario)&room(mildred)&room(david)&(![X]:(room(X)=>(X='rosario'|X='mildred'|X='david')))&
enjoys_spelunking(david) | [
"p0",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 6923371304700102776306395
% SZS output start Proof for 6923371304700102776306395
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
52. predk(fred) [input p8]
64. ~(predk(fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis]
154. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
155. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 154]
159. ~predk(fred) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 64]
160. ~predk(fred) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 159]
169. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) [choice axiom]
170. ~predk(fred) | (fred != sK2 & paul != sK2 & mary != sK2 & room(sK2)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 160,169]
251. room(mary) [cnf transformation 155]
252. room(paul) [cnf transformation 155]
253. room(fred) [cnf transformation 155]
254. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 155]
256. predk(fred) [cnf transformation 52]
267. ~predk(fred) | room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 170]
268. ~predk(fred) | mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 170]
269. ~predk(fred) | paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 170]
270. ~predk(fred) | fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 170]
271. fred != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 270,256]
272. fred != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 271,253]
273. fred != sK2 | ~room(mary) [subsumption resolution 272,252]
274. fred != sK2 [subsumption resolution 273,251]
275. paul != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 269,256]
276. paul != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 275,253]
277. paul != sK2 | ~room(mary) [subsumption resolution 276,252]
278. paul != sK2 [subsumption resolution 277,251]
279. mary != sK2 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 268,256]
280. mary != sK2 | ~room(paul) | ~room(mary) [subsumption resolution 279,253]
281. mary != sK2 | ~room(mary) [subsumption resolution 280,252]
282. mary != sK2 [subsumption resolution 281,251]
283. room(sK2) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 267,256]
284. room(sK2) | ~room(paul) | ~room(mary) [subsumption resolution 283,253]
285. room(sK2) | ~room(mary) [subsumption resolution 284,252]
286. room(sK2) [subsumption resolution 285,251]
333. paul = sK2 | mary = sK2 | fred = sK2 [resolution 254,286]
347. mary = sK2 | fred = sK2 [subsumption resolution 333,278]
348. fred = sK2 [subsumption resolution 347,282]
349. $false [subsumption resolution 348,274]
% SZS output end Proof for 6923371304700102776306395
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
James, Bart, Thelma are the only persons in the room. Either "Thelma is right-handed" or "Bart practices kickboxing" but not both. Everyone outside the room either composes and performs experimental electronic music or trains for and competes in international triathlons but not both only if they enjoys salsa dancing. Bart either enjoys deep-sea diving and exploring underwater caves or practices archery but not both. Bart hosts regular game nights featuring complex strategy games. Bart is a client of Costco. Bart enjoys deep-sea diving and exploring underwater caves. Everyone in the room is a wine connoisseur only if they enjoys skydiving. Everyone outside the room enjoys snowboarding or does not enjoy snowboarding. If someone enjoys snowboarding then he/she either practices kickboxing or enjoys making ceramics but not both. Everyone in the room does not enjoy making ceramics or practices kickboxing. If someone is a certified scuba diver with advanced underwater photography skills then he/she enjoys salsa dancing or trains for and competes in international triathlons or both and vice versa. Everyone in the room trains for and competes in international triathlons only if they enjoys salsa dancing. Everyone anywhere enjoys salsa dancing or does not enjoy skydiving. If someone practices kickboxing then he/she composes and performs experimental electronic music, practices archery and trains for and competes in international triathlons. James who is a client of Costco neither is not a wine connoisseur nor enjoys snowboarding. Thelma either enjoys skydiving or practices tai chi but not both. Thelma either composes and performs experimental electronic music or trains for and competes in international triathlons but not both. Everyone in the room who enjoys snowboarding composes and performs experimental electronic music. Only one person in the room is a wine connoisseur. Bart is right-handed. Bart trains for and competes in international triathlons. | Bart enjoys snowboarding. | contradiction | room(james)&room(bart)&room(thelma)&(![X]:(room(X)=>(X='james'|X='bart'|X='thelma')))&
((is_right-handed(thelma))<~>(practices_kickboxing(bart)))&
(![X]:(~room(X)=>(((enjoys_salsa_dancing(X))<=(((composes_and_performs_experimental_electronic_music(X))<~>(trains_for_and_competes_in_international_triathlons(X))))))))&
(((enjoys_deep-sea_diving_and_exploring_underwater_caves(bart))<~>(practices_archery(bart))))&
(hosts_regular_game_nights_featuring_complex_strategy_games(bart))&
(is_a_client_of_Costco(bart))&
(enjoys_deep-sea_diving_and_exploring_underwater_caves(bart))&
(![X]:(room(X)=>(((enjoys_skydiving(X))<=(is_a_wine_connoisseur(X))))))&
(![X]:(~room(X)=>(((does_not_enjoy_snowboarding(X))|(enjoys_snowboarding(X))))))&
((![X]:((enjoys_snowboarding(X))=>(((practices_kickboxing(X))<~>(enjoys_making_ceramics(X)))))))&
(![X]:(room(X)=>(((practices_kickboxing(X))|(does_not_enjoy_making_ceramics(X))))))&
((![X]:((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))<=>(((enjoys_salsa_dancing(X))|(trains_for_and_competes_in_international_triathlons(X)))))))&
(![X]:(room(X)=>(((enjoys_salsa_dancing(X))<=(trains_for_and_competes_in_international_triathlons(X))))))&
(![X]:(anywhere(X)=>(((does_not_enjoy_skydiving(X))|(enjoys_salsa_dancing(X))))))&
((![X]:((practices_kickboxing(X))=>(((composes_and_performs_experimental_electronic_music(X))&(practices_archery(X))&(trains_for_and_competes_in_international_triathlons(X)))))))&
((is_a_client_of_Costco(james))&(~((is_not_a_wine_connoisseur(james))|(enjoys_snowboarding(james)))))&
(((enjoys_skydiving(thelma))<~>(practices_tai_chi(thelma))))&
(((composes_and_performs_experimental_electronic_music(thelma))<~>(trains_for_and_competes_in_international_triathlons(thelma))))&
(![X]:(room(X)=>(((enjoys_snowboarding(X))=>(composes_and_performs_experimental_electronic_music(X))))))&
(((?[X]:(room(X)&is_a_wine_connoisseur(X)))&(![X,Y]:((room(X)&room(Y)&(is_a_wine_connoisseur(X))&(is_a_wine_connoisseur(Y)))=>(X=Y)))))&
(is_right-handed(bart))&
(trains_for_and_competes_in_international_triathlons(bart)) | room(james)&room(bart)&room(thelma)&(![X]:(room(X)=>(X='james'|X='bart'|X='thelma')))&
enjoys_snowboarding(bart) | [
"p0",
"p3",
"p6",
"p9",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4933130649970132837109142
% SZS output start Proof for 4933130649970132837109142
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
47. predp(paul) <~> predo(paul) [input p3]
50. predp(paul) [input p6]
53. ! [X0] : (predj(X0) => (prede(X0) <~> predm(X0))) [input p9]
54. ! [X0] : (room(X0) => (~predm(X0) | prede(X0))) [input p10]
58. ! [X0] : (prede(X0) => (predn(X0) & predo(X0) & predk(X0))) [input p14]
66. predj(paul) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input hypothesis]
146. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
147. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 146]
152. ! [X0] : ((prede(X0) <~> predm(X0)) | ~predj(X0)) [ennf transformation 53]
153. ! [X0] : ((~predm(X0) | prede(X0)) | ~room(X0)) [ennf transformation 54]
154. ! [X0] : (~predm(X0) | prede(X0) | ~room(X0)) [flattening 153]
155. ! [X0] : ((predn(X0) & predo(X0) & predk(X0)) | ~prede(X0)) [ennf transformation 58]
161. predj(paul) & ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 66]
162. predj(paul) & ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 161]
165. (~predo(paul) | ~predp(paul)) & (predo(paul) | predp(paul)) [nnf transformation 47]
166. ! [X0] : (((~predm(X0) | ~prede(X0)) & (predm(X0) | prede(X0))) | ~predj(X0)) [nnf transformation 152]
252. room(paul) [cnf transformation 147]
258. ~predo(paul) | ~predp(paul) [cnf transformation 165]
259. predp(paul) [cnf transformation 50]
262. ~predj(X0) | prede(X0) | predm(X0) [cnf transformation 166]
264. ~predm(X0) | prede(X0) | ~room(X0) [cnf transformation 154]
266. ~prede(X0) | predo(X0) [cnf transformation 155]
284. predj(paul) [cnf transformation 162]
290. 2 <=> prede(paul) [avatar definition]
291. prede(paul) <- (2) [avatar component clause 290]
292. ~prede(paul) <- (~2) [avatar component clause 290]
296. 3 <=> predp(paul) [avatar definition]
300. 4 <=> predo(paul) [avatar definition]
302. ~predo(paul) <- (~4) [avatar component clause 300]
303. ~3 | ~4 [avatar split clause 258,300,296]
305. 3 [avatar split clause 259,296]
327. predo(paul) <- (2) [resolution 266,291]
328. $false <- (2, ~4) [subsumption resolution 327,302]
329. ~2 | 4 [avatar contradiction clause 328]
334. prede(paul) | predm(paul) [resolution 262,284]
335. predm(paul) <- (~2) [subsumption resolution 334,292]
337. prede(paul) | ~room(paul) <- (~2) [resolution 264,335]
338. ~room(paul) <- (~2) [subsumption resolution 337,292]
339. $false <- (~2) [subsumption resolution 338,252]
340. 2 [avatar contradiction clause 339]
341. $false [avatar sat refutation 303,305,329,340]
% SZS output end Proof for 4933130649970132837109142
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0.333294 |
There is a room.
