TSTP Solution File: SEU682^1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU682^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:50:39 EDT 2024
% Result : Theorem 8.72s 1.63s
% Output : Refutation 8.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU682^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.15 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.12/0.36 % Computer : n007.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8042.1875MB
% 0.12/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Sun May 19 17:27:53 EDT 2024
% 0.12/0.36 % CPUTime :
% 0.12/0.36 This is a TH0_THM_EQU_NAR problem
% 0.12/0.36 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.39 % (27428)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.12/0.39 % (27429)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.12/0.39 % (27430)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.12/0.39 % (27431)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.12/0.39 % (27432)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.12/0.39 % (27428)Instruction limit reached!
% 0.12/0.39 % (27428)------------------------------
% 0.12/0.39 % (27428)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.39 % (27428)Termination reason: Unknown
% 0.12/0.39 % (27428)Termination phase: shuffling
% 0.12/0.39
% 0.12/0.39 % (27429)Instruction limit reached!
% 0.12/0.39 % (27429)------------------------------
% 0.12/0.39 % (27429)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.39 % (27429)Termination reason: Unknown
% 0.12/0.39 % (27429)Termination phase: shuffling
% 0.12/0.39
% 0.12/0.39 % (27429)Memory used [KB]: 1407
% 0.12/0.39 % (27429)Time elapsed: 0.003 s
% 0.12/0.39 % (27429)Instructions burned: 2 (million)
% 0.12/0.39 % (27429)------------------------------
% 0.12/0.39 % (27429)------------------------------
% 0.12/0.39 % (27428)Memory used [KB]: 1407
% 0.12/0.39 % (27428)Time elapsed: 0.003 s
% 0.12/0.39 % (27428)Instructions burned: 2 (million)
% 0.12/0.39 % (27428)------------------------------
% 0.12/0.39 % (27428)------------------------------
% 0.12/0.39 % (27425)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.12/0.39 % (27432)Instruction limit reached!
% 0.12/0.39 % (27432)------------------------------
% 0.12/0.39 % (27432)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.39 % (27432)Termination reason: Unknown
% 0.12/0.39 % (27432)Termination phase: shuffling
% 0.12/0.39
% 0.12/0.39 % (27432)Memory used [KB]: 1407
% 0.12/0.39 % (27432)Time elapsed: 0.004 s
% 0.12/0.39 % (27432)Instructions burned: 4 (million)
% 0.12/0.39 % (27432)------------------------------
% 0.12/0.39 % (27432)------------------------------
% 0.20/0.40 % (27427)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.20/0.40 % (27431)Instruction limit reached!
% 0.20/0.40 % (27431)------------------------------
% 0.20/0.40 % (27431)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.40 % (27431)Termination reason: Unknown
% 0.20/0.40 % (27431)Termination phase: Property scanning
% 0.20/0.40
% 0.20/0.40 % (27431)Memory used [KB]: 1791
% 0.20/0.40 % (27431)Time elapsed: 0.011 s
% 0.20/0.40 % (27431)Instructions burned: 18 (million)
% 0.20/0.40 % (27431)------------------------------
% 0.20/0.40 % (27431)------------------------------
% 0.20/0.40 % (27426)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.20/0.41 % (27426)Instruction limit reached!
% 0.20/0.41 % (27426)------------------------------
% 0.20/0.41 % (27426)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.41 % (27426)Termination reason: Unknown
% 0.20/0.41 % (27426)Termination phase: shuffling
% 0.20/0.41
% 0.20/0.41 % (27426)Memory used [KB]: 1407
% 0.20/0.41 % (27426)Time elapsed: 0.004 s
% 0.20/0.41 % (27426)Instructions burned: 5 (million)
% 0.20/0.41 % (27426)------------------------------
% 0.20/0.41 % (27426)------------------------------
% 0.20/0.41 % (27434)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.20/0.41 % (27435)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.41 % (27433)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.20/0.41 % (27435)Instruction limit reached!
% 0.20/0.41 % (27435)------------------------------
% 0.20/0.41 % (27435)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.41 % (27435)Termination reason: Unknown
% 0.20/0.41 % (27435)Termination phase: shuffling
% 0.20/0.41
% 0.20/0.41 % (27435)Memory used [KB]: 1407
% 0.20/0.41 % (27435)Time elapsed: 0.003 s
% 0.20/0.41 % (27435)Instructions burned: 3 (million)
% 0.20/0.41 % (27435)------------------------------
% 0.20/0.41 % (27435)------------------------------
% 0.20/0.41 % (27427)Instruction limit reached!
% 0.20/0.41 % (27427)------------------------------
% 0.20/0.41 % (27427)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.41 % (27427)Termination reason: Unknown
% 0.20/0.41 % (27427)Termination phase: shuffling
% 0.20/0.41
% 0.20/0.41 % (27427)Memory used [KB]: 1918
% 0.20/0.41 % (27427)Time elapsed: 0.016 s
% 0.20/0.41 % (27427)Instructions burned: 27 (million)
% 0.20/0.41 % (27427)------------------------------
% 0.20/0.41 % (27427)------------------------------
% 0.20/0.41 % (27434)Instruction limit reached!
% 0.20/0.41 % (27434)------------------------------
% 0.20/0.41 % (27434)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.41 % (27434)Termination reason: Unknown
% 0.20/0.41 % (27434)Termination phase: shuffling
% 0.20/0.41
% 0.20/0.41 % (27434)Memory used [KB]: 1663
% 0.20/0.41 % (27434)Time elapsed: 0.009 s
% 0.20/0.41 % (27434)Instructions burned: 15 (million)
% 0.20/0.41 % (27434)------------------------------
% 0.20/0.41 % (27434)------------------------------
% 0.20/0.42 % (27437)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.42 % (27436)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.20/0.42 % (27438)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.20/0.42 % (27437)Instruction limit reached!
% 0.20/0.42 % (27437)------------------------------
% 0.20/0.42 % (27437)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.42 % (27437)Termination reason: Unknown
% 0.20/0.42 % (27437)Termination phase: shuffling
% 0.20/0.42
% 0.20/0.42 % (27437)Memory used [KB]: 1535
% 0.20/0.42 % (27437)Time elapsed: 0.005 s
% 0.20/0.42 % (27437)Instructions burned: 7 (million)
% 0.20/0.42 % (27437)------------------------------
% 0.20/0.42 % (27437)------------------------------
% 0.20/0.42 % (27433)Instruction limit reached!
% 0.20/0.42 % (27433)------------------------------
% 0.20/0.42 % (27433)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.42 % (27433)Termination reason: Unknown
% 0.20/0.42 % (27433)Termination phase: Property scanning
% 0.20/0.42
% 0.20/0.42 % (27433)Memory used [KB]: 2174
% 0.20/0.42 % (27433)Time elapsed: 0.018 s
% 0.20/0.42 % (27433)Instructions burned: 37 (million)
% 0.20/0.42 % (27433)------------------------------
% 0.20/0.42 % (27433)------------------------------
% 0.20/0.43 % (27439)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.43 % (27440)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.43 % (27440)Instruction limit reached!
% 0.20/0.43 % (27440)------------------------------
% 0.20/0.43 % (27440)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.43 % (27440)Termination reason: Unknown
% 0.20/0.43 % (27440)Termination phase: shuffling
% 0.20/0.43
% 0.20/0.43 % (27440)Memory used [KB]: 1407
% 0.20/0.43 % (27440)Time elapsed: 0.003 s
% 0.20/0.43 % (27440)Instructions burned: 3 (million)
% 0.20/0.43 % (27440)------------------------------
% 0.20/0.43 % (27440)------------------------------
% 0.20/0.43 % (27439)Instruction limit reached!
% 0.20/0.43 % (27439)------------------------------
% 0.20/0.43 % (27439)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.43 % (27439)Termination reason: Unknown
% 0.20/0.43 % (27439)Termination phase: shuffling
% 0.20/0.43
% 0.20/0.43 % (27439)Memory used [KB]: 1407
% 0.20/0.43 % (27439)Time elapsed: 0.004 s
% 0.20/0.43 % (27439)Instructions burned: 4 (million)
% 0.20/0.43 % (27439)------------------------------
% 0.20/0.43 % (27439)------------------------------
% 0.20/0.43 % (27438)Instruction limit reached!
% 0.20/0.43 % (27438)------------------------------
% 0.20/0.43 % (27438)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.43 % (27438)Termination reason: Unknown
% 0.20/0.43 % (27438)Termination phase: shuffling
% 0.20/0.43
% 0.20/0.43 % (27438)Memory used [KB]: 1663
% 0.20/0.43 % (27438)Time elapsed: 0.009 s
% 0.20/0.43 % (27438)Instructions burned: 16 (million)
% 0.20/0.43 % (27438)------------------------------
% 0.20/0.43 % (27438)------------------------------
% 0.20/0.44 % (27443)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.44 % (27443)Instruction limit reached!
% 0.20/0.44 % (27443)------------------------------
% 0.20/0.44 % (27443)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.44 % (27443)Termination reason: Unknown
% 0.20/0.44 % (27443)Termination phase: shuffling
% 0.20/0.44
% 0.20/0.44 % (27443)Memory used [KB]: 1407
% 0.20/0.44 % (27443)Time elapsed: 0.003 s
% 0.20/0.44 % (27443)Instructions burned: 3 (million)
% 0.20/0.44 % (27443)------------------------------
% 0.20/0.44 % (27443)------------------------------
% 0.20/0.44 % (27444)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.20/0.44 % (27442)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.44 % (27445)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.20/0.44 % (27444)Instruction limit reached!
% 0.20/0.44 % (27444)------------------------------
% 0.20/0.44 % (27444)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.44 % (27444)Termination reason: Unknown
% 0.20/0.44 % (27444)Termination phase: shuffling
% 0.20/0.44
% 0.20/0.44 % (27444)Memory used [KB]: 1407
% 0.20/0.44 % (27444)Time elapsed: 0.004 s
% 0.20/0.44 % (27444)Instructions burned: 5 (million)
% 0.20/0.44 % (27444)------------------------------
% 0.20/0.44 % (27444)------------------------------
% 0.20/0.44 % (27442)Instruction limit reached!
% 0.20/0.44 % (27442)------------------------------
% 0.20/0.44 % (27442)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.44 % (27442)Termination reason: Unknown
% 0.20/0.44 % (27442)Termination phase: shuffling
% 0.20/0.44
% 0.20/0.44 % (27442)Memory used [KB]: 1535
% 0.20/0.44 % (27442)Time elapsed: 0.005 s
% 0.20/0.44 % (27442)Instructions burned: 7 (million)
% 0.20/0.44 % (27442)------------------------------
% 0.20/0.44 % (27442)------------------------------
% 0.20/0.45 % (27446)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.20/0.45 % (27445)Instruction limit reached!
% 0.20/0.45 % (27445)------------------------------
% 0.20/0.45 % (27445)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.45 % (27445)Termination reason: Unknown
% 0.20/0.45 % (27445)Termination phase: shuffling
% 0.20/0.45
% 0.20/0.45 % (27445)Memory used [KB]: 1791
% 0.20/0.45 % (27445)Time elapsed: 0.011 s
% 0.20/0.45 % (27445)Instructions burned: 19 (million)
% 0.20/0.45 % (27445)------------------------------
% 0.20/0.45 % (27445)------------------------------
% 0.20/0.45 % (27447)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.20/0.45 % (27448)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on theBenchmark for (2999ds/902Mi)
% 0.20/0.46 % (27447)Instruction limit reached!
% 0.20/0.46 % (27447)------------------------------
% 0.20/0.46 % (27447)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.46 % (27447)Termination reason: Unknown
% 0.20/0.46 % (27447)Termination phase: shuffling
% 0.20/0.46
% 0.20/0.46 % (27447)Memory used [KB]: 1407
% 0.20/0.46 % (27447)Time elapsed: 0.005 s
% 0.20/0.46 % (27447)Instructions burned: 7 (million)
% 0.20/0.46 % (27447)------------------------------
% 0.20/0.46 % (27447)------------------------------
% 0.20/0.46 % (27449)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on theBenchmark for (2999ds/21Mi)
% 0.20/0.46 % (27450)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.20/0.46 % (27450)Instruction limit reached!
% 0.20/0.46 % (27450)------------------------------
% 0.20/0.46 % (27450)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.46 % (27450)Termination reason: Unknown
% 0.20/0.46 % (27450)Termination phase: shuffling
% 0.20/0.46
% 0.20/0.46 % (27450)Memory used [KB]: 1535
% 0.20/0.46 % (27450)Time elapsed: 0.004 s
% 0.20/0.46 % (27450)Instructions burned: 8 (million)
% 0.20/0.46 % (27450)------------------------------
% 0.20/0.46 % (27450)------------------------------
% 0.20/0.47 % (27449)Instruction limit reached!
% 0.20/0.47 % (27449)------------------------------
% 0.20/0.47 % (27449)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.47 % (27449)Termination reason: Unknown
% 0.20/0.47 % (27449)Termination phase: shuffling
% 0.20/0.47
% 0.20/0.47 % (27449)Memory used [KB]: 1791
% 0.20/0.47 % (27449)Time elapsed: 0.011 s
% 0.20/0.47 % (27449)Instructions burned: 21 (million)
% 0.20/0.47 % (27449)------------------------------
% 0.20/0.47 % (27449)------------------------------
% 0.20/0.47 % (27451)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.20/0.47 % (27452)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.20/0.47 % (27451)Instruction limit reached!
% 0.20/0.47 % (27451)------------------------------
% 0.20/0.47 % (27451)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.47 % (27451)Termination reason: Unknown
% 0.20/0.47 % (27451)Termination phase: shuffling
% 0.20/0.47
% 0.20/0.47 % (27451)Memory used [KB]: 1407
% 0.20/0.47 % (27451)Time elapsed: 0.005 s
% 0.20/0.47 % (27451)Instructions burned: 7 (million)
% 0.20/0.47 % (27451)------------------------------
% 0.20/0.47 % (27451)------------------------------
% 0.20/0.49 % (27425)Instruction limit reached!
% 0.20/0.49 % (27425)------------------------------
% 0.20/0.49 % (27425)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.49 % (27425)Termination reason: Unknown
% 0.20/0.49 % (27425)Termination phase: Saturation
% 0.20/0.49
% 0.20/0.49 % (27425)Memory used [KB]: 7547
% 0.20/0.49 % (27425)Time elapsed: 0.096 s
% 0.20/0.49 % (27425)Instructions burned: 183 (million)
% 0.20/0.49 % (27425)------------------------------
% 0.20/0.49 % (27425)------------------------------
% 0.20/0.49 % (27454)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on theBenchmark for (2999ds/19Mi)
% 0.20/0.49 % (27453)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on theBenchmark for (2999ds/779Mi)
% 0.20/0.50 % (27454)Instruction limit reached!
% 0.20/0.50 % (27454)------------------------------
% 0.20/0.50 % (27454)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.50 % (27454)Termination reason: Unknown
% 0.20/0.50 % (27454)Termination phase: shuffling
% 0.20/0.50
% 0.20/0.50 % (27454)Memory used [KB]: 1791
% 0.20/0.50 % (27454)Time elapsed: 0.010 s
% 0.20/0.50 % (27454)Instructions burned: 19 (million)
% 0.20/0.50 % (27454)------------------------------
% 0.20/0.50 % (27454)------------------------------
% 0.20/0.50 % (27455)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on theBenchmark for (2998ds/879Mi)
% 0.20/0.51 % (27456)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2998ds/17Mi)
% 0.20/0.52 % (27456)Instruction limit reached!
% 0.20/0.52 % (27456)------------------------------
% 0.20/0.52 % (27456)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.52 % (27456)Termination reason: Unknown
% 0.20/0.52 % (27456)Termination phase: shuffling
% 0.20/0.52
% 0.20/0.52 % (27456)Memory used [KB]: 1791
% 0.20/0.52 % (27456)Time elapsed: 0.010 s
% 0.20/0.52 % (27456)Instructions burned: 18 (million)
% 0.20/0.52 % (27456)------------------------------
% 0.20/0.52 % (27456)------------------------------
% 0.20/0.52 % (27430)Instruction limit reached!
% 0.20/0.52 % (27430)------------------------------
% 0.20/0.52 % (27430)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.52 % (27430)Termination reason: Unknown
% 0.20/0.52 % (27430)Termination phase: Saturation
% 0.20/0.52
% 0.20/0.52 % (27430)Memory used [KB]: 8955
% 0.20/0.52 % (27430)Time elapsed: 0.134 s
% 0.20/0.52 % (27430)Instructions burned: 276 (million)
% 0.20/0.52 % (27430)------------------------------
% 0.20/0.52 % (27430)------------------------------
% 0.20/0.54 % (27457)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.20/0.54 % (27457)Instruction limit reached!
% 0.20/0.54 % (27457)------------------------------
% 0.20/0.54 % (27457)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.54 % (27457)Termination reason: Unknown
% 0.20/0.54 % (27457)Termination phase: shuffling
% 0.20/0.54
% 0.20/0.54 % (27457)Memory used [KB]: 1407
% 0.20/0.54 % (27457)Time elapsed: 0.003 s
% 0.20/0.54 % (27457)Instructions burned: 3 (million)
% 0.20/0.54 % (27457)------------------------------
% 0.20/0.54 % (27457)------------------------------
% 0.20/0.54 % (27458)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on theBenchmark for (2998ds/30Mi)
% 0.20/0.55 % (27459)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on theBenchmark for (2998ds/127Mi)
% 0.20/0.55 % (27458)Instruction limit reached!
% 0.20/0.55 % (27458)------------------------------
% 0.20/0.55 % (27458)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.55 % (27458)Termination reason: Unknown
% 0.20/0.55 % (27458)Termination phase: shuffling
% 0.20/0.55
% 0.20/0.55 % (27458)Memory used [KB]: 2046
% 0.20/0.55 % (27458)Time elapsed: 0.016 s
% 0.20/0.55 % (27458)Instructions burned: 32 (million)
% 0.20/0.55 % (27458)------------------------------
% 0.20/0.55 % (27458)------------------------------
% 0.20/0.57 % (27460)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on theBenchmark for (2998ds/100Mi)
% 1.77/0.59 % (27459)Instruction limit reached!
% 1.77/0.59 % (27459)------------------------------
% 1.77/0.59 % (27459)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.77/0.59 % (27459)Termination reason: Unknown
% 1.77/0.59 % (27459)Termination phase: Saturation
% 1.77/0.59
% 1.77/0.59 % (27459)Memory used [KB]: 7036
% 1.77/0.59 % (27459)Time elapsed: 0.045 s
% 1.77/0.59 % (27459)Instructions burned: 127 (million)
% 1.77/0.59 % (27459)------------------------------
% 1.77/0.59 % (27459)------------------------------
% 1.77/0.61 % (27461)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on theBenchmark for (2997ds/3Mi)
% 1.77/0.61 % (27460)Instruction limit reached!
% 1.77/0.61 % (27460)------------------------------
% 1.77/0.61 % (27460)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.77/0.61 % (27460)Termination reason: Unknown
% 1.77/0.61 % (27460)Termination phase: Saturation
% 1.77/0.61
% 1.77/0.61 % (27460)Memory used [KB]: 6780
% 1.77/0.61 % (27460)Time elapsed: 0.045 s
% 1.77/0.61 % (27460)Instructions burned: 101 (million)
% 1.77/0.61 % (27460)------------------------------
% 1.77/0.61 % (27460)------------------------------
% 1.90/0.61 % (27461)Instruction limit reached!
% 1.90/0.61 % (27461)------------------------------
% 1.90/0.61 % (27461)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.90/0.61 % (27461)Termination reason: Unknown
% 1.90/0.61 % (27461)Termination phase: shuffling
% 1.90/0.61
% 1.90/0.61 % (27461)Memory used [KB]: 1407
% 1.90/0.61 % (27461)Time elapsed: 0.003 s
% 1.90/0.61 % (27461)Instructions burned: 4 (million)
% 1.90/0.61 % (27461)------------------------------
% 1.90/0.61 % (27461)------------------------------
% 1.90/0.62 % (27463)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on theBenchmark for (2997ds/86Mi)
% 1.90/0.63 % (27462)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on theBenchmark for (2997ds/20Mi)
% 2.02/0.63 % (27462)Instruction limit reached!
% 2.02/0.63 % (27462)------------------------------
% 2.02/0.63 % (27462)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.02/0.63 % (27462)Termination reason: Unknown
% 2.02/0.63 % (27462)Termination phase: Property scanning
% 2.02/0.63
% 2.02/0.63 % (27462)Memory used [KB]: 1791
% 2.02/0.63 % (27462)Time elapsed: 0.011 s
% 2.02/0.63 % (27462)Instructions burned: 21 (million)
% 2.02/0.63 % (27462)------------------------------
% 2.02/0.63 % (27462)------------------------------
% 2.02/0.64 % (27464)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on theBenchmark for (2997ds/107Mi)
% 2.02/0.65 % (27452)Instruction limit reached!
% 2.02/0.65 % (27452)------------------------------
% 2.02/0.65 % (27452)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.02/0.65 % (27452)Termination reason: Unknown
% 2.02/0.65 % (27452)Termination phase: Saturation
% 2.02/0.65
% 2.02/0.65 % (27452)Memory used [KB]: 8571
% 2.02/0.65 % (27452)Time elapsed: 0.164 s
% 2.02/0.65 % (27452)Instructions burned: 378 (million)
% 2.02/0.65 % (27452)------------------------------
% 2.02/0.65 % (27452)------------------------------
% 2.02/0.66 % (27463)Instruction limit reached!
% 2.02/0.66 % (27463)------------------------------
% 2.02/0.66 % (27463)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.02/0.66 % (27463)Termination reason: Unknown
% 2.02/0.66 % (27463)Termination phase: Property scanning
% 2.02/0.66
% 2.02/0.66 % (27463)Memory used [KB]: 2302
% 2.02/0.66 % (27463)Time elapsed: 0.039 s
% 2.02/0.66 % (27463)Instructions burned: 88 (million)
% 2.02/0.66 % (27463)------------------------------
% 2.02/0.66 % (27463)------------------------------
% 2.02/0.67 % (27464)Instruction limit reached!
% 2.02/0.67 % (27464)------------------------------
% 2.02/0.67 % (27464)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.02/0.67 % (27464)Termination reason: Unknown
% 2.02/0.67 % (27464)Termination phase: Property scanning
% 2.02/0.67
% 2.02/0.67 % (27464)Memory used [KB]: 2302
% 2.02/0.67 % (27464)Time elapsed: 0.028 s
% 2.02/0.67 % (27464)Instructions burned: 109 (million)
% 2.02/0.67 % (27464)------------------------------
% 2.02/0.67 % (27464)------------------------------
% 2.02/0.67 % (27465)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on theBenchmark for (2997ds/39Mi)
% 2.02/0.68 % (27467)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on theBenchmark for (2996ds/46Mi)
% 2.02/0.68 % (27466)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on theBenchmark for (2997ds/448Mi)
% 2.02/0.68 % (27465)Instruction limit reached!
% 2.02/0.68 % (27465)------------------------------
% 2.02/0.68 % (27465)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.02/0.68 % (27465)Termination reason: Unknown
% 2.02/0.68 % (27465)Termination phase: Property scanning
% 2.02/0.68
% 2.02/0.68 % (27465)Memory used [KB]: 2174
% 2.02/0.68 % (27465)Time elapsed: 0.012 s
% 2.02/0.68 % (27465)Instructions burned: 41 (million)
% 2.02/0.68 % (27465)------------------------------
% 2.02/0.68 % (27465)------------------------------
% 2.02/0.69 % (27468)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on theBenchmark for (2996ds/98Mi)
% 2.02/0.69 % (27467)Instruction limit reached!
% 2.02/0.69 % (27467)------------------------------
% 2.02/0.69 % (27467)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.02/0.69 % (27467)Termination reason: Unknown
% 2.02/0.69 % (27467)Termination phase: Property scanning
% 2.02/0.69
% 2.02/0.69 % (27467)Memory used [KB]: 2046
% 2.02/0.69 % (27467)Time elapsed: 0.014 s
% 2.02/0.69 % (27467)Instructions burned: 49 (million)
% 2.02/0.69 % (27467)------------------------------
% 2.02/0.69 % (27467)------------------------------
% 2.02/0.70 % (27469)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on theBenchmark for (2996ds/507Mi)
% 2.02/0.71 % (27468)Instruction limit reached!
% 2.02/0.71 % (27468)------------------------------
% 2.02/0.71 % (27468)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.02/0.71 % (27468)Termination reason: Unknown
% 2.02/0.71 % (27468)Termination phase: Property scanning
% 2.02/0.71
% 2.02/0.71 % (27468)Memory used [KB]: 2302
% 2.02/0.71 % (27468)Time elapsed: 0.025 s
% 2.02/0.71 % (27468)Instructions burned: 99 (million)
% 2.02/0.71 % (27468)------------------------------
% 2.02/0.71 % (27468)------------------------------
% 2.67/0.72 % (27453)Instruction limit reached!
% 2.67/0.72 % (27453)------------------------------
% 2.67/0.72 % (27453)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.67/0.72 % (27453)Termination reason: Unknown
% 2.67/0.72 % (27453)Termination phase: Saturation
% 2.67/0.72
% 2.67/0.72 % (27453)Memory used [KB]: 7164
% 2.67/0.72 % (27453)Time elapsed: 0.230 s
% 2.67/0.72 % (27453)Instructions burned: 780 (million)
% 2.67/0.72 % (27453)------------------------------
% 2.67/0.72 % (27453)------------------------------
% 2.67/0.72 % (27446)Instruction limit reached!
% 2.67/0.72 % (27446)------------------------------
% 2.67/0.72 % (27446)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.67/0.72 % (27446)Termination reason: Unknown
% 2.67/0.72 % (27446)Termination phase: Saturation
% 2.67/0.72
% 2.67/0.72 % (27446)Memory used [KB]: 9850
% 2.67/0.72 % (27446)Time elapsed: 0.275 s
% 2.67/0.72 % (27446)Instructions burned: 711 (million)
% 2.67/0.72 % (27446)------------------------------
% 2.67/0.72 % (27446)------------------------------
% 2.67/0.72 % (27470)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on theBenchmark for (2996ds/149Mi)
% 2.67/0.73 % (27471)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on theBenchmark for (2996ds/39Mi)
% 2.67/0.74 % (27472)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on theBenchmark for (2996ds/6Mi)
% 2.67/0.74 % (27472)Instruction limit reached!
% 2.67/0.74 % (27472)------------------------------
% 2.67/0.74 % (27472)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.67/0.74 % (27472)Termination reason: Unknown
% 2.67/0.74 % (27472)Termination phase: shuffling
% 2.67/0.74
% 2.67/0.74 % (27472)Memory used [KB]: 1407
% 2.67/0.74 % (27472)Time elapsed: 0.005 s
% 2.67/0.74 % (27472)Instructions burned: 7 (million)
% 2.67/0.74 % (27472)------------------------------
% 2.67/0.74 % (27472)------------------------------
% 2.67/0.74 % (27436)First to succeed.
% 2.67/0.75 % (27471)Instruction limit reached!
% 2.67/0.75 % (27471)------------------------------
% 2.67/0.75 % (27471)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.67/0.75 % (27473)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on theBenchmark for (2996ds/1087Mi)
% 2.67/0.75 % (27471)Termination reason: Unknown
% 2.67/0.75 % (27471)Termination phase: Property scanning
% 2.67/0.75
% 2.67/0.75 % (27471)Memory used [KB]: 2046
% 2.67/0.75 % (27471)Time elapsed: 0.021 s
% 2.67/0.75 % (27471)Instructions burned: 40 (million)
% 2.67/0.75 % (27471)------------------------------
% 2.67/0.75 % (27471)------------------------------
% 2.67/0.77 % (27470)Instruction limit reached!
% 2.67/0.77 % (27470)------------------------------
% 2.67/0.77 % (27470)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.67/0.77 % (27470)Termination reason: Unknown
% 2.67/0.77 % (27470)Termination phase: Saturation
% 2.67/0.77
% 2.67/0.77 % (27470)Memory used [KB]: 7419
% 2.67/0.77 % (27470)Time elapsed: 0.048 s
% 2.67/0.77 % (27470)Instructions burned: 151 (million)
% 2.67/0.77 % (27470)------------------------------
% 2.67/0.77 % (27470)------------------------------
% 2.67/0.77 % (27474)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on theBenchmark for (2996ds/47Mi)
% 2.67/0.77 % (27475)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on theBenchmark for (2995ds/44Mi)
% 2.98/0.79 % (27474)Instruction limit reached!
% 2.98/0.79 % (27474)------------------------------
% 2.98/0.79 % (27474)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.98/0.79 % (27474)Termination reason: Unknown
% 2.98/0.79 % (27474)Termination phase: Property scanning
% 2.98/0.79
% 2.98/0.79 % (27474)Memory used [KB]: 2046
% 2.98/0.79 % (27474)Time elapsed: 0.024 s
% 2.98/0.79 % (27474)Instructions burned: 47 (million)
% 2.98/0.79 % (27474)------------------------------
% 2.98/0.79 % (27474)------------------------------
% 2.98/0.79 % (27475)Instruction limit reached!
% 2.98/0.79 % (27475)------------------------------
% 2.98/0.79 % (27475)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.98/0.79 % (27475)Termination reason: Unknown
% 2.98/0.79 % (27475)Termination phase: Property scanning
% 2.98/0.79
% 2.98/0.79 % (27475)Memory used [KB]: 2174
% 2.98/0.79 % (27475)Time elapsed: 0.018 s
% 2.98/0.79 % (27475)Instructions burned: 45 (million)
% 2.98/0.79 % (27475)------------------------------
% 2.98/0.79 % (27475)------------------------------
% 2.98/0.80 % (27466)Instruction limit reached!
% 2.98/0.80 % (27466)------------------------------
% 2.98/0.80 % (27466)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.98/0.80 % (27466)Termination reason: Unknown
% 2.98/0.80 % (27466)Termination phase: Saturation
% 2.98/0.80
% 2.98/0.80 % (27466)Memory used [KB]: 7164
% 2.98/0.80 % (27466)Time elapsed: 0.120 s
% 2.98/0.80 % (27466)Instructions burned: 451 (million)
% 2.98/0.80 % (27466)------------------------------
% 2.98/0.80 % (27466)------------------------------
% 2.98/0.80 % (27477)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on theBenchmark for (2995ds/62Mi)
% 2.98/0.80 % (27478)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on theBenchmark for (2995ds/31Mi)
% 2.98/0.81 % (27476)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on theBenchmark for (2995ds/432Mi)
% 2.98/0.81 % (27478)Instruction limit reached!
% 2.98/0.81 % (27478)------------------------------
% 2.98/0.81 % (27478)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.98/0.81 % (27478)Termination reason: Unknown
% 2.98/0.81 % (27478)Termination phase: shuffling
% 2.98/0.81
% 2.98/0.81 % (27478)Memory used [KB]: 1918
% 2.98/0.81 % (27478)Time elapsed: 0.010 s
% 2.98/0.81 % (27478)Instructions burned: 31 (million)
% 2.98/0.81 % (27478)------------------------------
% 2.98/0.81 % (27478)------------------------------
% 2.98/0.82 % (27479)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on theBenchmark for (2995ds/96Mi)
% 2.98/0.83 % (27477)Instruction limit reached!
% 2.98/0.83 % (27477)------------------------------
% 2.98/0.83 % (27477)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.98/0.83 % (27477)Termination reason: Unknown
% 2.98/0.83 % (27477)Termination phase: Property scanning
% 2.98/0.83
% 2.98/0.83 % (27477)Memory used [KB]: 2174
% 2.98/0.83 % (27477)Time elapsed: 0.029 s
% 2.98/0.83 % (27477)Instructions burned: 64 (million)
% 2.98/0.83 % (27477)------------------------------
% 2.98/0.83 % (27477)------------------------------
% 2.98/0.85 % (27479)Instruction limit reached!
% 2.98/0.85 % (27479)------------------------------
% 2.98/0.85 % (27479)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.98/0.85 % (27479)Termination reason: Unknown
% 2.98/0.85 % (27479)Termination phase: Property scanning
% 2.98/0.85
% 2.98/0.85 % (27479)Memory used [KB]: 2302
% 2.98/0.85 % (27479)Time elapsed: 0.026 s
% 2.98/0.85 % (27479)Instructions burned: 99 (million)
% 2.98/0.85 % (27479)------------------------------
% 2.98/0.85 % (27479)------------------------------
% 2.98/0.85 % (27480)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on theBenchmark for (2995ds/453Mi)
% 2.98/0.85 % (27448)Instruction limit reached!
% 2.98/0.85 % (27448)------------------------------
% 2.98/0.85 % (27448)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.98/0.85 % (27448)Termination reason: Unknown
% 2.98/0.85 % (27448)Termination phase: Saturation
% 2.98/0.85
% 2.98/0.85 % (27448)Memory used [KB]: 10490
% 2.98/0.85 % (27448)Time elapsed: 0.392 s
% 2.98/0.85 % (27448)Instructions burned: 902 (million)
% 2.98/0.85 % (27448)------------------------------
% 2.98/0.85 % (27448)------------------------------
% 2.98/0.85 % (27481)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on theBenchmark for (2995ds/71Mi)
% 3.53/0.87 % (27482)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on theBenchmark for (2995ds/83Mi)
% 3.53/0.87 % (27481)Instruction limit reached!
% 3.53/0.87 % (27481)------------------------------
% 3.53/0.87 % (27481)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.53/0.87 % (27481)Termination reason: Unknown
% 3.53/0.87 % (27481)Termination phase: Function definition elimination
% 3.53/0.87
% 3.53/0.87 % (27481)Memory used [KB]: 2174
% 3.53/0.87 % (27481)Time elapsed: 0.020 s
% 3.53/0.87 % (27481)Instructions burned: 74 (million)
% 3.53/0.87 % (27481)------------------------------
% 3.53/0.87 % (27481)------------------------------
% 3.58/0.88 % (27483)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on theBenchmark for (2994ds/11Mi)
% 3.58/0.89 % (27483)Instruction limit reached!
% 3.58/0.89 % (27483)------------------------------
% 3.58/0.89 % (27483)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.58/0.89 % (27483)Termination reason: Unknown
% 3.58/0.89 % (27483)Termination phase: shuffling
% 3.58/0.89
% 3.58/0.89 % (27483)Memory used [KB]: 1535
% 3.58/0.89 % (27483)Time elapsed: 0.006 s
% 3.58/0.89 % (27483)Instructions burned: 11 (million)
% 3.58/0.89 % (27483)------------------------------
% 3.58/0.89 % (27483)------------------------------
% 3.58/0.90 % (27455)Instruction limit reached!
% 3.58/0.90 % (27455)------------------------------
% 3.58/0.90 % (27455)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.58/0.90 % (27455)Termination reason: Unknown
% 3.58/0.90 % (27455)Termination phase: Saturation
% 3.58/0.90
% 3.58/0.90 % (27455)Memory used [KB]: 8827
% 3.58/0.90 % (27455)Time elapsed: 0.399 s
% 3.58/0.90 % (27455)Instructions burned: 882 (million)
% 3.58/0.90 % (27455)------------------------------
% 3.58/0.90 % (27455)------------------------------
% 3.58/0.90 % (27482)Instruction limit reached!