If everyone in the room practices zumba or is not an expert in identifying and foraging wild edible plants then not everyone in the room either owns a smartwatch or enjoys landscape photography but not both if they practices zumba.
If everyone in the room is not a coffee connoisseur or enjoys coding in Python then everyone outside the room who does not host themed dinner parties featuring gourmet home-cooked meals is a coffee connoisseur.
Not everyone anywhere enjoys landscape photography.
Everyone in the room who practices zumba is not a coffee connoisseur, is a coffee connoisseur or writes and illustrates their own graphic novels.
Not everyone outside the room hosts themed dinner parties featuring gourmet home-cooked meals if they is not a coffee connoisseur, is a coffee connoisseur or writes and illustrates their own graphic novels.
Everyone in the room practices zumba or is not an expert in identifying and foraging wild edible plants.
Everyone in the room who collects historical artifacts related to ancient civilizations does not own a smartwatch.
It is true that only one person in the room writes and illustrates their own graphic novels.
Everyone in the room writes and illustrates their own graphic novels or enjoys coding in Python or both if they enjoys landscape photography.
Someone in the room practices tai chi.
Everyone anywhere who hosts themed dinner parties featuring gourmet home-cooked meals or does not practice graffiti art or both practices zumba.
Everyone in the room is a coffee connoisseur if they practices zumba. | Everyone in the room does not collect historical artifacts related to ancient civilizations or practices zumba. | neutral | (there_is_a_room)&
((![X]:(room(X)=>(((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(practices_zumba(X))))))=>(~![X]:(room(X)=>(((practices_zumba(X))=>(((owns_a_smartwatch(X))<~>(enjoys_landscape_photography(X)))))))))&
((![X]:(room(X)=>(((enjoys_coding_in_Python(X))|(is_not_a_coffee_connoisseur(X))))))=>(![X]:(~room(X)=>(((does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))=>(is_a_coffee_connoisseur(X)))))))&
(~![X]:(anywhere(X)=>(enjoys_landscape_photography(X))))&
(![X]:(room(X)=>(((practices_zumba(X))=>(((is_not_a_coffee_connoisseur(X))|(is_a_coffee_connoisseur(X))|(writes_and_illustrates_their_own_graphic_novels(X))))))))&
(~![X]:(~room(X)=>(((((is_not_a_coffee_connoisseur(X))|(is_a_coffee_connoisseur(X))|(writes_and_illustrates_their_own_graphic_novels(X))))=>(hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))))))&
(![X]:(room(X)=>(((is_not_an_expert_in_identifying_and_foraging_wild_edible_plants(X))|(practices_zumba(X))))))&
(![X]:(room(X)=>(((collects_historical_artifacts_related_to_ancient_civilizations(X))=>(does_not_own_a_smartwatch(X))))))&
(((?[X]:(room(X)&writes_and_illustrates_their_own_graphic_novels(X)))&(![X,Y]:((room(X)&room(Y)&(writes_and_illustrates_their_own_graphic_novels(X))&(writes_and_illustrates_their_own_graphic_novels(Y)))=>(X=Y)))))&
(![X]:(room(X)=>(((enjoys_landscape_photography(X))=>(((writes_and_illustrates_their_own_graphic_novels(X))|(enjoys_coding_in_Python(X))))))))&
(?[X]:(room(X)&(practices_tai_chi(X))))&
(![X]:(anywhere(X)=>(((((hosts_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X))|(does_not_practice_graffiti_art(X))))=>(practices_zumba(X))))))&
(![X]:(room(X)=>(((practices_zumba(X))=>(is_a_coffee_connoisseur(X))))))&
(![X]:(anywhere(X)=>(practices_graffiti_art(X))))&
(?[X]:(~room(X)&(does_not_enjoy_origami(X))))&
(![X]:(room(X)=>(((enjoys_coding_in_Python(X))|(is_not_a_coffee_connoisseur(X))))))&
(![X]:(room(X)=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(does_not_host_themed_dinner_parties_featuring_gourmet_home-cooked_meals(X)))))) | (there_is_a_room)&
![X]:(room(X)=>(((practices_zumba(X))|(does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))))) | [] | null | 0.041311 |
Corey is the only person in the room. 'It is not the case that 'Corey collects first edition books'' unless 'it is not the case that 'Corey does not build model airplanes''. 'Corey writes poetry' unless 'Corey hosts regular game nights featuring complex strategy games'. Either 'Corey has a tattoo' or 'Corey plays as a goalkeeper for a local amateur soccer team' but not both. Corey is a wine connoisseur with a private cellar of vintage wines. Corey practices zumba. If someone is a wine connoisseur then he/she writes poetry and vice versa. Corey neither has a pet dog nor enjoys skydiving. Corey collects comic books. It is true that 'it is not the case that 'Corey owns an extensive assortment of vintage comic book memorabilia''. Corey hosts regular game nights featuring complex strategy games. Corey plays as a goalkeeper for a local amateur soccer team. Corey collects first edition books. Corey writes poetry. Corey does enjoy mountain biking. Corey is right-handed. Corey knows morse code. Corey practices archery. Corey collects luxury watches. | Corey enjoys skydiving. | contradiction | room(corey)&(![X]:(room(X)=>(X='corey')))&
(~(~(does_not_build_model_airplanes(corey)))=>(~(collects_first_edition_books(corey))))&
(~(hosts_regular_game_nights_featuring_complex_strategy_games(corey))=>(writes_poetry(corey)))&
((has_a_tattoo(corey))<~>(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(corey)))&
(is_a_wine_connoisseur_with_a_private_cellar_of_vintage_wines(corey))&
(practices_zumba(corey))&
((![X]:((is_a_wine_connoisseur(X))<=>(writes_poetry(X)))))&
(~((has_a_pet_dog(corey))|(enjoys_skydiving(corey))))&
(collects_comic_books(corey))&
(~(owns_an_extensive_assortment_of_vintage_comic_book_memorabilia(corey)))&
(hosts_regular_game_nights_featuring_complex_strategy_games(corey))&
(plays_as_a_goalkeeper_for_a_local_amateur_soccer_team(corey))&
(collects_first_edition_books(corey))&
(writes_poetry(corey))&
(does_enjoy_mountain_biking(corey))&
(is_right-handed(corey))&
(knows_morse_code(corey))&
(practices_archery(corey))&
(collects_luxury_watches(corey))&
(is_a_wine_connoisseur(corey)) | room(corey)&(![X]:(room(X)=>(X='corey')))&
enjoys_skydiving(corey) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 1172182401679526441484
% SZS output start Proof for 1172182401679526441484
51. ~(predj(mary) | predc(mary)) [input p7]
64. predj(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary) [input hypothesis]
77. ~predj(mary) [pure predicate removal 51]
156. ~predj(mary) [ennf transformation 77]
157. predj(mary) & ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 64]
244. ~predj(mary) [cnf transformation 156]
248. predj(mary) [cnf transformation 157]
260. $false [subsumption resolution 248,244]
% SZS output end Proof for 1172182401679526441484
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0.199031 |