% 3.58/0.90 % (27482)------------------------------
% 3.58/0.90 % (27482)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.58/0.90 % (27482)Termination reason: Unknown
% 3.58/0.90 % (27482)Termination phase: Property scanning
% 3.58/0.90
% 3.58/0.90 % (27482)Memory used [KB]: 2046
% 3.58/0.90 % (27482)Time elapsed: 0.036 s
% 3.58/0.90 % (27482)Instructions burned: 83 (million)
% 3.58/0.90 % (27482)------------------------------
% 3.58/0.90 % (27482)------------------------------
% 3.58/0.91 % (27485)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2994ds/6Mi)
% 3.58/0.91 % (27484)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on theBenchmark for (2994ds/41Mi)
% 3.58/0.91 % (27469)Instruction limit reached!
% 3.58/0.91 % (27469)------------------------------
% 3.58/0.91 % (27469)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.58/0.91 % (27469)Termination reason: Unknown
% 3.58/0.91 % (27469)Termination phase: Saturation
% 3.58/0.91
% 3.58/0.91 % (27469)Memory used [KB]: 7803
% 3.58/0.91 % (27469)Time elapsed: 0.212 s
% 3.58/0.91 % (27469)Instructions burned: 510 (million)
% 3.58/0.91 % (27469)------------------------------
% 3.58/0.91 % (27469)------------------------------
% 3.70/0.91 % (27485)Instruction limit reached!
% 3.70/0.91 % (27485)------------------------------
% 3.70/0.91 % (27485)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.70/0.91 % (27485)Termination reason: Unknown
% 3.70/0.91 % (27485)Termination phase: shuffling
% 3.70/0.91
% 3.70/0.91 % (27485)Memory used [KB]: 1535
% 3.70/0.91 % (27485)Time elapsed: 0.004 s
% 3.70/0.91 % (27485)Instructions burned: 9 (million)
% 3.70/0.91 % (27485)------------------------------
% 3.70/0.91 % (27485)------------------------------
% 3.70/0.92 % (27487)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on theBenchmark for (2994ds/343Mi)
% 3.70/0.92 % (27486)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on theBenchmark for (2994ds/150Mi)
% 3.70/0.93 % (27484)Instruction limit reached!
% 3.70/0.93 % (27484)------------------------------
% 3.70/0.93 % (27484)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.70/0.93 % (27484)Termination reason: Unknown
% 3.70/0.93 % (27484)Termination phase: Property scanning
% 3.70/0.93
% 3.70/0.93 % (27484)Memory used [KB]: 2174
% 3.70/0.93 % (27484)Time elapsed: 0.020 s
% 3.70/0.93 % (27484)Instructions burned: 41 (million)
% 3.70/0.93 % (27484)------------------------------
% 3.70/0.93 % (27484)------------------------------
% 3.70/0.93 % (27488)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on theBenchmark for (2994ds/109Mi)
% 3.98/0.94 % (27489)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on theBenchmark for (2994ds/253Mi)
% 3.98/0.96 % (27486)Instruction limit reached!
% 3.98/0.96 % (27486)------------------------------
% 3.98/0.96 % (27486)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.98/0.96 % (27486)Termination reason: Unknown
% 3.98/0.96 % (27486)Termination phase: Saturation
% 3.98/0.96
% 3.98/0.96 % (27486)Memory used [KB]: 8315
% 3.98/0.96 % (27486)Time elapsed: 0.043 s
% 3.98/0.96 % (27486)Instructions burned: 151 (million)
% 3.98/0.96 % (27486)------------------------------
% 3.98/0.96 % (27486)------------------------------
% 3.98/0.97 % (27490)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on theBenchmark for (2994ds/140Mi)
% 3.98/0.97 % (27476)Instruction limit reached!
% 3.98/0.97 % (27476)------------------------------
% 3.98/0.97 % (27476)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.98/0.97 % (27476)Termination reason: Unknown
% 3.98/0.97 % (27476)Termination phase: Saturation
% 3.98/0.97
% 3.98/0.97 % (27476)Memory used [KB]: 3198
% 3.98/0.97 % (27476)Time elapsed: 0.165 s
% 3.98/0.97 % (27476)Instructions burned: 433 (million)
% 3.98/0.97 % (27476)------------------------------
% 3.98/0.97 % (27476)------------------------------
% 3.98/0.97 % (27488)Instruction limit reached!
% 3.98/0.97 % (27488)------------------------------
% 3.98/0.97 % (27488)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.98/0.97 % (27488)Termination reason: Unknown
% 3.98/0.97 % (27488)Termination phase: Property scanning
% 3.98/0.97
% 3.98/0.97 % (27488)Memory used [KB]: 2302
% 3.98/0.97 % (27488)Time elapsed: 0.047 s
% 3.98/0.97 % (27488)Instructions burned: 109 (million)
% 3.98/0.97 % (27488)------------------------------
% 3.98/0.97 % (27488)------------------------------
% 3.98/0.99 % (27491)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on theBenchmark for (2994ds/614Mi)
% 3.98/0.99 % (27492)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on theBenchmark for (2994ds/202Mi)
% 3.98/1.01 % (27490)Instruction limit reached!
% 3.98/1.01 % (27490)------------------------------
% 3.98/1.01 % (27490)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.98/1.01 % (27490)Termination reason: Unknown
% 3.98/1.01 % (27490)Termination phase: Saturation
% 3.98/1.01
% 3.98/1.01 % (27490)Memory used [KB]: 6908
% 3.98/1.01 % (27490)Time elapsed: 0.038 s
% 3.98/1.01 % (27490)Instructions burned: 143 (million)
% 3.98/1.01 % (27490)------------------------------
% 3.98/1.01 % (27490)------------------------------
% 3.98/1.01 % (27480)Instruction limit reached!
% 3.98/1.01 % (27480)------------------------------
% 3.98/1.01 % (27480)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.98/1.01 % (27480)Termination reason: Unknown
% 3.98/1.01 % (27480)Termination phase: Saturation
% 3.98/1.01
% 3.98/1.01 % (27480)Memory used [KB]: 7164
% 3.98/1.01 % (27480)Time elapsed: 0.165 s
% 3.98/1.01 % (27480)Instructions burned: 453 (million)
% 3.98/1.01 % (27480)------------------------------
% 3.98/1.01 % (27480)------------------------------
% 3.98/1.01 % (27493)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on theBenchmark for (2993ds/339Mi)
% 4.57/1.02 % (27494)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on theBenchmark for (2993ds/283Mi)
% 4.57/1.02 % (27487)Instruction limit reached!
% 4.57/1.02 % (27487)------------------------------
% 4.57/1.02 % (27487)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.57/1.02 % (27487)Termination reason: Unknown
% 4.57/1.02 % (27487)Termination phase: Saturation
% 4.57/1.02
% 4.57/1.02 % (27487)Memory used [KB]: 8315
% 4.57/1.02 % (27487)Time elapsed: 0.096 s
% 4.57/1.02 % (27487)Instructions burned: 345 (million)
% 4.57/1.02 % (27487)------------------------------
% 4.57/1.02 % (27487)------------------------------
% 4.57/1.03 % (27495)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on theBenchmark for (2993ds/134Mi)
% 4.57/1.07 % (27489)Instruction limit reached!
% 4.57/1.07 % (27489)------------------------------
% 4.57/1.07 % (27489)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.57/1.07 % (27489)Termination reason: Unknown
% 4.57/1.07 % (27489)Termination phase: Saturation
% 4.57/1.07
% 4.57/1.07 % (27489)Memory used [KB]: 8699
% 4.57/1.07 % (27489)Time elapsed: 0.125 s
% 4.57/1.07 % (27489)Instructions burned: 253 (million)
% 4.57/1.07 % (27489)------------------------------
% 4.57/1.07 % (27489)------------------------------
% 4.57/1.07 % (27495)Instruction limit reached!
% 4.57/1.07 % (27495)------------------------------
% 4.57/1.07 % (27495)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.57/1.07 % (27495)Termination reason: Unknown
% 4.57/1.07 % (27495)Termination phase: Saturation
% 4.57/1.07
% 4.57/1.07 % (27495)Memory used [KB]: 7036
% 4.57/1.07 % (27495)Time elapsed: 0.036 s
% 4.57/1.07 % (27495)Instructions burned: 134 (million)
% 4.57/1.07 % (27495)------------------------------
% 4.57/1.07 % (27495)------------------------------
% 4.57/1.08 % (27496)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on theBenchmark for (2993ds/298Mi)
% 4.92/1.09 % (27497)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on theBenchmark for (2993ds/192Mi)
% 4.92/1.10 % (27494)Instruction limit reached!
% 4.92/1.10 % (27494)------------------------------
% 4.92/1.10 % (27494)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.92/1.10 % (27494)Termination reason: Unknown
% 4.92/1.10 % (27494)Termination phase: Saturation
% 4.92/1.10
% 4.92/1.10 % (27494)Memory used [KB]: 7164
% 4.92/1.10 % (27494)Time elapsed: 0.076 s
% 4.92/1.10 % (27494)Instructions burned: 284 (million)
% 4.92/1.10 % (27494)------------------------------
% 4.92/1.10 % (27494)------------------------------
% 4.92/1.10 % (27492)Instruction limit reached!
% 4.92/1.10 % (27492)------------------------------
% 4.92/1.10 % (27492)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.92/1.10 % (27492)Termination reason: Unknown
% 4.92/1.10 % (27492)Termination phase: Saturation
% 4.92/1.10
% 4.92/1.10 % (27492)Memory used [KB]: 9466
% 4.92/1.10 % (27492)Time elapsed: 0.098 s
% 4.92/1.10 % (27492)Instructions burned: 202 (million)
% 4.92/1.10 % (27492)------------------------------
% 4.92/1.10 % (27492)------------------------------
% 4.92/1.11 % (27498)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on theBenchmark for (2992ds/258Mi)
% 4.92/1.12 % (27499)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on theBenchmark for (2992ds/90Mi)
% 4.92/1.16 % (27499)Instruction limit reached!
% 4.92/1.16 % (27499)------------------------------
% 4.92/1.16 % (27499)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.92/1.16 % (27499)Termination reason: Unknown
% 4.92/1.16 % (27499)Termination phase: Twee Goal Transformation
% 4.92/1.16
% 4.92/1.16 % (27499)Memory used [KB]: 2686
% 4.92/1.16 % (27499)Time elapsed: 0.041 s
% 4.92/1.16 % (27499)Instructions burned: 91 (million)
% 4.92/1.16 % (27499)------------------------------
% 4.92/1.16 % (27499)------------------------------
% 4.92/1.17 % (27493)Instruction limit reached!
% 4.92/1.17 % (27493)------------------------------
% 4.92/1.17 % (27493)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.92/1.17 % (27493)Termination reason: Unknown
% 4.92/1.17 % (27493)Termination phase: Saturation
% 4.92/1.17
% 4.92/1.17 % (27493)Memory used [KB]: 8315
% 4.92/1.17 % (27493)Time elapsed: 0.153 s
% 4.92/1.17 % (27493)Instructions burned: 339 (million)
% 4.92/1.17 % (27493)------------------------------
% 4.92/1.17 % (27493)------------------------------
% 4.92/1.17 % (27497)Instruction limit reached!
% 4.92/1.17 % (27497)------------------------------
% 4.92/1.17 % (27497)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.92/1.17 % (27497)Termination reason: Unknown
% 4.92/1.17 % (27497)Termination phase: Saturation
% 4.92/1.17
% 4.92/1.17 % (27497)Memory used [KB]: 7547
% 4.92/1.17 % (27497)Time elapsed: 0.085 s
% 4.92/1.17 % (27497)Instructions burned: 193 (million)
% 4.92/1.17 % (27497)------------------------------
% 4.92/1.17 % (27497)------------------------------
% 6.28/1.18 % (27500)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on theBenchmark for (2992ds/231Mi)
% 6.28/1.18 % (27498)Instruction limit reached!
% 6.28/1.18 % (27498)------------------------------
% 6.28/1.18 % (27498)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.28/1.18 % (27498)Termination reason: Unknown
% 6.28/1.18 % (27498)Termination phase: Saturation
% 6.28/1.18
% 6.28/1.18 % (27498)Memory used [KB]: 7931
% 6.28/1.18 % (27498)Time elapsed: 0.072 s
% 6.28/1.18 % (27498)Instructions burned: 258 (million)
% 6.28/1.18 % (27498)------------------------------
% 6.28/1.18 % (27498)------------------------------
% 6.28/1.18 % (27501)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on theBenchmark for (2992ds/458Mi)
% 6.28/1.18 % (27496)Instruction limit reached!
% 6.28/1.18 % (27496)------------------------------
% 6.28/1.18 % (27496)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.28/1.18 % (27496)Termination reason: Unknown
% 6.28/1.18 % (27496)Termination phase: Saturation
% 6.28/1.18
% 6.28/1.18 % (27496)Memory used [KB]: 7291
% 6.28/1.18 % (27496)Time elapsed: 0.110 s
% 6.28/1.18 % (27496)Instructions burned: 300 (million)
% 6.28/1.18 % (27496)------------------------------
% 6.28/1.18 % (27496)------------------------------
% 6.28/1.19 % (27502)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on theBenchmark for (2992ds/31Mi)
% 6.38/1.19 % (27503)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on theBenchmark for (2992ds/297Mi)
% 6.38/1.20 % (27504)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on theBenchmark for (2991ds/987Mi)
% 6.38/1.20 % (27502)Instruction limit reached!
% 6.38/1.20 % (27502)------------------------------
% 6.38/1.20 % (27502)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.38/1.20 % (27502)Termination reason: Unknown
% 6.38/1.20 % (27502)Termination phase: shuffling
% 6.38/1.20
% 6.38/1.20 % (27502)Memory used [KB]: 1918
% 6.38/1.20 % (27502)Time elapsed: 0.016 s
% 6.38/1.20 % (27502)Instructions burned: 31 (million)
% 6.38/1.20 % (27502)------------------------------
% 6.38/1.20 % (27502)------------------------------
% 6.38/1.22 % (27491)Instruction limit reached!
% 6.38/1.22 % (27491)------------------------------
% 6.38/1.22 % (27491)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.38/1.22 % (27491)Termination reason: Unknown
% 6.38/1.22 % (27491)Termination phase: Saturation
% 6.38/1.22
% 6.38/1.22 % (27491)Memory used [KB]: 8955
% 6.38/1.22 % (27491)Time elapsed: 0.240 s
% 6.38/1.22 % (27491)Instructions burned: 615 (million)
% 6.38/1.22 % (27491)------------------------------
% 6.38/1.22 % (27491)------------------------------
% 6.53/1.22 % (27505)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on theBenchmark for (2991ds/182Mi)
% 6.53/1.23 % (27506)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on theBenchmark for (2991ds/182Mi)
% 6.56/1.27 % (27500)Instruction limit reached!
% 6.56/1.27 % (27500)------------------------------
% 6.56/1.27 % (27500)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.56/1.27 % (27500)Termination reason: Unknown
% 6.56/1.27 % (27500)Termination phase: Saturation
% 6.56/1.27
% 6.56/1.27 % (27500)Memory used [KB]: 12281
% 6.56/1.27 % (27500)Time elapsed: 0.115 s
% 6.56/1.27 % (27500)Instructions burned: 232 (million)
% 6.56/1.27 % (27500)------------------------------
% 6.56/1.27 % (27500)------------------------------
% 6.56/1.27 % (27505)Instruction limit reached!
% 6.56/1.27 % (27505)------------------------------
% 6.56/1.27 % (27505)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.56/1.27 % (27505)Termination reason: Unknown
% 6.56/1.27 % (27505)Termination phase: Saturation
% 6.56/1.27
% 6.56/1.27 % (27505)Memory used [KB]: 7547
% 6.56/1.27 % (27505)Time elapsed: 0.048 s
% 6.56/1.27 % (27505)Instructions burned: 184 (million)
% 6.56/1.27 % (27505)------------------------------
% 6.56/1.27 % (27505)------------------------------
% 6.56/1.28 % (27473)Instruction limit reached!
% 6.56/1.28 % (27473)------------------------------
% 6.56/1.28 % (27473)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.56/1.28 % (27473)Termination reason: Unknown
% 6.56/1.28 % (27473)Termination phase: Saturation
% 6.56/1.28
% 6.56/1.28 % (27473)Memory used [KB]: 11513
% 6.56/1.28 % (27473)Time elapsed: 0.527 s
% 6.56/1.28 % (27473)Instructions burned: 1087 (million)
% 6.56/1.28 % (27473)------------------------------
% 6.56/1.28 % (27473)------------------------------
% 6.56/1.28 % (27508)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on theBenchmark for (2990ds/79Mi)
% 6.56/1.28 % (27507)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on theBenchmark for (2990ds/154Mi)
% 6.56/1.28 % (27506)Instruction limit reached!
% 6.56/1.28 % (27506)------------------------------
% 6.56/1.28 % (27506)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.56/1.28 % (27506)Termination reason: Unknown
% 6.56/1.28 % (27506)Termination phase: Saturation
% 6.56/1.28
% 6.56/1.28 % (27506)Memory used [KB]: 10490
% 6.56/1.28 % (27506)Time elapsed: 0.060 s
% 6.56/1.28 % (27506)Instructions burned: 183 (million)
% 6.56/1.28 % (27506)------------------------------
% 6.56/1.28 % (27506)------------------------------
% 6.56/1.29 % (27509)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on theBenchmark for (2990ds/216Mi)
% 6.56/1.30 % (27508)Instruction limit reached!
% 6.56/1.30 % (27508)------------------------------
% 6.56/1.30 % (27508)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.56/1.30 % (27508)Termination reason: Unknown
% 6.56/1.30 % (27508)Termination phase: Property scanning
% 6.56/1.30
% 6.56/1.30 % (27508)Memory used [KB]: 2302
% 6.56/1.30 % (27508)Time elapsed: 0.022 s
% 6.56/1.30 % (27508)Instructions burned: 80 (million)
% 6.56/1.30 % (27508)------------------------------
% 6.56/1.30 % (27508)------------------------------
% 6.56/1.30 % (27510)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on theBenchmark for (2990ds/114Mi)
% 6.88/1.31 % (27511)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on theBenchmark for (2990ds/922Mi)
% 6.88/1.31 % (27503)Instruction limit reached!
% 6.88/1.31 % (27503)------------------------------
% 6.88/1.31 % (27503)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.88/1.31 % (27503)Termination reason: Unknown
% 6.88/1.31 % (27503)Termination phase: Saturation
% 6.88/1.31
% 6.88/1.31 % (27503)Memory used [KB]: 7291
% 6.88/1.31 % (27503)Time elapsed: 0.118 s
% 6.88/1.31 % (27503)Instructions burned: 297 (million)
% 6.88/1.31 % (27503)------------------------------
% 6.88/1.31 % (27503)------------------------------
% 6.88/1.32 % (27512)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on theBenchmark for (2990ds/182Mi)
% 6.88/1.33 % (27507)Instruction limit reached!
% 6.88/1.33 % (27507)------------------------------
% 6.88/1.33 % (27507)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.88/1.33 % (27507)Termination reason: Unknown
% 6.88/1.33 % (27507)Termination phase: Saturation
% 6.88/1.33
% 6.88/1.33 % (27507)Memory used [KB]: 6908
% 6.88/1.33 % (27507)Time elapsed: 0.048 s
% 6.88/1.33 % (27507)Instructions burned: 155 (million)
% 6.88/1.33 % (27507)------------------------------
% 6.88/1.33 % (27507)------------------------------
% 6.88/1.34 % (27513)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on theBenchmark for (2990ds/164Mi)
% 6.88/1.35 % (27510)Instruction limit reached!
% 6.88/1.35 % (27510)------------------------------
% 6.88/1.35 % (27510)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.88/1.35 % (27510)Termination reason: Unknown
% 6.88/1.35 % (27510)Termination phase: Saturation
% 6.88/1.35
% 6.88/1.35 % (27510)Memory used [KB]: 6908
% 6.88/1.35 % (27510)Time elapsed: 0.052 s
% 6.88/1.35 % (27510)Instructions burned: 116 (million)
% 6.88/1.35 % (27510)------------------------------
% 6.88/1.35 % (27510)------------------------------
% 6.88/1.37 % (27509)Instruction limit reached!
% 6.88/1.37 % (27509)------------------------------
% 6.88/1.37 % (27509)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.88/1.37 % (27509)Termination reason: Unknown
% 6.88/1.37 % (27509)Termination phase: Saturation
% 6.88/1.37
% 6.88/1.37 % (27509)Memory used [KB]: 6908
% 6.88/1.37 % (27509)Time elapsed: 0.078 s
% 6.88/1.37 % (27509)Instructions burned: 218 (million)
% 6.88/1.37 % (27509)------------------------------
% 6.88/1.37 % (27509)------------------------------
% 7.21/1.37 % (27514)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on theBenchmark for (2990ds/50Mi)
% 7.21/1.38 % (27513)Instruction limit reached!
% 7.21/1.38 % (27513)------------------------------
% 7.21/1.38 % (27513)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.21/1.38 % (27513)Termination reason: Unknown
% 7.21/1.38 % (27513)Termination phase: Saturation
% 7.21/1.38
% 7.21/1.38 % (27513)Memory used [KB]: 2558
% 7.21/1.38 % (27513)Time elapsed: 0.044 s
% 7.21/1.38 % (27513)Instructions burned: 165 (million)
% 7.21/1.38 % (27513)------------------------------
% 7.21/1.38 % (27513)------------------------------
% 7.21/1.38 % (27515)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on theBenchmark for (2989ds/368Mi)
% 7.21/1.39 % (27516)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on theBenchmark for (2989ds/1021Mi)
% 7.21/1.39 % (27501)Instruction limit reached!
% 7.21/1.39 % (27501)------------------------------
% 7.21/1.39 % (27501)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.21/1.39 % (27501)Termination reason: Unknown
% 7.21/1.39 % (27501)Termination phase: Saturation
% 7.21/1.39
% 7.21/1.39 % (27501)Memory used [KB]: 8699
% 7.21/1.39 % (27501)Time elapsed: 0.213 s
% 7.21/1.39 % (27501)Instructions burned: 459 (million)
% 7.21/1.39 % (27501)------------------------------
% 7.21/1.39 % (27501)------------------------------
% 7.21/1.40 % (27514)Instruction limit reached!
% 7.21/1.40 % (27514)------------------------------
% 7.21/1.40 % (27514)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.21/1.40 % (27514)Termination reason: Unknown
% 7.21/1.40 % (27514)Termination phase: Property scanning
% 7.21/1.40
% 7.21/1.40 % (27514)Memory used [KB]: 2174
% 7.21/1.40 % (27514)Time elapsed: 0.021 s
% 7.21/1.40 % (27514)Instructions burned: 50 (million)
% 7.21/1.40 % (27514)------------------------------
% 7.21/1.40 % (27514)------------------------------
% 7.21/1.40 % (27512)Instruction limit reached!
% 7.21/1.40 % (27512)------------------------------
% 7.21/1.40 % (27512)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.21/1.40 % (27512)Termination reason: Unknown
% 7.21/1.40 % (27512)Termination phase: Saturation
% 7.21/1.40
% 7.21/1.40 % (27512)Memory used [KB]: 6908
% 7.21/1.40 % (27512)Time elapsed: 0.075 s
% 7.21/1.40 % (27512)Instructions burned: 183 (million)
% 7.21/1.40 % (27512)------------------------------
% 7.21/1.40 % (27512)------------------------------
% 7.21/1.41 % (27517)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on theBenchmark for (2989ds/267Mi)
% 7.21/1.41 % (27518)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on theBenchmark for (2989ds/204Mi)
% 7.21/1.41 % (27519)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on theBenchmark for (2989ds/26Mi)
% 7.21/1.43 % (27519)Instruction limit reached!
% 7.21/1.43 % (27519)------------------------------
% 7.21/1.43 % (27519)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.21/1.43 % (27519)Termination reason: Unknown
% 7.21/1.43 % (27519)Termination phase: shuffling
% 7.21/1.43
% 7.21/1.43 % (27519)Memory used [KB]: 1918
% 7.21/1.43 % (27519)Time elapsed: 0.013 s
% 7.21/1.43 % (27519)Instructions burned: 27 (million)
% 7.21/1.43 % (27519)------------------------------
% 7.21/1.43 % (27519)------------------------------
% 7.21/1.45 % (27520)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on theBenchmark for (2989ds/53Mi)
% 7.79/1.47 % (27520)Instruction limit reached!
% 7.79/1.47 % (27520)------------------------------
% 7.79/1.47 % (27520)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.79/1.47 % (27520)Termination reason: Unknown
% 7.79/1.47 % (27520)Termination phase: Property scanning
% 7.79/1.47
% 7.79/1.47 % (27520)Memory used [KB]: 2174
% 7.79/1.47 % (27520)Time elapsed: 0.017 s
% 7.79/1.47 % (27520)Instructions burned: 55 (million)
% 7.79/1.47 % (27520)------------------------------
% 7.79/1.47 % (27520)------------------------------
% 7.79/1.48 % (27521)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on theBenchmark for (2988ds/4436Mi)
% 7.79/1.49 % (27518)Instruction limit reached!
% 7.79/1.49 % (27518)------------------------------
% 7.79/1.49 % (27518)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.79/1.49 % (27518)Termination reason: Unknown
% 7.79/1.49 % (27518)Termination phase: Saturation
% 7.79/1.49
% 7.79/1.49 % (27518)Memory used [KB]: 7547
% 7.79/1.49 % (27518)Time elapsed: 0.079 s
% 7.79/1.49 % (27518)Instructions burned: 205 (million)
% 7.79/1.49 % (27518)------------------------------
% 7.79/1.49 % (27518)------------------------------
% 7.95/1.50 % (27522)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on theBenchmark for (2988ds/1539Mi)
% 7.95/1.51 % (27517)Instruction limit reached!
% 7.95/1.51 % (27517)------------------------------
% 7.95/1.51 % (27517)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.95/1.51 % (27517)Termination reason: Unknown
% 7.95/1.51 % (27517)Termination phase: Saturation
% 7.95/1.51
% 7.95/1.51 % (27517)Memory used [KB]: 7164
% 7.95/1.51 % (27517)Time elapsed: 0.106 s
% 7.95/1.51 % (27517)Instructions burned: 268 (million)
% 7.95/1.51 % (27517)------------------------------
% 7.95/1.51 % (27517)------------------------------
% 8.10/1.54 % (27523)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on theBenchmark for (2988ds/408Mi)
% 8.10/1.54 % (27504)Instruction limit reached!
% 8.10/1.54 % (27504)------------------------------
% 8.10/1.54 % (27504)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 8.10/1.54 % (27504)Termination reason: Unknown
% 8.10/1.54 % (27504)Termination phase: Saturation
% 8.10/1.54
% 8.10/1.54 % (27504)Memory used [KB]: 11897
% 8.10/1.54 % (27504)Time elapsed: 0.368 s
% 8.10/1.54 % (27504)Instructions burned: 989 (million)
% 8.10/1.54 % (27504)------------------------------
% 8.10/1.54 % (27504)------------------------------
% 8.10/1.55 % (27515)Instruction limit reached!
% 8.10/1.55 % (27515)------------------------------
% 8.10/1.55 % (27515)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 8.10/1.55 % (27515)Termination reason: Unknown
% 8.10/1.55 % (27515)Termination phase: Saturation
% 8.10/1.55
% 8.10/1.55 % (27515)Memory used [KB]: 8443
% 8.10/1.55 % (27515)Time elapsed: 0.175 s
% 8.10/1.56 % (27515)Instructions burned: 369 (million)
% 8.10/1.56 % (27515)------------------------------
% 8.10/1.56 % (27515)------------------------------
% 8.10/1.56 % (27524)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on theBenchmark for (2988ds/5205Mi)
% 8.10/1.58 % (27525)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on theBenchmark for (2988ds/1913Mi)
% 8.72/1.63 % (27436)Refutation found. Thanks to Tanya!
% 8.72/1.63 % SZS status Theorem for theBenchmark
% 8.72/1.63 % SZS output start Proof for theBenchmark
% 8.72/1.63 thf(func_def_0, type, in: $i > $i > $o).
% 8.72/1.63 thf(func_def_1, type, exu: ($i > $o) > $o).
% 8.72/1.63 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 8.72/1.63 thf(func_def_8, type, powerset: $i > $i).
% 8.72/1.63 thf(func_def_10, type, setunion: $i > $i).
% 8.72/1.63 thf(func_def_19, type, descr: ($i > $o) > $i).
% 8.72/1.63 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 8.72/1.63 thf(func_def_26, type, prop2set: $o > $i).
% 8.72/1.63 thf(func_def_36, type, nonempty: $i > $o).
% 8.72/1.63 thf(func_def_69, type, set2prop: $i > $o).
% 8.72/1.63 thf(func_def_88, type, subset: $i > $i > $o).
% 8.72/1.63 thf(func_def_89, type, disjoint: $i > $i > $o).
% 8.72/1.63 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 8.72/1.63 thf(func_def_114, type, binunion: $i > $i > $i).
% 8.72/1.63 thf(func_def_122, type, binintersect: $i > $i > $i).
% 8.72/1.63 thf(func_def_135, type, regular: $i > $o).
% 8.72/1.63 thf(func_def_136, type, setminus: $i > $i > $i).
% 8.72/1.63 thf(func_def_147, type, symdiff: $i > $i > $i).
% 8.72/1.63 thf(func_def_153, type, iskpair: $i > $o).
% 8.72/1.63 thf(func_def_158, type, kpair: $i > $i > $i).
% 8.72/1.63 thf(func_def_160, type, cartprod: $i > $i > $i).
% 8.72/1.63 thf(func_def_177, type, singleton: $i > $o).
% 8.72/1.63 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 8.72/1.63 thf(func_def_184, type, atmost1p: $i > $o).
% 8.72/1.63 thf(func_def_185, type, atleast2p: $i > $o).
% 8.72/1.63 thf(func_def_186, type, atmost2p: $i > $o).
% 8.72/1.63 thf(func_def_187, type, upairsetp: $i > $o).
% 8.72/1.63 thf(func_def_191, type, kfst: $i > $i).
% 8.72/1.63 thf(func_def_203, type, ksnd: $i > $i).
% 8.72/1.63 thf(func_def_213, type, breln: $i > $i > $i > $o).
% 8.72/1.63 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 8.72/1.63 thf(func_def_222, type, func: $i > $i > $i > $o).
% 8.72/1.63 thf(func_def_223, type, funcSet: $i > $i > $i).
% 8.72/1.63 thf(func_def_226, type, ap: $i > $i > $i > $i > $i).
% 8.72/1.63 thf(func_def_232, type, lam: $i > $i > ($i > $i) > $i).
% 8.72/1.63 thf(f1064,plain,(
% 8.72/1.63 $false),
% 8.72/1.63 inference(trivial_inequality_removal,[],[f1063])).
% 8.72/1.63 thf(f1063,plain,(
% 8.72/1.63 ($true = $false)),
% 8.72/1.63 inference(boolean_simplification,[],[f1062])).
% 8.72/1.63 thf(f1062,plain,(
% 8.72/1.63 ($true = (~ $true))),
% 8.72/1.63 inference(boolean_simplification,[],[f1061])).
% 8.72/1.63 thf(f1061,plain,(
% 8.72/1.63 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => $true)))),
% 8.72/1.63 inference(boolean_simplification,[],[f1060])).
% 8.72/1.63 thf(f1060,plain,(
% 8.72/1.63 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => $true))))),
% 8.72/1.63 inference(boolean_simplification,[],[f1059])).
% 8.72/1.63 thf(f1059,plain,(
% 8.72/1.63 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => $true)))))),
% 8.72/1.63 inference(boolean_simplification,[],[f1058])).
% 8.72/1.63 thf(f1058,plain,(
% 8.72/1.63 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => $true))))))),
% 8.72/1.63 inference(boolean_simplification,[],[f1057])).
% 8.72/1.63 thf(f1057,plain,(
% 8.72/1.63 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => $true)))))))),
% 8.72/1.63 inference(boolean_simplification,[],[f1056])).
% 8.72/1.63 thf(f1056,plain,(
% 8.72/1.63 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => $true))))))))),
% 8.72/1.63 inference(boolean_simplification,[],[f1055])).
% 8.72/1.63 thf(f1055,plain,(
% 8.72/1.63 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => $true)))))))))),
% 8.72/1.63 inference(boolean_simplification,[],[f1054])).
% 8.72/1.63 thf(f1054,plain,(
% 8.72/1.63 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => $true))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f1053])).
% 8.72/1.64 thf(f1053,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => $true)))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f1052])).
% 8.72/1.64 thf(f1052,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => $true))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f1051])).
% 8.72/1.64 thf(f1051,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => $true)))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f1050])).
% 8.72/1.64 thf(f1050,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => $true))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f1049])).
% 8.72/1.64 thf(f1049,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => $true)))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f1048])).
% 8.72/1.64 thf(f1048,plain,(
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% 8.72/1.64 inference(boolean_simplification,[],[f1047])).
% 8.72/1.64 thf(f1047,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => $true)))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f1046])).
% 8.72/1.64 thf(f1046,plain,(
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% 8.72/1.64 inference(boolean_simplification,[],[f1045])).
% 8.72/1.64 thf(f1045,plain,(
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% 8.72/1.64 inference(boolean_simplification,[],[f1044])).
% 8.72/1.64 thf(f1044,plain,(
% 8.72/1.64 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => $true))))))))))))))))))) = $true)),
% 8.72/1.64 inference(boolean_simplification,[],[f1043])).
% 8.72/1.64 thf(f1043,plain,(
% 8.72/1.64 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => $true)))))))))))))))))))) = $true)),
% 8.72/1.64 inference(boolean_simplification,[],[f1042])).
% 8.72/1.64 thf(f1042,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => $true))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f1041])).
% 8.72/1.64 thf(f1041,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => $true)))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f1040])).
% 8.72/1.64 thf(f1040,plain,(
% 8.72/1.64 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => $true))))))))))))))))))))))) = $true)),
% 8.72/1.64 inference(boolean_simplification,[],[f1039])).
% 8.72/1.64 thf(f1039,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => $true)))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f1038])).
% 8.72/1.64 thf(f1038,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => $true))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f1037])).
% 8.72/1.64 thf(f1037,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => $true)))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f1036])).
% 8.72/1.64 thf(f1036,plain,(
% 8.72/1.64 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => $true))))))))))))))))))))))))))) = $true)),
% 8.72/1.64 inference(boolean_simplification,[],[f1035])).
% 8.72/1.64 thf(f1035,plain,(
% 8.72/1.64 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => $true)))))))))))))))))))))))))))) = $true)),
% 8.72/1.64 inference(boolean_simplification,[],[f1034])).
% 8.72/1.64 thf(f1034,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => $true))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f1033])).
% 8.72/1.64 thf(f1033,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => $true)))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f1032])).
% 8.72/1.64 thf(f1032,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => $true))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f1031])).
% 8.72/1.64 thf(f1031,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => $true)))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f1030])).
% 8.72/1.64 thf(f1030,plain,(
% 8.72/1.64 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => $true))))))))))))))))))))))))))))))))) = $true)),
% 8.72/1.64 inference(boolean_simplification,[],[f1029])).
% 8.72/1.64 thf(f1029,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => $true)))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f1028])).
% 8.72/1.64 thf(f1028,plain,(
% 8.72/1.64 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => $true))))))))))))))))))))))))))))))))))) = $true)),
% 8.72/1.64 inference(boolean_simplification,[],[f1027])).
% 8.72/1.64 thf(f1027,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? 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% 8.72/1.64 inference(boolean_simplification,[],[f1026])).