There is a room. Everyone outside the room is richer than Diane if and only if they is richer than Mark. Everyone in the room who is a kind old person is quieter than Mark. It is not the case that more than one person in the room is a quiet person. Everyone in the room is quiet. Everyone in the room who is not a tall kind person is richer than Mark. Everyone in the room is richer than Mark only if they is a tall person. Everyone in the room is quieter than Connie if they is not a kind tall old quiet person. Everyone in the room is richer than Diane only if they is kind. | More than one person anywhere is richer than Mark and is quieter than Mark. | neutral | (there_is_a_room)&
(![X]:(~room(X)=>(((richer(diane,X))<=>(richer(mark,X))))))&
(![X]:(room(X)=>(((kind(X)&old(X)&person(X))=>(quieter(mark,X))))))&
(~((?[X,Y]:(room(X)&room(Y)&(quiet(X)&person(X)&quiet(Y)&person(Y))&(X!=Y)))))&
(![X]:(room(X)=>(quiet(X))))&
(![X]:(room(X)=>(((~(tall(X)&kind(X)&person(X)))=>(richer(mark,X))))))&
(![X]:(room(X)=>(((tall(X)&person(X))<=(richer(mark,X))))))&
(![X]:(room(X)=>(((~(kind(X)&tall(X)&old(X)&quiet(X)&person(X)))=>(quieter(connie,X))))))&
(![X]:(room(X)=>(((kind(X))<=(richer(diane,X))))))&
(~![X]:(room(X)=>(quieter(mark,X))))&
(![X]:(room(X)=>(((~old(X)&~tall(X))=>(~(old(X)&person(X)))))))&
(![X]:(room(X)=>(((~kind(X)&~old(X)&~tall(X))=>(~(tall(X)&person(X)))))))&
(![X]:(~room(X)=>(((~(tall(X)&person(X)))=>(~(quiet(X)&person(X)))))))&
(![X]:(tall(X)=>quiet(X)))&
((mark_dream=>(![X]:(anywhere(X)=>(((~((richer(connie,X))|(quiet(X))))=>(~(old(X)&person(X)))))))))&
(![X]:(room(X)=>(((kind(X))=>(quiet(X))))))&
(![X]:(room(X)=>(((quiet(X))=>(older(mark,X))))))&
(![X]:(kind(X)=>old(X))) | (there_is_a_room)&
(?[X,Y]:(anywhere(X)&anywhere(Y)&(((richer(mark,X))&(quieter(mark,X)))&((richer(mark,Y))&(quieter(mark,Y))))&(X!=Y))) | [] | null | 0.089038 |
Reid is the only person in the room.
Everyone in the room who has completed a triathlon enjoys watercolor painting.
Reid neither has completed a triathlon nor enjoys origami.
It is not the case that “Reid enjoys origami”.
Everyone anywhere who has completed a triathlon enjoys origami.
If someone participates in long-distance cycling events across the country then he/she does not have completed a triathlon and vice versa.
Everyone in the room who has completed a triathlon, enjoys origami or is an enthusiastic bird watcher who travels for rare sightings enjoys watercolor painting.
Everyone in the room participates in long-distance cycling events across the country if they enjoys watercolor painting.
Someone in the room is an enthusiastic bird watcher who travels for rare sightings.
Reid enjoys watercolor painting.
Not everyone in the room enjoys origami if they is an enthusiastic bird watcher who travels for rare sightings.
Reid has completed a triathlon, enjoys origami or is an enthusiastic bird watcher who travels for rare sightings.
At least one person in the room participates in long-distance cycling events across the country.
Reid participates in long-distance cycling events across the country. | Reid enjoys watercolor painting, is an enthusiastic bird watcher who travels for rare sightings and participates in long-distance cycling events across the country. | entailment | room(reid)&(![X]:(room(X)=>(X='reid')))&
(![X]:(room(X)=>(((has_completed_a_triathlon(X))=>(enjoys_watercolor_painting(X))))))&
(~((has_completed_a_triathlon(reid))|(enjoys_origami(reid))))&
(~(enjoys_origami(reid)))&
(![X]:(anywhere(X)=>(((has_completed_a_triathlon(X))=>(enjoys_origami(X))))))&
((![X]:((participates_in_long-distance_cycling_events_across_the_country(X))<=>(does_not_have_completed_a_triathlon(X)))))&
(![X]:(room(X)=>(((((has_completed_a_triathlon(X))|(enjoys_origami(X))|(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))=>(enjoys_watercolor_painting(X))))))&
(![X]:(room(X)=>(((enjoys_watercolor_painting(X))=>(participates_in_long-distance_cycling_events_across_the_country(X))))))&
(?[X]:(room(X)&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))&
(enjoys_watercolor_painting(reid))&
(~![X]:(room(X)=>(((is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))=>(enjoys_origami(X))))))&
(((has_completed_a_triathlon(reid))|(enjoys_origami(reid))|(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(reid))))&
(((?[X]:(room(X)&participates_in_long-distance_cycling_events_across_the_country(X)))))&
(?[X]:(anywhere(X)&(enjoys_watercolor_painting(X))))&
(participates_in_long-distance_cycling_events_across_the_country(reid))&
(![X]:(room(X)=>(((does_not_have_completed_a_triathlon(X))=>(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(X))))))&
(![X]:(room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))=>(((enjoys_watercolor_painting(X))|(participates_in_long-distance_cycling_events_across_the_country(X))))))))&
(![X]:(room(X)=>(((enjoys_watercolor_painting(X))<=(((enjoys_watercolor_painting(X))|(participates_in_long-distance_cycling_events_across_the_country(X))))))))&
((reid_dream=>(((enjoys_origami(reid))<~>(enjoys_watercolor_painting(reid)))))) | room(reid)&(![X]:(room(X)=>(X='reid')))&
((enjoys_watercolor_painting(reid))&(is_an_enthusiastic_bird_watcher_who_travels_for_rare_sightings(reid))&(participates_in_long-distance_cycling_events_across_the_country(reid))) | [
"p0",
"p2",
"p9",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5958022589895993795402735
% SZS output start Proof for 5958022589895993795402735
44. ! [X0] : (room(X0) => mary = X0) & room(mary) [input p0]
46. ~(predd(mary) | predc(mary)) [input p2]
53. prede(mary) [input p9]
55. preda(mary) | predd(mary) | predc(mary) [input p11]
58. predb(mary) [input p14]
63. ~(predb(mary) & preda(mary) & prede(mary) & ! [X0] : (room(X0) => mary = X0) & room(mary)) [input hypothesis]
136. ! [X0] : (mary = X0 | ~room(X0)) & room(mary) [ennf transformation 44]
139. ~predd(mary) & ~predc(mary) [ennf transformation 46]
154. ~predb(mary) | ~preda(mary) | ~prede(mary) | ? [X0] : (mary != X0 & room(X0)) | ~room(mary) [ennf transformation 63]
165. ? [X0] : (mary != X0 & room(X0)) => (mary != sK4 & room(sK4)) [choice axiom]
166. ~predb(mary) | ~preda(mary) | ~prede(mary) | (mary != sK4 & room(sK4)) | ~room(mary) [skolemisation 154,165]
248. room(mary) [cnf transformation 136]
249. ~room(X0) | mary = X0 [cnf transformation 136]
251. ~predc(mary) [cnf transformation 139]
252. ~predd(mary) [cnf transformation 139]
263. prede(mary) [cnf transformation 53]
267. preda(mary) | predd(mary) | predc(mary) [cnf transformation 55]
272. predb(mary) [cnf transformation 58]
277. ~predb(mary) | ~preda(mary) | ~prede(mary) | room(sK4) | ~room(mary) [cnf transformation 166]
278. ~predb(mary) | ~preda(mary) | ~prede(mary) | mary != sK4 | ~room(mary) [cnf transformation 166]
280. preda(mary) | predc(mary) [subsumption resolution 267,252]