% 8.72/1.64 thf(f1026,plain,(
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% 8.72/1.64 inference(boolean_simplification,[],[f1025])).
% 8.72/1.64 thf(f1025,plain,(
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% 8.72/1.64 inference(boolean_simplification,[],[f1024])).
% 8.72/1.64 thf(f1024,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? 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% 8.72/1.64 inference(boolean_simplification,[],[f1023])).
% 8.72/1.64 thf(f1023,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? 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% 8.72/1.64 inference(boolean_simplification,[],[f1022])).
% 8.72/1.64 thf(f1022,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? 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% 8.72/1.64 inference(boolean_simplification,[],[f1021])).
% 8.72/1.64 thf(f1021,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? 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% 8.72/1.64 inference(boolean_simplification,[],[f1020])).
% 8.72/1.64 thf(f1020,plain,(
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% 8.72/1.64 inference(boolean_simplification,[],[f1019])).
% 8.72/1.64 thf(f1019,plain,(
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@ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f1018])).
% 8.72/1.64 thf(f1018,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? 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@ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => $true))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f1017])).
% 8.72/1.64 thf(f1017,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f1016])).
% 8.72/1.64 thf(f1016,plain,(
% 8.72/1.64 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 8.72/1.64 inference(boolean_simplification,[],[f1015])).
% 8.72/1.64 thf(f1015,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? 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@ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f1014])).
% 8.72/1.64 thf(f1014,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? 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@ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f1013])).
% 8.72/1.64 thf(f1013,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f1012])).
% 8.72/1.64 thf(f1012,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f1011])).
% 8.72/1.64 thf(f1011,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f1010])).
% 8.72/1.64 thf(f1010,plain,(
% 8.72/1.64 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 8.72/1.64 inference(boolean_simplification,[],[f1009])).
% 8.72/1.64 thf(f1009,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f1008])).
% 8.72/1.64 thf(f1008,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f1007])).
% 8.72/1.64 thf(f1007,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? 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@ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f1006])).
% 8.72/1.64 thf(f1006,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? 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@ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f1005])).
% 8.72/1.64 thf(f1005,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f1004])).
% 8.72/1.64 thf(f1004,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f1003])).
% 8.72/1.64 thf(f1003,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f1002])).
% 8.72/1.64 thf(f1002,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f1001])).
% 8.72/1.64 thf(f1001,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f1000])).
% 8.72/1.64 thf(f1000,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f999])).
% 8.72/1.64 thf(f999,plain,(
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@ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? 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@ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f998])).
% 8.72/1.64 thf(f998,plain,(
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@ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? 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@ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f997])).
% 8.72/1.64 thf(f997,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f996])).
% 8.72/1.64 thf(f996,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f995])).
% 8.72/1.64 thf(f995,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f994])).
% 8.72/1.64 thf(f994,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f993])).
% 8.72/1.64 thf(f993,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f992])).
% 8.72/1.64 thf(f992,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f991])).
% 8.72/1.64 thf(f991,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f990])).
% 8.72/1.64 thf(f990,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f989])).
% 8.72/1.64 thf(f989,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f988])).
% 8.72/1.64 thf(f988,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f987])).
% 8.72/1.64 thf(f987,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f986])).
% 8.72/1.64 thf(f986,plain,(
% 8.72/1.64 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 8.72/1.64 inference(boolean_simplification,[],[f985])).
% 8.72/1.64 thf(f985,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f984])).
% 8.72/1.64 thf(f984,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f983])).
% 8.72/1.64 thf(f983,plain,(
% 8.72/1.64 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 8.72/1.64 inference(boolean_simplification,[],[f982])).
% 8.72/1.64 thf(f982,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f981])).
% 8.72/1.64 thf(f981,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? 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@ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f980])).
% 8.72/1.64 thf(f980,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f979])).
% 8.72/1.64 thf(f979,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? 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@ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? 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@ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f978])).
% 8.72/1.64 thf(f978,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? 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@ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? 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@ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? 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@ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f977])).
% 8.72/1.64 thf(f977,plain,(
% 8.72/1.64 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 8.72/1.64 inference(boolean_simplification,[],[f976])).
% 8.72/1.64 thf(f976,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? 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@ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? 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@ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f975])).
% 8.72/1.64 thf(f975,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? 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@ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? 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@ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f974])).
% 8.72/1.64 thf(f974,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? 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@ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? 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@ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f973])).
% 8.72/1.64 thf(f973,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f972])).
% 8.72/1.64 thf(f972,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f971])).
% 8.72/1.64 thf(f971,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? 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@ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f970])).
% 8.72/1.64 thf(f970,plain,(
% 8.72/1.64 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 8.72/1.64 inference(boolean_simplification,[],[f969])).
% 8.72/1.64 thf(f969,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f968])).
% 8.72/1.64 thf(f968,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? 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@ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? 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@ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f967])).
% 8.72/1.64 thf(f967,plain,(
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@ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? 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@ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f966])).
% 8.72/1.64 thf(f966,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? 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@ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (subset @ (powerset @ Y1) @ (powerset @ Y0))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f965])).
% 8.72/1.64 thf(f965,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (subset @ (powerset @ Y1) @ (powerset @ Y0))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f964])).
% 8.72/1.64 thf(f964,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (subset @ (powerset @ Y1) @ (powerset @ Y0))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f963])).
% 8.72/1.64 thf(f963,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (subset @ (powerset @ Y1) @ (powerset @ Y0))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f962])).
% 8.72/1.64 thf(f962,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (subset @ (powerset @ Y1) @ (powerset @ Y0))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f961])).
% 8.72/1.64 thf(f961,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (subset @ (powerset @ Y1) @ (powerset @ Y0))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y1 @ Y2))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f960])).
% 8.72/1.64 thf(f960,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (subset @ (powerset @ Y1) @ (powerset @ Y0))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y0 @ Y1)) => (((in @ Y3 @ Y0) => Y2) => (((in @ Y3 @ Y1) => Y2) => Y2))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f959])).
% 8.72/1.64 thf(f959,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (subset @ (powerset @ Y1) @ (powerset @ Y0))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y0 @ Y1)) => (((in @ Y3 @ Y0) => Y2) => (((in @ Y3 @ Y1) => Y2) => Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y1) | (in @ Y2 @ Y0))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f958])).
% 8.72/1.64 thf(f958,plain,(
% 8.72/1.64 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (subset @ (powerset @ Y1) @ (powerset @ Y0))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y0 @ Y1)) => (((in @ Y3 @ Y0) => Y2) => (((in @ Y3 @ Y1) => Y2) => Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y1) | (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0)))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 8.72/1.64 inference(boolean_simplification,[],[f957])).
% 8.72/1.64 thf(f957,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (subset @ (powerset @ Y1) @ (powerset @ Y0))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y0 @ Y1)) => (((in @ Y3 @ Y0) => Y2) => (((in @ Y3 @ Y1) => Y2) => Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y1) | (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f956])).
% 8.72/1.64 thf(f956,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (subset @ (powerset @ Y1) @ (powerset @ Y0))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y0 @ Y1)) => (((in @ Y3 @ Y0) => Y2) => (((in @ Y3 @ Y1) => Y2) => Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y1) | (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f955])).
% 8.72/1.64 thf(f955,plain,(
% 8.72/1.64 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (subset @ (powerset @ Y1) @ (powerset @ Y0))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y0 @ Y1)) => (((in @ Y3 @ Y0) => Y2) => (((in @ Y3 @ Y1) => Y2) => Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y1) | (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y0 @ Y2) => (subset @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 8.72/1.64 inference(boolean_simplification,[],[f954])).
% 8.72/1.64 thf(f954,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (subset @ (powerset @ Y1) @ (powerset @ Y0))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y0 @ Y1)) => (((in @ Y3 @ Y0) => Y2) => (((in @ Y3 @ Y1) => Y2) => Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y1) | (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y0 @ Y2) => (subset @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f953])).
% 8.72/1.64 thf(f953,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (subset @ (powerset @ Y1) @ (powerset @ Y0))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y0 @ Y1)) => (((in @ Y3 @ Y0) => Y2) => (((in @ Y3 @ Y1) => Y2) => Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y1) | (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y0 @ Y2) => (subset @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f952])).
% 8.72/1.64 thf(f952,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (subset @ (powerset @ Y1) @ (powerset @ Y0))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y0 @ Y1)) => (((in @ Y3 @ Y0) => Y2) => (((in @ Y3 @ Y1) => Y2) => Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y1) | (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y0 @ Y2) => (subset @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f951])).
% 8.72/1.64 thf(f951,plain,(
% 8.72/1.64 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! 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@ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! 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@ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (subset @ (powerset @ Y1) @ (powerset @ Y0))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y0 @ Y1)) => (((in @ Y3 @ Y0) => Y2) => (((in @ Y3 @ Y1) => Y2) => Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y1) | (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y0 @ Y2) => (subset @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 8.72/1.64 inference(boolean_simplification,[],[f950])).
% 8.72/1.64 thf(f950,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (subset @ (powerset @ Y1) @ (powerset @ Y0))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y0 @ Y1)) => (((in @ Y3 @ Y0) => Y2) => (((in @ Y3 @ Y1) => Y2) => Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y1) | (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y0 @ Y2) => (subset @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y0 @ Y1)) => (in @ Y2 @ Y1)))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f949])).
% 8.72/1.64 thf(f949,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! 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@ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (subset @ (powerset @ Y1) @ (powerset @ Y0))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y0 @ Y1)) => (((in @ Y3 @ Y0) => Y2) => (((in @ Y3 @ Y1) => Y2) => Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y1) | (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y0 @ Y2) => (subset @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y0 @ Y1)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y0 @ Y1))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f948])).
% 8.72/1.64 thf(f948,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! 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@ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (subset @ (powerset @ Y1) @ (powerset @ Y0))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y0 @ Y1)) => (((in @ Y3 @ Y0) => Y2) => (((in @ Y3 @ Y1) => Y2) => Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y1) | (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y0 @ Y2) => (subset @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y0 @ Y1)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f947])).
% 8.72/1.64 thf(f947,plain,(
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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y0 @ Y2) => (subset @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y0 @ Y1)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f946])).
% 8.72/1.64 thf(f946,plain,(
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@ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (subset @ (powerset @ Y1) @ (powerset @ Y0))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y0 @ Y1)) => (((in @ Y3 @ Y0) => Y2) => (((in @ Y3 @ Y1) => Y2) => Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y1) | (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y0 @ Y2) => (subset @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y0 @ Y1)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y0) => (subset @ Y0 @ Y1)))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f945])).
% 8.72/1.64 thf(f945,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (subset @ (powerset @ Y1) @ (powerset @ Y0))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y0 @ Y1)) => (((in @ Y3 @ Y0) => Y2) => (((in @ Y3 @ Y1) => Y2) => Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y1) | (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y0 @ Y2) => (subset @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y0 @ Y1)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y0) @ (binintersect @ Y2 @ Y1)) = (binintersect @ Y2 @ (binunion @ Y0 @ Y1))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f944])).
% 8.72/1.64 thf(f944,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y0 @ Y2) => (subset @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y0 @ Y1)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y0) @ (binintersect @ Y2 @ Y1)) = (binintersect @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (in @ Y1 @ (setminus @ Y2 @ Y0)))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f943])).
% 8.72/1.64 thf(f943,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! 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@ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (subset @ (powerset @ Y1) @ (powerset @ Y0))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y0 @ Y1)) => (((in @ Y3 @ Y0) => Y2) => (((in @ Y3 @ Y1) => Y2) => Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y1) | (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y0 @ Y2) => (subset @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y0 @ Y1)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y0) @ (binintersect @ Y2 @ Y1)) = (binintersect @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (in @ Y1 @ (setminus @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f942])).
% 8.72/1.64 thf(f942,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (subset @ (powerset @ Y1) @ (powerset @ Y0))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y0 @ Y1)) => (((in @ Y3 @ Y0) => Y2) => (((in @ Y3 @ Y1) => Y2) => Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y1) | (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y0 @ Y2) => (subset @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y0 @ Y1)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y0) @ (binintersect @ Y2 @ Y1)) = (binintersect @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (in @ Y1 @ (setminus @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y2 @ Y1)) => (~ (in @ Y0 @ Y1))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f941])).
% 8.72/1.64 thf(f941,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y0) @ (binintersect @ Y2 @ Y1)) = (binintersect @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (in @ Y1 @ (setminus @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y2 @ Y1)) => (~ (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f940])).
% 8.72/1.64 thf(f940,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! 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@ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (subset @ (powerset @ Y1) @ (powerset @ Y0))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y0 @ Y1)) => (((in @ Y3 @ Y0) => Y2) => (((in @ Y3 @ Y1) => Y2) => Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y1) | (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y0 @ Y2) => (subset @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y0 @ Y1)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y0) @ (binintersect @ Y2 @ Y1)) = (binintersect @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (in @ Y1 @ (setminus @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y2 @ Y1)) => (~ (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f939])).
% 8.72/1.64 thf(f939,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (subset @ (powerset @ Y1) @ (powerset @ Y0))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y0 @ Y1)) => (((in @ Y3 @ Y0) => Y2) => (((in @ Y3 @ Y1) => Y2) => Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y1) | (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y0 @ Y2) => (subset @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y0 @ Y1)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y0) @ (binintersect @ Y2 @ Y1)) = (binintersect @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (in @ Y1 @ (setminus @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y2 @ Y1)) => (~ (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ Y0)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f938])).
% 8.72/1.64 thf(f938,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y0 @ Y2) => (subset @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y0 @ Y1)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y0) @ (binintersect @ Y2 @ Y1)) = (binintersect @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (in @ Y1 @ (setminus @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y2 @ Y1)) => (~ (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f937])).
% 8.72/1.64 thf(f937,plain,(
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@ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! 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@ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (subset @ (powerset @ Y1) @ (powerset @ Y0))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y0 @ Y1)) => (((in @ Y3 @ Y0) => Y2) => (((in @ Y3 @ Y1) => Y2) => Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y1) | (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y0 @ Y2) => (subset @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y0 @ Y1)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y0) @ (binintersect @ Y2 @ Y1)) = (binintersect @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (in @ Y1 @ (setminus @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y2 @ Y1)) => (~ (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (setminus @ Y0 @ Y2)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f936])).
% 8.72/1.64 thf(f936,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (subset @ (powerset @ Y1) @ (powerset @ Y0))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y0 @ Y1)) => (((in @ Y3 @ Y0) => Y2) => (((in @ Y3 @ Y1) => Y2) => Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y1) | (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y0 @ Y2) => (subset @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y0 @ Y1)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y0) @ (binintersect @ Y2 @ Y1)) = (binintersect @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (in @ Y1 @ (setminus @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y2 @ Y1)) => (~ (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (setminus @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f935])).
% 8.72/1.64 thf(f935,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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% 8.72/1.64 inference(boolean_simplification,[],[f934])).
% 8.72/1.64 thf(f934,plain,(
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@ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (subset @ (powerset @ Y1) @ (powerset @ Y0))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y0 @ Y1)) => (((in @ Y3 @ Y0) => Y2) => (((in @ Y3 @ Y1) => Y2) => Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y1) | (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y0 @ Y2) => (subset @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y0 @ Y1)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y0) @ (binintersect @ Y2 @ Y1)) = (binintersect @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (in @ Y1 @ (setminus @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y2 @ Y1)) => (~ (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (setminus @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y0 @ Y1)) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => Y3)) => (((~ (in @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => Y3)) => Y3))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f933])).
% 8.72/1.64 thf(f933,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! 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@ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y2 @ Y1)) => (~ (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (setminus @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y0 @ Y1)) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => Y3)) => (((~ (in @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f932])).
% 8.72/1.64 thf(f932,plain,(
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@ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! 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@ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! 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@ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (subset @ (powerset @ Y1) @ (powerset @ Y0))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y0 @ Y1)) => (((in @ Y3 @ Y0) => Y2) => (((in @ Y3 @ Y1) => Y2) => Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y1) | (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y0 @ Y2) => (subset @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y0 @ Y1)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y0) @ (binintersect @ Y2 @ Y1)) = (binintersect @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (in @ Y1 @ (setminus @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y2 @ Y1)) => (~ (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (setminus @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y0 @ Y1)) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => Y3)) => (((~ (in @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 8.72/1.64 inference(boolean_simplification,[],[f931])).
% 8.72/1.64 thf(f931,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => Y3)) => (((~ (in @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (symdiff @ Y0 @ Y2))))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f930])).
% 8.72/1.64 thf(f930,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! 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@ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y0 @ Y2) => (subset @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y0 @ Y1)) => (in @ Y2 @ Y1)))))))) => ((!! 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@ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y2 @ Y1)) => (~ (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (setminus @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y0 @ Y1)) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => Y3)) => (((~ (in @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (symdiff @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (symdiff @ Y1 @ Y0))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f929])).
% 8.72/1.64 thf(f929,plain,(
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@ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y0 @ Y2) => (subset @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y0 @ Y1)) => (in @ Y2 @ Y1)))))))) => ((!! 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@ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y2 @ Y1)) => (~ (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (setminus @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y0 @ Y1)) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => Y3)) => (((~ (in @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (symdiff @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (symdiff @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f928])).
% 8.72/1.64 thf(f928,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => Y3)) => (((~ (in @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (symdiff @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (symdiff @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! 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% 8.72/1.64 inference(boolean_simplification,[],[f927])).
% 8.72/1.64 thf(f927,plain,(
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@ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (subset @ (powerset @ Y1) @ (powerset @ Y0))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y0 @ Y1)) => (((in @ Y3 @ Y0) => Y2) => (((in @ Y3 @ Y1) => Y2) => Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y1) | (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y0 @ Y2) => (subset @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y0 @ Y1)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y0) @ (binintersect @ Y2 @ Y1)) = (binintersect @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (in @ Y1 @ (setminus @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y2 @ Y1)) => (~ (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (setminus @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y0 @ Y1)) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => Y3)) => (((~ (in @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (symdiff @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (symdiff @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f926])).
% 8.72/1.64 thf(f926,plain,(
% 8.72/1.64 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! 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@ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => Y3)) => (((~ (in @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (symdiff @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (symdiff @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 8.72/1.64 inference(boolean_simplification,[],[f925])).
% 8.72/1.64 thf(f925,plain,(
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@ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (subset @ (powerset @ Y1) @ (powerset @ Y0))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y0 @ Y1)) => (((in @ Y3 @ Y0) => Y2) => (((in @ Y3 @ Y1) => Y2) => Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y1) | (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y0 @ Y2) => (subset @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y0 @ Y1)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y0) @ (binintersect @ Y2 @ Y1)) = (binintersect @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (in @ Y1 @ (setminus @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y2 @ Y1)) => (~ (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (setminus @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y0 @ Y1)) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => Y3)) => (((~ (in @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (symdiff @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (symdiff @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y0 @ Y1)))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f924])).
% 8.72/1.64 thf(f924,plain,(
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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => Y3)) => (((~ (in @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (symdiff @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (symdiff @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f923])).
% 8.72/1.64 thf(f923,plain,(
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@ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (subset @ (powerset @ Y1) @ (powerset @ Y0))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y0 @ Y1)) => (((in @ Y3 @ Y0) => Y2) => (((in @ Y3 @ Y1) => Y2) => Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y1) | (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y0 @ Y2) => (subset @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y0 @ Y1)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y0) @ (binintersect @ Y2 @ Y1)) = (binintersect @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (in @ Y1 @ (setminus @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y2 @ Y1)) => (~ (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (setminus @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y0 @ Y1)) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => Y3)) => (((~ (in @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (symdiff @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (symdiff @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ Y0))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 8.72/1.64 inference(boolean_simplification,[],[f922])).
% 8.72/1.64 thf(f922,plain,(
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% 8.72/1.64 inference(boolean_simplification,[],[f921])).
% 8.72/1.64 thf(f921,plain,(
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@ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (subset @ (powerset @ Y1) @ (powerset @ Y0))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y0 @ Y1)) => (((in @ Y3 @ Y0) => Y2) => (((in @ Y3 @ Y1) => Y2) => Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y1) | (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y0 @ Y2) => (subset @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y0 @ Y1)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y0) @ (binintersect @ Y2 @ Y1)) = (binintersect @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (in @ Y1 @ (setminus @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y2 @ Y1)) => (~ (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (setminus @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y0 @ Y1)) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => Y3)) => (((~ (in @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (symdiff @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (symdiff @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f920])).
% 8.72/1.64 thf(f920,plain,(
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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y2)))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f919])).
% 8.72/1.64 thf(f919,plain,(
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@ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! 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@ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y0 @ Y2) => (subset @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y0 @ Y1)) => (in @ Y2 @ Y1)))))))) => ((!! 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@ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y2 @ Y1)) => (~ (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (setminus @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y0 @ Y1)) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => Y3)) => (((~ (in @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (symdiff @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (symdiff @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f918])).
% 8.72/1.64 thf(f918,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f917])).
% 8.72/1.64 thf(f917,plain,(
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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f916])).
% 8.72/1.64 thf(f916,plain,(
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@ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! 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@ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! 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@ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (setadjoin @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => (subset @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (subset @ (powerset @ Y1) @ (powerset @ Y0))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y0 @ Y1)) => (((in @ Y3 @ Y0) => Y2) => (((in @ Y3 @ Y1) => Y2) => Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y1) | (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y0 @ Y2) => (subset @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y0 @ Y1)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y0) @ (binintersect @ Y2 @ Y1)) = (binintersect @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (in @ Y1 @ (setminus @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y2 @ Y1)) => (~ (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (setminus @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y0 @ Y1)) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => Y3)) => (((~ (in @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (symdiff @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (symdiff @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 8.72/1.64 inference(boolean_simplification,[],[f915])).
% 8.72/1.64 thf(f915,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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% 8.72/1.64 inference(boolean_simplification,[],[f914])).
% 8.72/1.64 thf(f914,plain,(
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@ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y2)))))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f913])).
% 8.72/1.64 thf(f913,plain,(
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@ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! 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@ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y0 @ Y1)) => (((in @ Y3 @ Y0) => Y2) => (((in @ Y3 @ Y1) => Y2) => Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y1) | (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y0 @ Y2) => (subset @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y0 @ Y1)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y0) @ (binintersect @ Y2 @ Y1)) = (binintersect @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (in @ Y1 @ (setminus @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y2 @ Y1)) => (~ (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (setminus @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y0 @ Y1)) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => Y3)) => (((~ (in @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (symdiff @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (symdiff @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (iskpair @ Y0)))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f912])).
% 8.72/1.64 thf(f912,plain,(
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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (iskpair @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f911])).
% 8.72/1.64 thf(f911,plain,(
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@ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (iskpair @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f910])).
% 8.72/1.64 thf(f910,plain,(
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@ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! 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@ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y0 @ Y1)) => (((in @ Y3 @ Y0) => Y2) => (((in @ Y3 @ Y1) => Y2) => Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y1) | (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y0 @ Y2) => (subset @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y0 @ Y1)) => (in @ Y2 @ Y1)))))))) => ((!! 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@ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y2 @ Y1)) => (~ (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (setminus @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y0 @ Y1)) => (subset @ Y0 @ Y1)))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (iskpair @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f909])).
% 8.72/1.64 thf(f909,plain,(
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@ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (iskpair @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f908])).
% 8.72/1.64 thf(f908,plain,(
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@ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (iskpair @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f907])).
% 8.72/1.64 thf(f907,plain,(
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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))) => (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f906])).
% 8.72/1.64 thf(f906,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! 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@ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y0 @ Y2) => (subset @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y0 @ Y1)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y0) @ (binintersect @ Y2 @ Y1)) = (binintersect @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (in @ Y1 @ (setminus @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y2 @ Y1)) => (~ (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (setminus @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y0 @ Y1)) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => Y3)) => (((~ (in @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (symdiff @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (symdiff @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (iskpair @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))) => (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)))))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f905])).
% 8.72/1.64 thf(f905,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))) => (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0))))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f904])).
% 8.72/1.64 thf(f904,plain,(
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@ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y2 @ Y1)) => (~ (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (setminus @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y0 @ Y1)) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => Y3)) => (((~ (in @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (symdiff @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (symdiff @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (iskpair @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))) => (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f903])).
% 8.72/1.64 thf(f903,plain,(
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@ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (iskpair @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))) => (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f902])).
% 8.72/1.64 thf(f902,plain,(
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@ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (iskpair @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))) => (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f901])).
% 8.72/1.64 thf(f901,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! 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@ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! 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% 8.72/1.64 inference(boolean_simplification,[],[f900])).
% 8.72/1.64 thf(f900,plain,(
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@ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0)))) => (in @ (setunion @ Y0) @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y0 @ Y1)) = Y0))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f899])).
% 8.72/1.64 thf(f899,plain,(
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@ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! 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@ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))) => (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0)))) => (in @ (setunion @ Y0) @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y0 @ Y1)) = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (in @ (kfst @ Y1) @ Y0)))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 8.72/1.64 inference(boolean_simplification,[],[f898])).
% 8.72/1.64 thf(f898,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y0 @ Y2) => (subset @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y0 @ Y1) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y0 @ Y1)) => (in @ Y2 @ Y1)))))))) => ((!! 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@ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y2 @ Y1)) => (~ (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (setminus @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y0 @ Y1)) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => Y3)) => (((~ (in @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (symdiff @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (symdiff @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (iskpair @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))) => (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0)))) => (in @ (setunion @ Y0) @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y0 @ Y1)) = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (in @ (kfst @ Y1) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y1)))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f897])).
% 8.72/1.64 thf(f897,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y0 @ Y1)) => (((in @ Y3 @ Y0) => Y2) => (((in @ Y3 @ Y1) => Y2) => Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y1) | (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0)))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (iskpair @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))) => (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0)))) => (in @ (setunion @ Y0) @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y0 @ Y1)) = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (in @ (kfst @ Y1) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y3 @ Y1) = (kpair @ Y0 @ Y2)) => (Y3 = Y0)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f896])).
% 8.72/1.64 thf(f896,plain,(
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@ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y2 @ Y1)) => (~ (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (setminus @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y0 @ Y1)) => (subset @ Y0 @ Y1)))))) => ((!! 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@ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0)))) => (in @ (setunion @ Y0) @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y0 @ Y1)) = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (in @ (kfst @ Y1) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y3 @ Y1) = (kpair @ Y0 @ Y2)) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f895])).
% 8.72/1.64 thf(f895,plain,(
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@ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y2 @ Y1)) => (~ (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (setminus @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y0 @ Y1)) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => Y3)) => (((~ (in @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (symdiff @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (symdiff @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (iskpair @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))) => (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0)))) => (in @ (setunion @ Y0) @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y0 @ Y1)) = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (in @ (kfst @ Y1) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y3 @ Y1) = (kpair @ Y0 @ Y2)) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ emptyset))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f894])).
% 8.72/1.64 thf(f894,plain,(
% 8.72/1.64 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => Y3)) => (((~ (in @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (symdiff @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (symdiff @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (iskpair @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))) => (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0)))) => (in @ (setunion @ Y0) @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y0 @ Y1)) = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (in @ (kfst @ Y1) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y3 @ Y1) = (kpair @ Y0 @ Y2)) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y3 = Y0))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 8.72/1.64 inference(boolean_simplification,[],[f893])).
% 8.72/1.64 thf(f893,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => Y3)) => (((~ (in @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (symdiff @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (symdiff @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (iskpair @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))) => (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0)))) => (in @ (setunion @ Y0) @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y0 @ Y1)) = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (in @ (kfst @ Y1) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y3 @ Y1) = (kpair @ Y0 @ Y2)) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y3 = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y1 @ emptyset) = (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset))) => (Y2 = Y0)))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f892])).
% 8.72/1.64 thf(f892,plain,(
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@ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => Y3)) => (((~ (in @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (symdiff @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (symdiff @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (iskpair @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))) => (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0)))) => (in @ (setunion @ Y0) @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y0 @ Y1)) = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (in @ (kfst @ Y1) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y3 @ Y1) = (kpair @ Y0 @ Y2)) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y3 = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y1 @ emptyset) = (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset))) => (Y2 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y3 = Y0)))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f891])).
% 8.72/1.64 thf(f891,plain,(
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@ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y3 @ Y1) = (kpair @ Y0 @ Y2)) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y3 = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y1 @ emptyset) = (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset))) => (Y2 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y3 = Y2)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f890])).
% 8.72/1.64 thf(f890,plain,(
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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (iskpair @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))) => (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0)))) => (in @ (setunion @ Y0) @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y0 @ Y1)) = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (in @ (kfst @ Y1) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y3 @ Y1) = (kpair @ Y0 @ Y2)) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y3 = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y1 @ emptyset) = (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset))) => (Y2 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y3 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((kpair @ (kfst @ Y0) @ Y2) = Y0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((kpair @ (kfst @ Y0) @ Y2) = Y0)))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f889])).
% 8.72/1.64 thf(f889,plain,(
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@ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (iskpair @ Y0)))))))) => ((!! 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@ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0)))) => (in @ (setunion @ Y0) @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y0 @ Y1)) = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (in @ (kfst @ Y1) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y3 @ Y1) = (kpair @ Y0 @ Y2)) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y3 = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y1 @ emptyset) = (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset))) => (Y2 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y3 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((kpair @ (kfst @ Y0) @ Y2) = Y0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((kpair @ (kfst @ Y0) @ Y2) = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y1 @ Y0)) = Y0))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f888])).
% 8.72/1.64 thf(f888,plain,(
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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (iskpair @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))) => (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0)))) => (in @ (setunion @ Y0) @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y0 @ Y1)) = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (in @ (kfst @ Y1) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y3 @ Y1) = (kpair @ Y0 @ Y2)) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y3 = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y1 @ emptyset) = (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset))) => (Y2 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y3 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((kpair @ (kfst @ Y0) @ Y2) = Y0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((kpair @ (kfst @ Y0) @ Y2) = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y1 @ Y0)) = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => ((kpair @ (kfst @ Y0) @ (ksnd @ Y0)) = Y0)))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f887])).
% 8.72/1.64 thf(f887,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (in @ (dsetconstr @ Y1 @ Y0) @ (powerset @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y0 @ Y1)) => (((in @ Y3 @ Y0) => Y2) => (((in @ Y3 @ Y1) => Y2) => Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binunion @ Y1 @ Y0)) => ((in @ Y2 @ Y1) | (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0)))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (iskpair @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))) => (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0)))) => (in @ (setunion @ Y0) @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y0 @ Y1)) = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (in @ (kfst @ Y1) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y3 @ Y1) = (kpair @ Y0 @ Y2)) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y3 = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y1 @ emptyset) = (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset))) => (Y2 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y3 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((kpair @ (kfst @ Y0) @ Y2) = Y0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((kpair @ (kfst @ Y0) @ Y2) = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y1 @ Y0)) = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => ((kpair @ (kfst @ Y0) @ (ksnd @ Y0)) = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (in @ (ksnd @ Y2) @ Y0)))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f886])).
% 8.72/1.64 thf(f886,plain,(
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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! 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@ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0)))) => (in @ (setunion @ Y0) @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y0 @ Y1)) = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (in @ (kfst @ Y1) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y3 @ Y1) = (kpair @ Y0 @ Y2)) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y3 = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y1 @ emptyset) = (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset))) => (Y2 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y3 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((kpair @ (kfst @ Y0) @ Y2) = Y0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((kpair @ (kfst @ Y0) @ Y2) = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y1 @ Y0)) = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => ((kpair @ (kfst @ Y0) @ (ksnd @ Y0)) = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (in @ (ksnd @ Y2) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y2) @ (cartprod @ Y0 @ Y1)) => (in @ Y3 @ Y0)))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f885])).
% 8.72/1.64 thf(f885,plain,(
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@ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y2 @ Y1)) => (~ (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y0 @ Y2))) => ((~ (in @ Y1 @ Y2)) => (~ (in @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (~ (in @ Y1 @ (setminus @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y0 @ Y1)) => (subset @ Y0 @ Y1)))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (iskpair @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))) => (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0)))) => (in @ (setunion @ Y0) @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y0 @ Y1)) = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (in @ (kfst @ Y1) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y3 @ Y1) = (kpair @ Y0 @ Y2)) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y3 = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y1 @ emptyset) = (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset))) => (Y2 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y3 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((kpair @ (kfst @ Y0) @ Y2) = Y0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((kpair @ (kfst @ Y0) @ Y2) = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y1 @ Y0)) = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => ((kpair @ (kfst @ Y0) @ (ksnd @ Y0)) = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (in @ (ksnd @ Y2) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y2) @ (cartprod @ Y0 @ Y1)) => (in @ Y3 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y0 @ Y2)) => (in @ Y3 @ Y2)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f884])).
% 8.72/1.64 thf(f884,plain,(
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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (iskpair @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))) => (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0)))) => (in @ (setunion @ Y0) @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y0 @ Y1)) = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (in @ (kfst @ Y1) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y3 @ Y1) = (kpair @ Y0 @ Y2)) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y3 = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y1 @ emptyset) = (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset))) => (Y2 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y3 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((kpair @ (kfst @ Y0) @ Y2) = Y0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((kpair @ (kfst @ Y0) @ Y2) = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y1 @ Y0)) = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => ((kpair @ (kfst @ Y0) @ (ksnd @ Y0)) = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (in @ (ksnd @ Y2) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y2) @ (cartprod @ Y0 @ Y1)) => (in @ Y3 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y0 @ Y2)) => (in @ Y3 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kpair @ Y2 @ Y3) = (kpair @ Y2 @ Y3)))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f883])).
% 8.72/1.64 thf(f883,plain,(
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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))) => (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0)))) => (in @ (setunion @ Y0) @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y0 @ Y1)) = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (in @ (kfst @ Y1) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y3 @ Y1) = (kpair @ Y0 @ Y2)) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y3 = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y1 @ emptyset) = (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset))) => (Y2 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y3 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((kpair @ (kfst @ Y0) @ Y2) = Y0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((kpair @ (kfst @ Y0) @ Y2) = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y1 @ Y0)) = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => ((kpair @ (kfst @ Y0) @ (ksnd @ Y0)) = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (in @ (ksnd @ Y2) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y2) @ (cartprod @ Y0 @ Y1)) => (in @ Y3 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y0 @ Y2)) => (in @ Y3 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kpair @ Y2 @ Y3) = (kpair @ Y2 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kfst @ (kpair @ Y0 @ Y3)) = Y0))))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f882])).
% 8.72/1.64 thf(f882,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))) => (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! 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@ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0)))) => (in @ (setunion @ Y0) @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y0 @ Y1)) = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (in @ (kfst @ Y1) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y3 @ Y1) = (kpair @ Y0 @ Y2)) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y3 = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y1 @ emptyset) = (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset))) => (Y2 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y3 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((kpair @ (kfst @ Y0) @ Y2) = Y0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((kpair @ (kfst @ Y0) @ Y2) = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y1 @ Y0)) = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => ((kpair @ (kfst @ Y0) @ (ksnd @ Y0)) = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (in @ (ksnd @ Y2) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y2) @ (cartprod @ Y0 @ Y1)) => (in @ Y3 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y0 @ Y2)) => (in @ Y3 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kpair @ Y2 @ Y3) = (kpair @ Y2 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kfst @ (kpair @ Y0 @ Y3)) = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((ksnd @ (kpair @ Y0 @ Y3)) = Y3))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f881])).
% 8.72/1.64 thf(f881,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (in @ (ksnd @ Y2) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y2) @ (cartprod @ Y0 @ Y1)) => (in @ Y3 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y0 @ Y2)) => (in @ Y3 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kpair @ Y2 @ Y3) = (kpair @ Y2 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kfst @ (kpair @ Y0 @ Y3)) = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((ksnd @ (kpair @ Y0 @ Y3)) = Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => ((kpair @ (kfst @ Y2) @ (ksnd @ Y2)) = Y2)))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f880])).