281. preda(mary) [subsumption resolution 280,251]
282. ~preda(mary) | ~prede(mary) | mary != sK4 | ~room(mary) [subsumption resolution 278,272]
283. ~prede(mary) | mary != sK4 | ~room(mary) [subsumption resolution 282,281]
284. mary != sK4 | ~room(mary) [subsumption resolution 283,263]
285. mary != sK4 [subsumption resolution 284,248]
286. ~preda(mary) | ~prede(mary) | room(sK4) | ~room(mary) [subsumption resolution 277,272]
287. ~prede(mary) | room(sK4) | ~room(mary) [subsumption resolution 286,281]
288. room(sK4) | ~room(mary) [subsumption resolution 287,263]
289. room(sK4) [subsumption resolution 288,248]
297. mary = sK4 [resolution 249,289]
306. $false [subsumption resolution 297,285]
% SZS output end Proof for 5958022589895993795402735
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.012088 |
There is a room. Everyone in the room does not collect comic books. Everyone in the room does not own an extensive assortment of vintage comic book memorabilia and does not collect rare and antique scientific instruments. If someone either does not play as a goalkeeper for a local amateur soccer team or does not collect comic books but not both then he/she does not have lived in exactly three countries. Everyone in the room is not a scotch connoisseur, does not collect comic books and does not practice calligraphy. Everyone in the room does not have a curated collection of mid-century modern furniture. Everyone in the room does not train for and competes in international triathlons. If someone does not maintain a personal blog focused on cybersecurity tips, is not a professional photographer specializing in portrait photography and does not collect action figures then he/she does not collect rare and antique scientific instruments and is not an avid hiker. Everyone in the room does not play as a goalkeeper for a local amateur soccer team and does not collect historical artifacts related to ancient civilizations. If someone does not collect historical artifacts related to ancient civilizations then he/she does not collect comic books and does not have a pet dog. Everyone in the room does not collect action figures. Everyone in the room does not have a pet dog, does not own a high-end gaming PC with custom-built components and does not use contact lenses. Everyone in the room either does not collect historical artifacts related to ancient civilizations or does not train for and competes in international triathlons but not both. If someone either does not work as a freelance web developer specializing in e-commerce sites or does not collect historical artifacts related to ancient civilizations but not both then he/she is not a scotch connoisseur, does not have a curated collection of mid-century modern furniture or does not train for and competes in international triathlons and vice versa. Everyone anywhere does not collect historical artifacts related to ancient civilizations. Everyone in the room does not play video games or does not have lived in exactly three countries or both. | Everyone in the room does not collect historical artifacts related to ancient civilizations or uses contact lenses. | entailment | (there_is_a_room)&
(![X]:(room(X)=>(does_not_collect_comic_books(X))))&
(![X]:(room(X)=>(((does_not_own_an_extensive_assortment_of_vintage_comic_book_memorabilia(X))&(does_not_collect_rare_and_antique_scientific_instruments(X))))))&
((![X]:((((does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))<~>(does_not_collect_comic_books(X))))=>(does_not_have_lived_in_exactly_three_countries(X)))))&
(![X]:(room(X)=>(((is_not_a_scotch_connoisseur(X))&(does_not_collect_comic_books(X))&(does_not_practice_calligraphy(X))))))&
(![X]:(room(X)=>(does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))))&
(![X]:(room(X)=>(does_not_train_for_and_competes_in_international_triathlons(X))))&
((![X]:((((does_not_maintain_a_personal_blog_focused_on_cybersecurity_tips(X))&(is_not_a_professional_photographer_specializing_in_portrait_photography(X))&(does_not_collect_action_figures(X))))=>(((does_not_collect_rare_and_antique_scientific_instruments(X))&(is_not_an_avid_hiker(X)))))))&
(![X]:(room(X)=>(((does_not_play_as_a_goalkeeper_for_a_local_amateur_soccer_team(X))&(does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))))))&
((![X]:((does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))=>(((does_not_collect_comic_books(X))&(does_not_have_a_pet_dog(X)))))))&
(![X]:(room(X)=>(does_not_collect_action_figures(X))))&
(![X]:(room(X)=>(((does_not_have_a_pet_dog(X))&(does_not_own_a_high-end_gaming_PC_with_custom-built_components(X))&(does_not_use_contact_lenses(X))))))&
(![X]:(room(X)=>(((does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))<~>(does_not_train_for_and_competes_in_international_triathlons(X))))))&
((![X]:((((does_not_work_as_a_freelance_web_developer_specializing_in_e-commerce_sites(X))<~>(does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))))<=>(((is_not_a_scotch_connoisseur(X))|(does_not_have_a_curated_collection_of_mid-century_modern_furniture(X))|(does_not_train_for_and_competes_in_international_triathlons(X)))))))&
(![X]:(anywhere(X)=>(does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))))&
(![X]:(room(X)=>(((does_not_play_video_games(X))|(does_not_have_lived_in_exactly_three_countries(X))))))&
((?[X,Y]:(~room(X)&~room(Y)&(((does_not_train_for_and_competes_in_international_triathlons(X))<~>(does_not_have_completed_a_triathlon(X)))&((does_not_train_for_and_competes_in_international_triathlons(Y))<~>(does_not_have_completed_a_triathlon(Y))))&(X!=Y)))) | (there_is_a_room)&
![X]:(room(X)=>(((uses_contact_lenses(X))|(does_not_collect_historical_artifacts_related_to_ancient_civilizations(X))))) | [
"b4",
"p0",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 9057038104660679647462640
% SZS output start Proof for 9057038104660679647462640
5. ! [X0] : anywhere(X0) [input b4]
44. there_is_a_room [input p0]
58. ! [X0] : (anywhere(X0) => ~predd(X0)) [input p14]
61. ~(! [X0] : (room(X0) => (~predd(X0) | predj(X0))) & there_is_a_room) [input hypothesis]
64. ~(! [X0] : (room(X0) => ~predd(X0)) & there_is_a_room) [pure predicate removal 61]
155. ! [X0] : (~predd(X0) | ~anywhere(X0)) [ennf transformation 58]
156. ? [X0] : (predd(X0) & room(X0)) | ~there_is_a_room [ennf transformation 64]
165. ? [X0] : (predd(X0) & room(X0)) => (predd(sK2) & room(sK2)) [choice axiom]
166. (predd(sK2) & room(sK2)) | ~there_is_a_room [skolemisation 156,165]
167. anywhere(X0) [cnf transformation 5]
248. there_is_a_room [cnf transformation 44]
263. ~predd(X0) | ~anywhere(X0) [cnf transformation 155]
272. predd(sK2) | ~there_is_a_room [cnf transformation 166]
275. ~predd(X0) [subsumption resolution 263,167]
296. ~there_is_a_room [subsumption resolution 272,275]
297. $false [subsumption resolution 296,248]
% SZS output end Proof for 9057038104660679647462640
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.163665 |
Mel, Thelma, Darryl, Paul are the only persons in the room. If “everyone in the room practices tai chi or does not practice tai chi” then “Paul hosts a YouTube channel dedicated to art tutorials”. Either “Thelma does practice yoga” or “someone in the room practices tai chi” but not both. | Paul hosts a YouTube channel dedicated to art tutorials. | entailment | room(mel)&room(thelma)&room(darryl)&room(paul)&(![X]:(room(X)=>(X='mel'|X='thelma'|X='darryl'|X='paul')))&
((![X]:(room(X)=>(((does_not_practice_tai_chi(X))|(practices_tai_chi(X))))))=>(hosts_a_YouTube_channel_dedicated_to_art_tutorials(paul)))&
((does_practice_yoga(thelma))<~>(?[X]:(room(X)&(practices_tai_chi(X)))))&
(![X]:(~room(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))=>(((is_a_wine_connoisseur(X))&(does_not_own_a_television(X))))))))&
(![X]:(room(X)=>(((((works_on_fridays(X))&(does_enjoy_mountain_biking(X))&(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))=>(does_not_develop_open-source_software_projects_in_their_free_time(X))))))&
(![X]:(room(X)=>(((does_not_develop_open-source_software_projects_in_their_free_time(X))=>(((creates_augmented_reality_experiences_for_mobile_applications(X))|(can_play_the_piano(X))|(plays_video_games(X))))))))&
(![X]:(anywhere(X)=>(((does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(X))<=>(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))))&
(![X]:(room(X)=>(((does_not_practice_tai_chi(X))|(practices_tai_chi(X))))))&
(collects_historical_artifacts_related_to_ancient_civilizations(darryl))&
(![X]:(room(X)=>(((((own_a_television(X))&(regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))))<=>(own_a_television(X))))))&
(develops_open-source_software_projects_in_their_free_time(darryl))&
(does_not_practice_tai_chi(thelma))&
(![X]:(anywhere(X)=>(((does_not_own_a_television(X))=>(is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))))))&
(![X]:(room(X)=>(((is_an_avid_mountain_climber_who_has_scaled_several_peaks(X))<=>(practices_urban_gardening(X))))))&
((works_on_fridays(darryl))&(collects_antique_jewelry(darryl)))&
(![X]:(~room(X)=>(((is_right-handed(X))|(does_not_practice_tai_chi(X))))))&
(does_not_create_bespoke_furniture_pieces_from_reclaimed_wood(thelma))&
(?[X]:(room(X)&(does_not_develop_open-source_software_projects_in_their_free_time(X))))&
(![X]:(anywhere(X)=>(((creates_bespoke_furniture_pieces_from_reclaimed_wood(X))=>(enjoys_kayaking(X))))))&
(practices_urban_gardening(paul))&
(![X]:(room(X)=>(((((collects_antique_jewelry(X))<~>(collects_rare_and_antique_scientific_instruments(X))))<=(is_a_wine_connoisseur(X))))))&
(![X]:(room(X)=>(((does_practice_yoga(X))=>(does_not_enjoy_mountain_biking(X))))))&
((?[X,Y]:(room(X)&room(Y)&(is_a_certified_yoga_instructor_teaching_classes_weekly(X)&is_a_certified_yoga_instructor_teaching_classes_weekly(Y))&(X!=Y))))&
(![X]:(room(X)=>(((regularly_goes_on_multi-day_backpacking_trips_in_national_parks(X))=>(collects_antique_jewelry(X)))))) | room(mel)&room(thelma)&room(darryl)&room(paul)&(![X]:(room(X)=>(X='mel'|X='thelma'|X='darryl'|X='paul')))&
hosts_a_YouTube_channel_dedicated_to_art_tutorials(paul) | [
"p0",
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 8851480405329981470354661
% SZS output start Proof for 8851480405329981470354661
44. ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
45. ! [X0] : (room(X0) => (predq(X0) | ~predq(X0))) => preda(alice) [input p1]
68. ~(preda(alice) & ! [X0] : (room(X0) => (alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(alice) & room(fred) & room(paul) & room(mary)) [input hypothesis]
148. ! [X0] : ((alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
149. ! [X0] : (alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 148]
150. preda(alice) | ? [X0] : ((~predq(X0) & predq(X0)) & room(X0)) [ennf transformation 45]
151. preda(alice) | ? [X0] : (~predq(X0) & predq(X0) & room(X0)) [flattening 150]
165. ~preda(alice) | ? [X0] : ((alice != X0 & fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 68]
166. ~preda(alice) | ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 165]
168. ? [X0] : (~predq(X0) & predq(X0) & room(X0)) => (~predq(sK0) & predq(sK0) & room(sK0)) [choice axiom]
169. preda(alice) | (~predq(sK0) & predq(sK0) & room(sK0)) [skolemisation 151,168]
183. ? [X0] : (alice != X0 & fred != X0 & paul != X0 & mary != X0 & room(X0)) => (alice != sK5 & fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) [choice axiom]
184. ~preda(alice) | (alice != sK5 & fred != sK5 & paul != sK5 & mary != sK5 & room(sK5)) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 166,183]
266. room(mary) [cnf transformation 149]
267. room(paul) [cnf transformation 149]
268. room(fred) [cnf transformation 149]
269. room(alice) [cnf transformation 149]
270. ~room(X0) | fred = X0 | paul = X0 | mary = X0 | alice = X0 [cnf transformation 149]
272. preda(alice) | predq(sK0) [cnf transformation 169]
273. preda(alice) | ~predq(sK0) [cnf transformation 169]
301. ~preda(alice) | room(sK5) | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 184]
302. ~preda(alice) | mary != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 184]
303. ~preda(alice) | paul != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 184]
304. ~preda(alice) | fred != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 184]
305. ~preda(alice) | alice != sK5 | ~room(alice) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 184]
307. 1 <=> predq(sK0) [avatar definition]
311. 2 <=> preda(alice) [avatar definition]
314. ~1 | 2 [avatar split clause 273,311,307]
315. 1 | 2 [avatar split clause 272,311,307]
342. ~preda(alice) | alice != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 305,269]
343. ~preda(alice) | alice != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 342,268]
344. ~preda(alice) | alice != sK5 | ~room(mary) [subsumption resolution 343,267]
345. ~preda(alice) | alice != sK5 [subsumption resolution 344,266]
347. 8 <=> alice = sK5 [avatar definition]
349. alice != sK5 <- (~8) [avatar component clause 347]
350. ~8 | ~2 [avatar split clause 345,311,347]
351. ~preda(alice) | fred != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 304,269]
352. ~preda(alice) | fred != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 351,268]
353. ~preda(alice) | fred != sK5 | ~room(mary) [subsumption resolution 352,267]
354. ~preda(alice) | fred != sK5 [subsumption resolution 353,266]
356. 9 <=> fred = sK5 [avatar definition]
358. fred != sK5 <- (~9) [avatar component clause 356]
359. ~9 | ~2 [avatar split clause 354,311,356]
360. ~preda(alice) | paul != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 303,269]