% 8.72/1.64 thf(f880,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (in @ (ksnd @ Y2) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y2) @ (cartprod @ Y0 @ Y1)) => (in @ Y3 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y0 @ Y2)) => (in @ Y3 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kpair @ Y2 @ Y3) = (kpair @ Y2 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kfst @ (kpair @ Y0 @ Y3)) = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((ksnd @ (kpair @ Y0 @ Y3)) = Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => ((kpair @ (kfst @ Y2) @ (ksnd @ Y2)) = Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((Y2 @ Y1 @ Y4) => (in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y0 @ Y3 @ Y2))))))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f879])).
% 8.72/1.64 thf(f879,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! 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@ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y3 @ Y1) = (kpair @ Y0 @ Y2)) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y3 = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y1 @ emptyset) = (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset))) => (Y2 = Y0)))))))) => ((!! 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@ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (in @ (ksnd @ Y2) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y2) @ (cartprod @ Y0 @ Y1)) => (in @ Y3 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y0 @ Y2)) => (in @ Y3 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kpair @ Y2 @ Y3) = (kpair @ Y2 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kfst @ (kpair @ Y0 @ Y3)) = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((ksnd @ (kpair @ Y0 @ Y3)) = Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => ((kpair @ (kfst @ Y2) @ (ksnd @ Y2)) = Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((Y2 @ Y1 @ Y4) => (in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y0 @ Y3 @ Y2))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y1 @ Y0 @ Y2) @ (cartprod @ Y1 @ Y0)))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f878])).
% 8.72/1.64 thf(f878,plain,(
% 8.72/1.64 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => ((kpair @ (kfst @ Y2) @ (ksnd @ Y2)) = Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((Y2 @ Y1 @ Y4) => (in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y0 @ Y3 @ Y2))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y1 @ Y0 @ Y2) @ (cartprod @ Y1 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y0 @ Y1 @ Y2) @ (cartprod @ Y0 @ Y1)))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f877])).
% 8.72/1.64 thf(f877,plain,(
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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y3 @ Y1) = (kpair @ Y0 @ Y2)) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y3 = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y1 @ emptyset) = (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset))) => (Y2 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y3 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((kpair @ (kfst @ Y0) @ Y2) = Y0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((kpair @ (kfst @ Y0) @ Y2) = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y1 @ Y0)) = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => ((kpair @ (kfst @ Y0) @ (ksnd @ Y0)) = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (in @ (ksnd @ Y2) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y2) @ (cartprod @ Y0 @ Y1)) => (in @ Y3 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y0 @ Y2)) => (in @ Y3 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kpair @ Y2 @ Y3) = (kpair @ Y2 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kfst @ (kpair @ Y0 @ Y3)) = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((ksnd @ (kpair @ Y0 @ Y3)) = Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => ((kpair @ (kfst @ Y2) @ (ksnd @ Y2)) = Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((Y2 @ Y1 @ Y4) => (in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y0 @ Y3 @ Y2))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y1 @ Y0 @ Y2) @ (cartprod @ Y1 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y0 @ Y1 @ Y2) @ (cartprod @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y3 @ Y1 @ Y2)) => (Y2 @ Y0 @ Y4)))))))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.64 inference(boolean_simplification,[],[f876])).
% 8.72/1.64 thf(f876,plain,(
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@ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! 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% 8.72/1.64 inference(boolean_simplification,[],[f874])).
% 8.72/1.64 thf(f874,plain,(
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@ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y0) @ (dpsetconstr @ Y2 @ Y3 @ Y1)) => (in @ Y4 @ Y2)))))))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y2) @ (dpsetconstr @ Y3 @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y3) @ (dpsetconstr @ Y2 @ Y1 @ Y0)) => (Y0 @ Y4 @ Y3)))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.65 inference(boolean_simplification,[],[f873])).
% 8.72/1.65 thf(f873,plain,(
% 8.72/1.65 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! 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@ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0)))) => (in @ (setunion @ Y0) @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y0 @ Y1)) = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (in @ (kfst @ Y1) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y3 @ Y1) = (kpair @ Y0 @ Y2)) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y3 = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y1 @ emptyset) = (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset))) => (Y2 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y3 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((kpair @ (kfst @ Y0) @ Y2) = Y0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((kpair @ (kfst @ Y0) @ Y2) = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y1 @ Y0)) = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => ((kpair @ (kfst @ Y0) @ (ksnd @ Y0)) = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (in @ (ksnd @ Y2) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y2) @ (cartprod @ Y0 @ Y1)) => (in @ Y3 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y0 @ Y2)) => (in @ Y3 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kpair @ Y2 @ Y3) = (kpair @ Y2 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kfst @ (kpair @ Y0 @ Y3)) = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((ksnd @ (kpair @ Y0 @ Y3)) = Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => ((kpair @ (kfst @ Y2) @ (ksnd @ Y2)) = Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((Y2 @ Y1 @ Y4) => (in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y0 @ Y3 @ Y2))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y1 @ Y0 @ Y2) @ (cartprod @ Y1 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y0 @ Y1 @ Y2) @ (cartprod @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y3 @ Y1 @ Y2)) => (Y2 @ Y0 @ Y4)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y0) @ (dpsetconstr @ Y2 @ Y3 @ Y1)) => (in @ Y4 @ Y2)))))))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y2) @ (dpsetconstr @ Y3 @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y3) @ (dpsetconstr @ Y2 @ Y1 @ Y0)) => (Y0 @ Y4 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y1 @ (cartprod @ Y0 @ Y2)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1))))))))))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.65 inference(boolean_simplification,[],[f872])).
% 8.72/1.65 thf(f872,plain,(
% 8.72/1.65 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (iskpair @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => ((!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))) => (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0)))) => (in @ (setunion @ Y0) @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y0 @ Y1)) = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (in @ (kfst @ Y1) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y3 @ Y1) = (kpair @ Y0 @ Y2)) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y3 = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y1 @ emptyset) = (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset))) => (Y2 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y3 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((kpair @ (kfst @ Y0) @ Y2) = Y0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((kpair @ (kfst @ Y0) @ Y2) = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y1 @ Y0)) = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => ((kpair @ (kfst @ Y0) @ (ksnd @ Y0)) = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (in @ (ksnd @ Y2) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y2) @ (cartprod @ Y0 @ Y1)) => (in @ Y3 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y0 @ Y2)) => (in @ Y3 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kpair @ Y2 @ Y3) = (kpair @ Y2 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kfst @ (kpair @ Y0 @ Y3)) = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((ksnd @ (kpair @ Y0 @ Y3)) = Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => ((kpair @ (kfst @ Y2) @ (ksnd @ Y2)) = Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((Y2 @ Y1 @ Y4) => (in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y0 @ Y3 @ Y2))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y1 @ Y0 @ Y2) @ (cartprod @ Y1 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y0 @ Y1 @ Y2) @ (cartprod @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y3 @ Y1 @ Y2)) => (Y2 @ Y0 @ Y4)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y0) @ (dpsetconstr @ Y2 @ Y3 @ Y1)) => (in @ Y4 @ Y2)))))))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y2) @ (dpsetconstr @ Y3 @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y3) @ (dpsetconstr @ Y2 @ Y1 @ Y0)) => (Y0 @ Y4 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y1 @ (cartprod @ Y0 @ Y2)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1))))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y1 @ Y0)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setunion @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))) @ Y0))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.65 inference(boolean_simplification,[],[f871])).
% 8.72/1.65 thf(f871,plain,(
% 8.72/1.65 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! 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@ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => ((kpair @ (kfst @ Y2) @ (ksnd @ Y2)) = Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((Y2 @ Y1 @ Y4) => (in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y0 @ Y3 @ Y2))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y1 @ Y0 @ Y2) @ (cartprod @ Y1 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y0 @ Y1 @ Y2) @ (cartprod @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y3 @ Y1 @ Y2)) => (Y2 @ Y0 @ Y4)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y0) @ (dpsetconstr @ Y2 @ Y3 @ Y1)) => (in @ Y4 @ Y2)))))))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y2) @ (dpsetconstr @ Y3 @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y3) @ (dpsetconstr @ Y2 @ Y1 @ Y0)) => (Y0 @ Y4 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y1 @ (cartprod @ Y0 @ Y2)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1))))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y1 @ Y0)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setunion @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))) @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y0 @ Y1)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setunion @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))) @ Y1))))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 8.72/1.65 inference(boolean_simplification,[],[f870])).
% 8.72/1.65 thf(f870,plain,(
% 8.72/1.65 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! 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@ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0)))) => (in @ (setunion @ Y0) @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y0 @ Y1)) = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (in @ (kfst @ Y1) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y3 @ Y1) = (kpair @ Y0 @ Y2)) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y3 = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y1 @ emptyset) = (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset))) => (Y2 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y3 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((kpair @ (kfst @ Y0) @ Y2) = Y0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((kpair @ (kfst @ Y0) @ Y2) = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y1 @ Y0)) = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => ((kpair @ (kfst @ Y0) @ (ksnd @ Y0)) = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (in @ (ksnd @ Y2) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y2) @ (cartprod @ Y0 @ Y1)) => (in @ Y3 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y0 @ Y2)) => (in @ Y3 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kpair @ Y2 @ Y3) = (kpair @ Y2 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kfst @ (kpair @ Y0 @ Y3)) = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((ksnd @ (kpair @ Y0 @ Y3)) = Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => ((kpair @ (kfst @ Y2) @ (ksnd @ Y2)) = Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((Y2 @ Y1 @ Y4) => (in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y0 @ Y3 @ Y2))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y1 @ Y0 @ Y2) @ (cartprod @ Y1 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y0 @ Y1 @ Y2) @ (cartprod @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y3 @ Y1 @ Y2)) => (Y2 @ Y0 @ Y4)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y0) @ (dpsetconstr @ Y2 @ Y3 @ Y1)) => (in @ Y4 @ Y2)))))))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y2) @ (dpsetconstr @ Y3 @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y3) @ (dpsetconstr @ Y2 @ Y1 @ Y0)) => (Y0 @ Y4 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y1 @ (cartprod @ Y0 @ Y2)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1))))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y1 @ Y0)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setunion @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))) @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y0 @ Y1)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setunion @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))) @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (funcSet @ Y2 @ Y1)) => ((subset @ Y0 @ (cartprod @ Y2 @ Y1)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0)))))))))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.65 inference(boolean_simplification,[],[f869])).
% 8.72/1.65 thf(f869,plain,(
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@ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y0) @ (dpsetconstr @ Y2 @ Y3 @ Y1)) => (in @ Y4 @ Y2)))))))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y2) @ (dpsetconstr @ Y3 @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y3) @ (dpsetconstr @ Y2 @ Y1 @ Y0)) => (Y0 @ Y4 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y1 @ (cartprod @ Y0 @ Y2)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1))))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y1 @ Y0)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setunion @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))) @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y0 @ Y1)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setunion @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))) @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (funcSet @ Y2 @ Y1)) => ((subset @ Y0 @ (cartprod @ Y2 @ Y1)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0)))))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y2 @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setunion @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y1)))) @ Y0))))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.65 inference(boolean_simplification,[],[f868])).
% 8.72/1.65 thf(f868,plain,(
% 8.72/1.65 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! 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@ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0)))) => (in @ (setunion @ Y0) @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y0 @ Y1)) = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (in @ (kfst @ Y1) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y3 @ Y1) = (kpair @ Y0 @ Y2)) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y3 = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y1 @ emptyset) = (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset))) => (Y2 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y3 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((kpair @ (kfst @ Y0) @ Y2) = Y0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((kpair @ (kfst @ Y0) @ Y2) = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y1 @ Y0)) = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => ((kpair @ (kfst @ Y0) @ (ksnd @ Y0)) = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (in @ (ksnd @ Y2) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y2) @ (cartprod @ Y0 @ Y1)) => (in @ Y3 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y0 @ Y2)) => (in @ Y3 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kpair @ Y2 @ Y3) = (kpair @ Y2 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kfst @ (kpair @ Y0 @ Y3)) = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((ksnd @ (kpair @ Y0 @ Y3)) = Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => ((kpair @ (kfst @ Y2) @ (ksnd @ Y2)) = Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((Y2 @ Y1 @ Y4) => (in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y0 @ Y3 @ Y2))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y1 @ Y0 @ Y2) @ (cartprod @ Y1 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y0 @ Y1 @ Y2) @ (cartprod @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y3 @ Y1 @ Y2)) => (Y2 @ Y0 @ Y4)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y0) @ (dpsetconstr @ Y2 @ Y3 @ Y1)) => (in @ Y4 @ Y2)))))))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y2) @ (dpsetconstr @ Y3 @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y3) @ (dpsetconstr @ Y2 @ Y1 @ Y0)) => (Y0 @ Y4 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y1 @ (cartprod @ Y0 @ Y2)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1))))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y1 @ Y0)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setunion @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))) @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y0 @ Y1)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setunion @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))) @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (funcSet @ Y2 @ Y1)) => ((subset @ Y0 @ (cartprod @ Y2 @ Y1)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0)))))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y2 @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setunion @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y1)))) @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y0 @ (cartprod @ Y1 @ Y2)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0))))))))))) => (in @ Y0 @ (funcSet @ Y1 @ Y2))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.65 inference(boolean_simplification,[],[f867])).
% 8.72/1.65 thf(f867,plain,(
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@ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y3 @ Y1) = (kpair @ Y0 @ Y2)) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y3 = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y1 @ emptyset) = (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset))) => (Y2 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y3 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((kpair @ (kfst @ Y0) @ Y2) = Y0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: ((kpair @ (kfst @ Y0) @ Y2) = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y1 @ Y0)) = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => ((kpair @ (kfst @ Y0) @ (ksnd @ Y0)) = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (in @ (ksnd @ Y2) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y2) @ (cartprod @ Y0 @ Y1)) => (in @ Y3 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y0 @ Y2)) => (in @ Y3 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kpair @ Y2 @ Y3) = (kpair @ Y2 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kfst @ (kpair @ Y0 @ Y3)) = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((ksnd @ (kpair @ Y0 @ Y3)) = Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => ((kpair @ (kfst @ Y2) @ (ksnd @ Y2)) = Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((Y2 @ Y1 @ Y4) => (in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y0 @ Y3 @ Y2))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y1 @ Y0 @ Y2) @ (cartprod @ Y1 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y0 @ Y1 @ Y2) @ (cartprod @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y3 @ Y1 @ Y2)) => (Y2 @ Y0 @ Y4)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y0) @ (dpsetconstr @ Y2 @ Y3 @ Y1)) => (in @ Y4 @ Y2)))))))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y2) @ (dpsetconstr @ Y3 @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y3) @ (dpsetconstr @ Y2 @ Y1 @ Y0)) => (Y0 @ Y4 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y1 @ (cartprod @ Y0 @ Y2)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1))))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y1 @ Y0)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setunion @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))) @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y0 @ Y1)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setunion @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))) @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (funcSet @ Y2 @ Y1)) => ((subset @ Y0 @ (cartprod @ Y2 @ Y1)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0)))))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y2 @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setunion @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y1)))) @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y0 @ (cartprod @ Y1 @ Y2)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0))))))))))) => (in @ Y0 @ (funcSet @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y1 @ Y3) @ Y2)))) => ((subset @ (dpsetconstr @ Y0 @ Y2 @ (^[Y3 : $i]: (= @ (Y1 @ Y3)))) @ (cartprod @ Y0 @ Y2)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ (dpsetconstr @ Y0 @ Y2 @ (^[Y6 : $i]: (= @ (Y1 @ Y6)))))))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ (dpsetconstr @ Y0 @ Y2 @ (^[Y6 : $i]: (= @ (Y1 @ Y6)))))))))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (Y1 @ Y3) @ Y0)))) => ((subset @ (dpsetconstr @ Y2 @ Y0 @ (^[Y3 : $i]: (= @ (Y1 @ Y3)))) @ (cartprod @ Y2 @ Y0)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ (dpsetconstr @ Y2 @ Y0 @ (^[Y6 : $i]: (= @ (Y1 @ Y6)))))))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ (dpsetconstr @ Y2 @ Y0 @ (^[Y6 : $i]: (= @ (Y1 @ Y6)))))))))))))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.65 inference(boolean_simplification,[],[f865])).
% 8.72/1.65 thf(f865,plain,(
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@ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ Y1) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (~ (subset @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ Y0)) => (~ (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => ((kpair @ (kfst @ Y2) @ (ksnd @ Y2)) = Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((Y2 @ Y1 @ Y4) => (in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y0 @ Y3 @ Y2))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y1 @ Y0 @ Y2) @ (cartprod @ Y1 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y0 @ Y1 @ Y2) @ (cartprod @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y3 @ Y1 @ Y2)) => (Y2 @ Y0 @ Y4)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y0) @ (dpsetconstr @ Y2 @ Y3 @ Y1)) => (in @ Y4 @ Y2)))))))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y2) @ (dpsetconstr @ Y3 @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y3) @ (dpsetconstr @ Y2 @ Y1 @ Y0)) => (Y0 @ Y4 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y1 @ (cartprod @ Y0 @ Y2)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1))))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y1 @ Y0)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setunion @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))) @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y2 @ (cartprod @ Y0 @ Y1)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y2))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setunion @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))) @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (funcSet @ Y2 @ Y1)) => ((subset @ Y0 @ (cartprod @ Y2 @ Y1)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y1 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0)))))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y2 @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setunion @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y1)))) @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((subset @ Y0 @ (cartprod @ Y1 @ Y2)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y0))))))))))) => (in @ Y0 @ (funcSet @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y1 @ Y3) @ Y2)))) => ((subset @ (dpsetconstr @ Y0 @ Y2 @ (^[Y3 : $i]: (= @ (Y1 @ Y3)))) @ (cartprod @ Y0 @ Y2)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ (dpsetconstr @ Y0 @ Y2 @ (^[Y6 : $i]: (= @ (Y1 @ Y6)))))))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y2 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ (dpsetconstr @ Y0 @ Y2 @ (^[Y6 : $i]: (= @ (Y1 @ Y6)))))))))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (Y1 @ Y3) @ Y0)))) => ((subset @ (dpsetconstr @ Y2 @ Y0 @ (^[Y3 : $i]: (= @ (Y1 @ Y3)))) @ (cartprod @ Y2 @ Y0)) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ (dpsetconstr @ Y2 @ Y0 @ (^[Y6 : $i]: (= @ (Y1 @ Y6)))))))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ (dpsetconstr @ Y2 @ Y0 @ (^[Y6 : $i]: (= @ (Y1 @ Y6)))))))))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y1 @ Y3) @ Y2)))) => (in @ (dpsetconstr @ Y0 @ Y2 @ (^[Y3 : $i]: (= @ (Y1 @ Y3)))) @ (funcSet @ Y0 @ Y2))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.65 inference(boolean_simplification,[],[f864])).