361. ~preda(alice) | paul != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 360,268]
362. ~preda(alice) | paul != sK5 | ~room(mary) [subsumption resolution 361,267]
363. ~preda(alice) | paul != sK5 [subsumption resolution 362,266]
365. 10 <=> paul = sK5 [avatar definition]
367. paul != sK5 <- (~10) [avatar component clause 365]
368. ~10 | ~2 [avatar split clause 363,311,365]
369. ~preda(alice) | mary != sK5 | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 302,269]
370. ~preda(alice) | mary != sK5 | ~room(paul) | ~room(mary) [subsumption resolution 369,268]
371. ~preda(alice) | mary != sK5 | ~room(mary) [subsumption resolution 370,267]
372. ~preda(alice) | mary != sK5 [subsumption resolution 371,266]
374. 11 <=> mary = sK5 [avatar definition]
376. mary != sK5 <- (~11) [avatar component clause 374]
377. ~11 | ~2 [avatar split clause 372,311,374]
378. ~preda(alice) | room(sK5) | ~room(fred) | ~room(paul) | ~room(mary) [subsumption resolution 301,269]
379. ~preda(alice) | room(sK5) | ~room(paul) | ~room(mary) [subsumption resolution 378,268]
380. ~preda(alice) | room(sK5) | ~room(mary) [subsumption resolution 379,267]
381. ~preda(alice) | room(sK5) [subsumption resolution 380,266]
383. 12 <=> room(sK5) [avatar definition]
385. room(sK5) <- (12) [avatar component clause 383]
386. 12 | ~2 [avatar split clause 381,311,383]
548. fred = sK5 | paul = sK5 | mary = sK5 | alice = sK5 <- (12) [resolution 270,385]
600. paul = sK5 | mary = sK5 | alice = sK5 <- (~9, 12) [subsumption resolution 548,358]
601. mary = sK5 | alice = sK5 <- (~9, ~10, 12) [subsumption resolution 600,367]
602. alice = sK5 <- (~9, ~10, ~11, 12) [subsumption resolution 601,376]
603. $false <- (~8, ~9, ~10, ~11, 12) [subsumption resolution 602,349]
604. 8 | 9 | 10 | 11 | ~12 [avatar contradiction clause 603]
605. $false [avatar sat refutation 314,315,350,359,368,377,386,604]
% SZS output end Proof for 8851480405329981470354661
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.024 s
% ------------------------------
% ------------------------------
| 0.096081 |
Elna, Jean, Jessica, Kathleen, Mary are the only persons in the room.
If someone in the room has a piercing then Jean either plays video games or owns a smart tv but not both.
Everyone in the room is not dedicated to sustainable living and zero-waste practices or has a piercing unless not everyone outside the room is not a certified scuba diver with advanced underwater photography skills or is dedicated to sustainable living and zero-waste practices.
Someone in the room is a skilled home brewer experimenting with craft beer recipes, collects modern art and enjoys stand-up paddleboarding unless Jean plays video games.
If everyone in the room cannot play the guitar or has a piercing then someone in the room either is a scotch connoisseur or has a piercing but not both.
Everyone in the room collects antique clocks if they enjoys wildlife photography, is a skilled home brewer experimenting with craft beer recipes and is a certified scuba diver with advanced underwater photography skills unless Jean enjoys deep-sea diving and exploring underwater caves.
Everyone in the room does not enjoy stand-up paddleboarding or collects antique clocks.
Everyone in the room who maintains a personal blog focused on cybersecurity tips owns a smart tv.
Everyone outside the room owns a smart tv only if they collects antique clocks.
Everyone outside the room collects antique clocks only if they either is a scotch connoisseur or participates in long-distance cycling events across the country but not both.
If someone enjoys deep-sea diving and exploring underwater caves then he/she plays video games and vice versa.
Everyone in the room who plays video games owns a smart tv, collects modern art and enjoys spelunking.
Not everyone in the room owns a smart tv, collects modern art and enjoys spelunking only if they is a certified scuba diver with advanced underwater photography skills.
Everyone in the room does not collect antique clocks if they is a certified scuba diver with advanced underwater photography skills.
Everyone in the room who has a piercing collects antique clocks and enjoys rooftop gardening.
Everyone in the room who is a certified scuba diver with advanced underwater photography skills has a piercing. | Elna is a certified scuba diver with advanced underwater photography skills. | contradiction | room(elna)&room(jean)&room(jessica)&room(kathleen)&room(mary)&(![X]:(room(X)=>(X='elna'|X='jean'|X='jessica'|X='kathleen'|X='mary')))&
((?[X]:(room(X)&(has_a_piercing(X))))=>(((plays_video_games(jean))<~>(owns_a_smart_tv(jean)))))&
(~(~![X]:(~room(X)=>(((is_dedicated_to_sustainable_living_and_zero-waste_practices(X))|(is_not_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))))=>(![X]:(room(X)=>(((has_a_piercing(X))|(is_not_dedicated_to_sustainable_living_and_zero-waste_practices(X)))))))&
(~(plays_video_games(jean))=>(?[X]:(room(X)&(((is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))&(collects_modern_art(X))&(enjoys_stand-up_paddleboarding(X)))))))&
((![X]:(room(X)=>(((has_a_piercing(X))|(cannot_play_the_guitar(X))))))=>(?[X]:(room(X)&(((is_a_scotch_connoisseur(X))<~>(has_a_piercing(X)))))))&
(~(enjoys_deep-sea_diving_and_exploring_underwater_caves(jean))=>(![X]:(room(X)=>(((((enjoys_wildlife_photography(X))&(is_a_skilled_home_brewer_experimenting_with_craft_beer_recipes(X))&(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))))=>(collects_antique_clocks(X)))))))&
(![X]:(room(X)=>(((collects_antique_clocks(X))|(does_not_enjoy_stand-up_paddleboarding(X))))))&
(![X]:(room(X)=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))=>(owns_a_smart_tv(X))))))&
(![X]:(~room(X)=>(((collects_antique_clocks(X))<=(owns_a_smart_tv(X))))))&
(![X]:(~room(X)=>(((((is_a_scotch_connoisseur(X))<~>(participates_in_long-distance_cycling_events_across_the_country(X))))<=(collects_antique_clocks(X))))))&
((![X]:((enjoys_deep-sea_diving_and_exploring_underwater_caves(X))<=>(plays_video_games(X)))))&
(![X]:(room(X)=>(((plays_video_games(X))=>(((owns_a_smart_tv(X))&(collects_modern_art(X))&(enjoys_spelunking(X))))))))&
(~![X]:(room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))<=(((owns_a_smart_tv(X))&(collects_modern_art(X))&(enjoys_spelunking(X))))))))&
(![X]:(room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))=>(does_not_collect_antique_clocks(X))))))&
((![X]:((((can_play_the_guitar(X))&(enjoys_wildlife_photography(X))))<=>(owns_a_telescope(X)))))&
((maintains_a_personal_blog_focused_on_cybersecurity_tips(jean))&(~((is_an_avid_mountain_climber_who_has_scaled_several_peaks(jean))|(does_not_participate_in_long-distance_cycling_events_across_the_country(jean)))))&
(![X]:(room(X)=>(((((is_not_an_avid_mountain_climber_who_has_scaled_several_peaks(X))<~>(enjoys_landscape_photography(X))))<=>(collects_rare_minerals(X))))))&
(![X]:(room(X)=>(((has_a_piercing(X))=>(((collects_antique_clocks(X))&(enjoys_rooftop_gardening(X))))))))&
(![X]:(~room(X)=>(((((collects_antique_clocks(X))&(enjoys_rooftop_gardening(X))))=>(enjoys_landscape_photography(X))))))&
(![X]:(room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))<=(enjoys_landscape_photography(X))))))&
(![X]:(room(X)=>(((is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X))=>(has_a_piercing(X))))))&
((![X]:((((does_not_enjoy_wildlife_photography(X))&(plays_video_games(X))))<=>(is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(X)))))&
(![X]:(room(X)=>(((participates_in_long-distance_cycling_events_across_the_country(X))<=>(((maintains_a_personal_blog_focused_on_cybersecurity_tips(X))&(does_not_collect_modern_art(X)))))))) | room(elna)&room(jean)&room(jessica)&room(kathleen)&room(mary)&(![X]:(room(X)=>(X='elna'|X='jean'|X='jessica'|X='kathleen'|X='mary')))&
is_a_certified_scuba_diver_with_advanced_underwater_photography_skills(elna) | [
"p0",
"p13",
"p17",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4531781193429269873906487
% SZS output start Proof for 4531781193429269873906487
44. ! [X0] : (room(X0) => (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [input p0]
57. ! [X0] : (room(X0) => (predn(X0) => ~predh(X0))) [input p13]
61. ! [X0] : (room(X0) => (predt(X0) => (predi(X0) & predh(X0)))) [input p17]
64. ! [X0] : (room(X0) => (predn(X0) => predt(X0))) [input p20]
67. predn(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]
148. ! [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]
149. ! [X0] : (john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [flattening 148]
168. ! [X0] : ((~predh(X0) | ~predn(X0)) | ~room(X0)) [ennf transformation 57]
169. ! [X0] : (~predh(X0) | ~predn(X0) | ~room(X0)) [flattening 168]
173. ! [X0] : (((predi(X0) & predh(X0)) | ~predt(X0)) | ~room(X0)) [ennf transformation 61]
174. ! [X0] : ((predi(X0) & predh(X0)) | ~predt(X0) | ~room(X0)) [flattening 173]
179. ! [X0] : ((predt(X0) | ~predn(X0)) | ~room(X0)) [ennf transformation 64]
180. ! [X0] : (predt(X0) | ~predn(X0) | ~room(X0)) [flattening 179]
182. predn(mary) & ! [X0] : ((john = X0 | alice = X0 | fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(john) & room(alice) & room(fred) & room(paul) & room(mary) [ennf transformation 67]
183. predn(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 182]
282. room(mary) [cnf transformation 149]
313. ~predh(X0) | ~predn(X0) | ~room(X0) [cnf transformation 169]
321. ~predt(X0) | predh(X0) | ~room(X0) [cnf transformation 174]
325. ~predn(X0) | predt(X0) | ~room(X0) [cnf transformation 180]
338. predn(mary) [cnf transformation 183]
424. predt(mary) | ~room(mary) [resolution 325,338]
425. predt(mary) [subsumption resolution 424,282]
441. predh(mary) | ~room(mary) [resolution 425,321]
444. predh(mary) [subsumption resolution 441,282]
455. ~predn(mary) | ~room(mary) [resolution 444,313]
456. ~room(mary) [subsumption resolution 455,338]
457. $false [subsumption resolution 456,282]
% SZS output end Proof for 4531781193429269873906487
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.540237 |
Jesse, Linda, Julie are the only persons in the room. Julie who does not compose and performs experimental electronic music or does not own a 3D printer or both does not have a vast collection of first-edition science fiction novels. Linda who does not own a 3D printer does not collect vintage vinyl records, does not have completed a triathlon and does not enjoy camping and organizing outdoor survival workshops. Everyone anywhere either does not enjoy coding in Python or does not create large-scale murals for public art installations but not both. If someone does not create large-scale murals for public art installations and does not write and illustrates their own graphic novels then he/she does not enjoy coding in Python and does not collect limited-edition art prints from contemporary artists. Everyone in the room either does not write poetry or does not own a microscope but not both. Not everyone in the room does not practice graffiti art. Everyone in the room does not own a 3D printer, does not have a vast collection of first-edition science fiction novels or is not a drone photographer. If someone cannot play the piano then he/she does not compose and performs experimental electronic music and vice versa. If someone does not write and illustrates their own graphic novels, does not create large-scale murals for public art installations and does not enjoy camping and organizing outdoor survival workshops then he/she does not host regular workshops on creative writing and vice versa. Everyone in the room does not own a 3D printer, does not enjoy camping and organizing outdoor survival workshops and does not own an Android phone. Everyone in the room does not practice digital art. If someone does not collect limited-edition art prints from contemporary artists, does not have a saltwater aquarium or is not a craft beer aficionado then he/she does not practice digital art or does not own a microscope or both. If someone is not a craft beer aficionado, does not write poetry or cannot play the piano then he/she does not own a microscope and vice versa. Everyone outside the room does not own a 3D printer. Everyone in the room does not practice graffiti art or is not a craft beer aficionado or both. | Julie writes poetry. | entailment | room(jesse)&room(linda)&room(julie)&(![X]:(room(X)=>(X='jesse'|X='linda'|X='julie')))&
((((does_not_compose_and_performs_experimental_electronic_music(julie))|(does_not_own_a_3D_printer(julie))))&(does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(julie)))&
((does_not_own_a_3D_printer(linda))&(((does_not_collect_vintage_vinyl_records(linda))&(does_not_have_completed_a_triathlon(linda))&(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(linda)))))&
(![X]:(anywhere(X)=>(((does_not_enjoy_coding_in_Python(X))<~>(does_not_create_large-scale_murals_for_public_art_installations(X))))))&
((![X]:((((does_not_create_large-scale_murals_for_public_art_installations(X))&(does_not_write_and_illustrates_their_own_graphic_novels(X))))=>(((does_not_enjoy_coding_in_Python(X))&(does_not_collect_limited-edition_art_prints_from_contemporary_artists(X)))))))&
(![X]:(room(X)=>(((does_not_write_poetry(X))<~>(does_not_own_a_microscope(X))))))&
(~![X]:(room(X)=>(does_not_practice_graffiti_art(X))))&
(![X]:(room(X)=>(((does_not_own_a_3D_printer(X))|(does_not_have_a_vast_collection_of_first-edition_science_fiction_novels(X))|(is_not_a_drone_photographer(X))))))&
((![X]:((cannot_play_the_piano(X))<=>(does_not_compose_and_performs_experimental_electronic_music(X)))))&
((![X]:((((does_not_write_and_illustrates_their_own_graphic_novels(X))&(does_not_create_large-scale_murals_for_public_art_installations(X))&(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))))<=>(does_not_host_regular_workshops_on_creative_writing(X)))))&
(![X]:(room(X)=>(((does_not_own_a_3D_printer(X))&(does_not_enjoy_camping_and_organizing_outdoor_survival_workshops(X))&(does_not_own_an_Android_phone(X))))))&
(![X]:(room(X)=>(does_not_practice_digital_art(X))))&
((![X]:((((does_not_collect_limited-edition_art_prints_from_contemporary_artists(X))|(does_not_have_a_saltwater_aquarium(X))|(is_not_a_craft_beer_aficionado(X))))=>(((does_not_practice_digital_art(X))|(does_not_own_a_microscope(X)))))))&
((![X]:((((is_not_a_craft_beer_aficionado(X))|(does_not_write_poetry(X))|(cannot_play_the_piano(X))))<=>(does_not_own_a_microscope(X)))))&
(![X]:(~room(X)=>(does_not_own_a_3D_printer(X))))&
(![X]:(room(X)=>(((does_not_practice_graffiti_art(X))|(is_not_a_craft_beer_aficionado(X)))))) | room(jesse)&room(linda)&room(julie)&(![X]:(room(X)=>(X='jesse'|X='linda'|X='julie')))&
writes_poetry(julie) | [
"p0",
"p5",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 618547383940259866456363
% SZS output start Proof for 618547383940259866456363
44. ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary) [input p0]
49. ! [X0] : (room(X0) => (~predn(X0) <~> ~predk(X0))) [input p5]
57. ! [X0] : ((~prede(X0) | ~predn(X0) | ~predu(X0)) <=> ~predk(X0)) [input p13]
60. ~(predn(fred) & ! [X0] : (room(X0) => (fred = X0 | paul = X0 | mary = X0)) & room(fred) & room(paul) & room(mary)) [input hypothesis]
148. ! [X0] : ((fred = X0 | paul = X0 | mary = X0) | ~room(X0)) & room(fred) & room(paul) & room(mary) [ennf transformation 44]
149. ! [X0] : (fred = X0 | paul = X0 | mary = X0 | ~room(X0)) & room(fred) & room(paul) & room(mary) [flattening 148]
151. ! [X0] : ((~predn(X0) <~> ~predk(X0)) | ~room(X0)) [ennf transformation 49]
155. ~predn(fred) | ? [X0] : ((fred != X0 & paul != X0 & mary != X0) & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [ennf transformation 60]
156. ~predn(fred) | ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) | ~room(fred) | ~room(paul) | ~room(mary) [flattening 155]
159. ! [X0] : (((predk(X0) | predn(X0)) & (~predk(X0) | ~predn(X0))) | ~room(X0)) [nnf transformation 151]
163. ! [X0] : (((~prede(X0) | ~predn(X0) | ~predu(X0)) | predk(X0)) & (~predk(X0) | (prede(X0) & predn(X0) & predu(X0)))) [nnf transformation 57]
164. ! [X0] : ((~prede(X0) | ~predn(X0) | ~predu(X0) | predk(X0)) & (~predk(X0) | (prede(X0) & predn(X0) & predu(X0)))) [flattening 163]
165. ? [X0] : (fred != X0 & paul != X0 & mary != X0 & room(X0)) => (fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) [choice axiom]
166. ~predn(fred) | (fred != sK1 & paul != sK1 & mary != sK1 & room(sK1)) | ~room(fred) | ~room(paul) | ~room(mary) [skolemisation 156,165]
248. room(mary) [cnf transformation 149]
249. room(paul) [cnf transformation 149]
250. room(fred) [cnf transformation 149]
251. ~room(X0) | paul = X0 | mary = X0 | fred = X0 [cnf transformation 149]
255. ~room(X0) | predn(X0) | predk(X0) [cnf transformation 159]
261. ~predk(X0) | predn(X0) [cnf transformation 164]
265. ~predn(fred) | room(sK1) | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166]
266. ~predn(fred) | mary != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166]
267. ~predn(fred) | paul != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166]
268. ~predn(fred) | fred != sK1 | ~room(fred) | ~room(paul) | ~room(mary) [cnf transformation 166]
271. ~predn(fred) | fred != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 268,250]
272. ~predn(fred) | fred != sK1 | ~room(mary) [subsumption resolution 271,249]
273. ~predn(fred) | fred != sK1 [subsumption resolution 272,248]
275. 1 <=> fred = sK1 [avatar definition]
277. fred != sK1 <- (~1) [avatar component clause 275]
279. 2 <=> predn(fred) [avatar definition]
282. ~1 | ~2 [avatar split clause 273,279,275]
283. ~predn(fred) | paul != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 267,250]
284. ~predn(fred) | paul != sK1 | ~room(mary) [subsumption resolution 283,249]
285. ~predn(fred) | paul != sK1 [subsumption resolution 284,248]
287. 3 <=> paul = sK1 [avatar definition]
289. paul != sK1 <- (~3) [avatar component clause 287]
290. ~3 | ~2 [avatar split clause 285,279,287]
291. ~predn(fred) | mary != sK1 | ~room(paul) | ~room(mary) [subsumption resolution 266,250]
292. ~predn(fred) | mary != sK1 | ~room(mary) [subsumption resolution 291,249]
293. ~predn(fred) | mary != sK1 [subsumption resolution 292,248]
295. 4 <=> mary = sK1 [avatar definition]
297. mary != sK1 <- (~4) [avatar component clause 295]
298. ~4 | ~2 [avatar split clause 293,279,295]
299. ~predn(fred) | room(sK1) | ~room(paul) | ~room(mary) [subsumption resolution 265,250]
300. ~predn(fred) | room(sK1) | ~room(mary) [subsumption resolution 299,249]
301. ~predn(fred) | room(sK1) [subsumption resolution 300,248]
303. 5 <=> room(sK1) [avatar definition]
305. room(sK1) <- (5) [avatar component clause 303]
306. 5 | ~2 [avatar split clause 301,279,303]
310. predn(fred) | predk(fred) [resolution 255,250]
322. predn(fred) [subsumption resolution 310,261]
323. 2 [avatar split clause 322,279]
366. paul = sK1 | mary = sK1 | fred = sK1 <- (5) [resolution 251,305]
380. mary = sK1 | fred = sK1 <- (~3, 5) [subsumption resolution 366,289]
381. fred = sK1 <- (~3, ~4, 5) [subsumption resolution 380,297]
382. $false <- (~1, ~3, ~4, 5) [subsumption resolution 381,277]
383. 1 | 3 | 4 | ~5 [avatar contradiction clause 382]
384. $false [avatar sat refutation 282,290,298,306,323,383]
% SZS output end Proof for 618547383940259866456363
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
% ------------------------------
| 0.229327 |
Maureen, Margaret, Irene are the only persons in the room.
Maureen either is not old, not tall, not quiet or is not not not old but not both. | Irene is quiet. | neutral | room(maureen)&room(margaret)&room(irene)&(![X]:(room(X)=>(X='maureen'|X='margaret'|X='irene')))&
(((~old(maureen)&~tall(maureen)&~quiet(maureen))<~>(~~~old(maureen))))&
(?[X,Y]:((((quiet(X))<~>(~old(X))))&(((~tall(Y))<~>(~old(Y)&~tall(Y))))&(older(X,Y))))&
(![X]:(room(X)=>(((~(quiet(X)&person(X)))<=>(~tall(X)&~quiet(X)&~old(X))))))&
(![X]:(room(X)=>(((~(old(X)&person(X)))<=(~(quiet(X)&person(X)))))))&
(~(quiet(irene)&tall(irene)&old(irene)&person(irene)))&
(((~(old(margaret)&person(margaret)))&(~(old(margaret)&quiet(margaret)&person(margaret)))&(~(tall(margaret)&person(margaret)))))&
((![X]:((~(tall(X)&person(X)))=>(~(old(X)&person(X))))))&
(~(old(irene)&tall(irene)&quiet(irene)&person(irene))) | room(maureen)&room(margaret)&room(irene)&(![X]:(room(X)=>(X='maureen'|X='margaret'|X='irene')))&
quiet(irene) | [] | null | 0.312287 |