% 8.72/1.65 thf(f864,plain,(
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@ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (~ (emptyset = (dsetconstr @ Y0 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y1 @ Y3) @ Y2)))) => (in @ (dpsetconstr @ Y0 @ Y2 @ (^[Y3 : $i]: (= @ (Y1 @ Y3)))) @ (funcSet @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ (cartprod @ Y0 @ Y1)) => (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ (kpair @ Y4 @ Y5) @ Y2) => (Y3 @ (kpair @ Y4 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (Y3 @ Y4)))))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ (cartprod @ Y0 @ Y1)) => (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ (kpair @ Y4 @ Y5) @ Y2) => (Y3 @ (kpair @ Y4 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (Y3 @ Y4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.65 inference(beta_eta_normalization,[],[f863])).
% 8.72/1.65 thf(f863,plain,(
% 8.72/1.65 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y1 @ Y0) | (Y2 = Y1)) = (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5) => (Y4 = Y5)))))))) @ (^[Y3 : $i]: (Y0 @ Y2 @ Y3)))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y3 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))))))) & (~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y4)))))) & (in @ Y4 @ Y1)) & (in @ Y3 @ Y2))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3))))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))))))) @ (^[Y1 : $i]: (Y0 @ Y1))) => (Y0 @ (descr @ (^[Y1 : $i]: (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3)))) => (in @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3)))) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))))))) @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))))))) @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) = (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (~ (emptyset = Y1))) @ Y0) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => ((^[Y3 : $i]: (~ (emptyset = Y3))) @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => ((^[Y1 : $i]: (~ (emptyset = Y1))) @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (setadjoin @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y1 @ Y2) => (in @ Y0 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))))))) @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (~ (emptyset = Y1))) @ Y0) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y1 @ (setadjoin @ Y0 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (((dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) = emptyset) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y1 @ Y3) @ Y2)))) => (in @ ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i > $i]: (dpsetconstr @ Y3 @ Y4 @ (^[Y6 : $i]: ((^[Y7 : $i]: ((Y5 @ Y6) = Y7)))))))))) @ Y0 @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3))) @ (funcSet @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y0 @ Y1 @ Y2) => (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ (kpair @ Y4 @ Y5) @ Y2) => (Y3 @ (kpair @ Y4 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (Y3 @ Y4)))))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y0 @ Y1 @ Y2) => (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ (kpair @ Y4 @ Y5) @ Y2) => (Y3 @ (kpair @ Y4 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (Y3 @ Y4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 8.72/1.65 inference(definition_unfolding,[],[f818,f722,f749,f773,f663,f650,f776,f766,f736,f827,f681,f687,f828,f629,f686,f678,f829,f664,f633,f779,f698,f830,f817,f682,f670,f731,f831,f832,f833,f737,f767,f703,f807,f697,f791,f777,f676,f793,f783,f739,f631,f774,f834,f835,f675,f672,f757,f628,f652,f679,f732,f810,f764,f688,f665,f658,f693,f654,f735,f780,f637,f836,f837,f838,f645,f769,f839,f840,f738,f701,f708,f666,f809,f841,f842,f638,f808,f636,f794,f685,f742,f802,f667,f796,f782,f622,f662,f707,f657,f640,f621,f761,f710,f784,f630,f649,f717,f797,f799,f789,f643,f733,f744,f819,f753,f760,f790,f661,f725,f815,f646,f721,f689,f785,f806,f651,f671,f624,f734,f695,f684,f786,f778,f813,f647,f655,f752,f775,f660,f743,f768,f644,f788,f763,f730,f627,f706,f656,f719,f755,f746,f702,f669,f699,f805,f720,f826,f781,f705,f824,f642,f704,f626,f715,f843,f845,f846,f847,f653,f772,f848,f849,f740,f800,f673,f713,f745,f692,f798,f724,f632,f659,f850,f822,f754,f758,f727,f677,f762,f825,f729,f623,f816,f741,f851,f700,f821,f620,f795,f853,f854,f855,f856,f857,f858,f859,f860,f861,f862,f634])).
% 8.72/1.65 thf(f634,plain,(
% 8.72/1.65 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f480])).
% 8.72/1.65 thf(f480,plain,(
% 8.72/1.65 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f479])).
% 8.72/1.65 thf(f479,plain,(
% 8.72/1.65 ((^[X0 : $i, X1 : $i, X2 : $i] : (subset @ X2 @ (cartprod @ X0 @ X1))) = breln)),
% 8.72/1.65 inference(rectify,[],[f186])).
% 8.72/1.65 thf(f186,axiom,(
% 8.72/1.65 ((^[X3 : $i, X4 : $i, X5 : $i] : (subset @ X5 @ (cartprod @ X3 @ X4))) = breln)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln)).
% 8.72/1.65 thf(f862,plain,(
% 8.72/1.65 (brelnall1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y0 @ Y1 @ Y2) => (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ (kpair @ Y4 @ Y5) @ Y2) => (Y3 @ (kpair @ Y4 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (Y3 @ Y4)))))))))))))))),
% 8.72/1.65 inference(definition_unfolding,[],[f748,f634])).
% 8.72/1.65 thf(f748,plain,(
% 8.72/1.65 (brelnall1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((breln @ Y0 @ Y1 @ Y2) => (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ (kpair @ Y4 @ Y5) @ Y2) => (Y3 @ (kpair @ Y4 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (Y3 @ Y4)))))))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f575])).
% 8.72/1.65 thf(f575,plain,(
% 8.72/1.65 (brelnall1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((breln @ Y0 @ Y1 @ Y2) => (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ (kpair @ Y4 @ Y5) @ Y2) => (Y3 @ (kpair @ Y4 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (Y3 @ Y4)))))))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f574])).
% 8.72/1.65 thf(f574,plain,(
% 8.72/1.65 (brelnall1 = ! [X0,X1,X2] : ((breln @ X2 @ X1 @ X0) => ! [X3 : $i > $o] : (! [X4] : ((in @ X4 @ X2) => ! [X5] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X0) => (X3 @ (kpair @ X4 @ X5))))) => ! [X6] : ((in @ X6 @ X0) => (X3 @ X6)))))),
% 8.72/1.65 inference(rectify,[],[f206])).
% 8.72/1.65 thf(f206,axiom,(
% 8.72/1.65 (brelnall1 = ! [X12,X4,X3] : ((breln @ X3 @ X4 @ X12) => ! [X0 : $i > $o] : (! [X1] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => ((in @ (kpair @ X1 @ X2) @ X12) => (X0 @ (kpair @ X1 @ X2))))) => ! [X1] : ((in @ X1 @ X12) => (X0 @ X1)))))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',brelnall1)).
% 8.72/1.65 thf(f861,plain,(
% 8.72/1.65 (lam2p = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y1 @ Y3) @ Y2)))) => (in @ ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i > $i]: (dpsetconstr @ Y3 @ Y4 @ (^[Y6 : $i]: ((^[Y7 : $i]: ((Y5 @ Y6) = Y7)))))))))) @ Y0 @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3))) @ (funcSet @ Y0 @ Y2))))))))))),
% 8.72/1.65 inference(definition_unfolding,[],[f803,f635])).
% 8.72/1.65 thf(f635,plain,(
% 8.72/1.65 (lam = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i]: (dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $i]: ((Y2 @ Y3) = Y4)))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f347])).
% 8.72/1.65 thf(f347,plain,(
% 8.72/1.65 (lam = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i]: (dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $i]: ((Y2 @ Y3) = Y4)))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f346])).
% 8.72/1.65 thf(f346,plain,(
% 8.72/1.65 ((^[X0 : $i, X1 : $i, X2 : $i > $i] : (dpsetconstr @ X0 @ X1 @ (^[X3 : $i, X4 : $i] : (((X2 @ X3) = X4))))) = lam)),
% 8.72/1.65 inference(rectify,[],[f203])).
% 8.72/1.65 thf(f203,axiom,(
% 8.72/1.65 ((^[X3 : $i, X4 : $i, X13 : $i > $i] : (dpsetconstr @ X3 @ X4 @ (^[X1 : $i, X2 : $i] : (((X13 @ X1) = X2))))) = lam)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lam)).
% 8.72/1.65 thf(f803,plain,(
% 8.72/1.65 (lam2p = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y1 @ Y3) @ Y2)))) => (in @ (lam @ Y0 @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3))) @ (funcSet @ Y0 @ Y2))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f235])).
% 8.72/1.65 thf(f235,plain,(
% 8.72/1.65 (lam2p = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y1 @ Y3) @ Y2)))) => (in @ (lam @ Y0 @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3))) @ (funcSet @ Y0 @ Y2))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f234])).
% 8.72/1.65 thf(f234,plain,(
% 8.72/1.65 (lam2p = ! [X0,X1 : $i > $i,X2] : (! [X3] : ((in @ X3 @ X2) => (in @ (X1 @ X3) @ X0)) => (in @ (lam @ X2 @ X0 @ (^[X4 : $i] : (X1 @ X4))) @ (funcSet @ X2 @ X0))))),
% 8.72/1.65 inference(rectify,[],[f205])).
% 8.72/1.65 thf(f205,axiom,(
% 8.72/1.65 (lam2p = ! [X4,X13 : $i > $i,X3] : (! [X1] : ((in @ X1 @ X3) => (in @ (X13 @ X1) @ X4)) => (in @ (lam @ X3 @ X4 @ (^[X1 : $i] : (X13 @ X1))) @ (funcSet @ X3 @ X4))))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lam2p)).
% 8.72/1.65 thf(f860,plain,(
% 8.72/1.65 (lamp = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (Y1 @ Y3) @ Y0)))) => ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (subset @ Y8 @ (cartprod @ Y6 @ Y7))))))) @ Y3 @ Y4 @ Y5) & (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y3) => ((^[Y7 : $i]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: (?? @ $i @ (^[Y10 : $i]: ((in @ Y10 @ Y9) & ((setadjoin @ Y10 @ emptyset) = Y9))))) @ (dsetconstr @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y4 @ (^[Y7 : $i]: (in @ (kpair @ Y6 @ Y7) @ Y5)))))))))))) @ Y2 @ Y0 @ ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i > $i]: (dpsetconstr @ Y3 @ Y4 @ (^[Y6 : $i]: ((^[Y7 : $i]: ((Y5 @ Y6) = Y7)))))))))) @ Y2 @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3))))))))))))),
% 8.72/1.65 inference(definition_unfolding,[],[f771,f852,f635])).
% 8.72/1.65 thf(f852,plain,(
% 8.72/1.65 (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y0 @ Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((^[Y4 : $i]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ Y6) & ((setadjoin @ Y7 @ emptyset) = Y6))))) @ (dsetconstr @ Y4 @ (^[Y6 : $i]: (Y5 @ Y6))))))) @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))))))))))),
% 8.72/1.65 inference(definition_unfolding,[],[f811,f634,f844])).
% 8.72/1.65 thf(f844,plain,(
% 8.72/1.65 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) & ((setadjoin @ Y3 @ emptyset) = Y2))))) @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 8.72/1.65 inference(definition_unfolding,[],[f804,f765])).
% 8.72/1.65 thf(f765,plain,(
% 8.72/1.65 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f221])).
% 8.72/1.65 thf(f221,plain,(
% 8.72/1.65 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0))))))),
% 8.72/1.65 inference(fool_elimination,[],[f220])).
% 8.72/1.65 thf(f220,plain,(
% 8.72/1.65 (singleton = (^[X0 : $i] : (? [X1] : (((setadjoin @ X1 @ emptyset) = X0) & (in @ X1 @ X0)))))),
% 8.72/1.65 inference(rectify,[],[f156])).
% 8.72/1.65 thf(f156,axiom,(
% 8.72/1.65 (singleton = (^[X3 : $i] : (? [X1] : (((setadjoin @ X1 @ emptyset) = X3) & (in @ X1 @ X3)))))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton)).
% 8.72/1.65 thf(f804,plain,(
% 8.72/1.65 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f261])).
% 8.72/1.65 thf(f261,plain,(
% 8.72/1.65 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f260])).
% 8.72/1.65 thf(f260,plain,(
% 8.72/1.65 (ex1 = (^[X0 : $i, X1 : $i > $o] : (singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))))))),
% 8.72/1.65 inference(rectify,[],[f158])).
% 8.72/1.65 thf(f158,axiom,(
% 8.72/1.65 (ex1 = (^[X3 : $i, X0 : $i > $o] : (singleton @ (dsetconstr @ X3 @ (^[X1 : $i] : (X0 @ X1))))))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1)).
% 8.72/1.65 thf(f811,plain,(
% 8.72/1.65 (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((breln @ Y0 @ Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (ex1 @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f255])).
% 8.72/1.65 thf(f255,plain,(
% 8.72/1.65 (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((breln @ Y0 @ Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (ex1 @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f254])).
% 8.72/1.65 thf(f254,plain,(
% 8.72/1.65 (func = (^[X0 : $i, X1 : $i, X2 : $i] : (! [X3] : ((in @ X3 @ X0) => (ex1 @ X1 @ (^[X4 : $i] : (in @ (kpair @ X3 @ X4) @ X2)))) & (breln @ X0 @ X1 @ X2))))),
% 8.72/1.65 inference(rectify,[],[f194])).
% 8.72/1.65 thf(f194,axiom,(
% 8.72/1.65 (func = (^[X3 : $i, X4 : $i, X12 : $i] : (! [X1] : ((in @ X1 @ X3) => (ex1 @ X4 @ (^[X2 : $i] : (in @ (kpair @ X1 @ X2) @ X12)))) & (breln @ X3 @ X4 @ X12))))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',func)).
% 8.72/1.65 thf(f771,plain,(
% 8.72/1.65 (lamp = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (Y1 @ Y3) @ Y0)))) => (func @ Y2 @ Y0 @ (lam @ Y2 @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3))))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f508])).
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% 8.72/1.65 inference(rectify,[],[f204])).
% 8.72/1.65 thf(f204,axiom,(
% 8.72/1.65 (lamp = ! [X3,X13 : $i > $i,X4] : (! [X1] : ((in @ X1 @ X3) => (in @ (X13 @ X1) @ X4)) => (func @ X3 @ X4 @ (lam @ X3 @ X4 @ (^[X1 : $i] : (X13 @ X1))))))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lamp)).
% 8.72/1.65 thf(f859,plain,(
% 8.72/1.65 (lamProp = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y1 @ Y3) @ Y2)))) => ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (subset @ Y8 @ (cartprod @ Y6 @ Y7))))))) @ Y3 @ Y4 @ Y5) & (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y3) => ((^[Y7 : $i]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: (?? @ $i @ (^[Y10 : $i]: ((in @ Y10 @ Y9) & ((setadjoin @ Y10 @ emptyset) = Y9))))) @ (dsetconstr @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y4 @ (^[Y7 : $i]: (in @ (kpair @ Y6 @ Y7) @ Y5)))))))))))) @ Y0 @ Y2 @ (dpsetconstr @ Y0 @ Y2 @ (^[Y3 : $i]: ((^[Y4 : $i]: ((Y1 @ Y3) = Y4))))))))))))))),
% 8.72/1.65 inference(definition_unfolding,[],[f801,f852])).
% 8.72/1.65 thf(f801,plain,(
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% 8.72/1.65 inference(cnf_transformation,[],[f377])).
% 8.72/1.65 thf(f377,plain,(
% 8.72/1.65 (lamProp = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (Y1 @ Y3) @ Y2)))) => (func @ Y0 @ Y2 @ (dpsetconstr @ Y0 @ Y2 @ (^[Y3 : $i]: ((^[Y4 : $i]: ((Y1 @ Y3) = Y4))))))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f376])).
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% 8.72/1.65 inference(rectify,[],[f202])).
% 8.72/1.65 thf(f202,axiom,(
% 8.72/1.65 (lamProp = ! [X4,X13 : $i > $i,X3] : (! [X1] : ((in @ X1 @ X3) => (in @ (X13 @ X1) @ X4)) => (func @ X3 @ X4 @ (dpsetconstr @ X3 @ X4 @ (^[X1 : $i, X2 : $i] : (((X13 @ X1) = X2)))))))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lamProp)).
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% 8.72/1.65 inference(definition_unfolding,[],[f641,f852])).
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% 8.72/1.65 (funcinfuncset = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y1 @ Y2 @ Y0) => (in @ Y0 @ (funcSet @ Y1 @ Y2))))))))))),
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% 8.72/1.65 thf(f467,plain,(
% 8.72/1.65 (funcinfuncset = ! [X0,X1,X2] : ((func @ X1 @ X0 @ X2) => (in @ X2 @ (funcSet @ X1 @ X0))))),
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% 8.72/1.65 thf(f201,axiom,(
% 8.72/1.65 (funcinfuncset = ! [X4,X3,X13] : ((func @ X3 @ X4 @ X13) => (in @ X13 @ (funcSet @ X3 @ X4))))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcinfuncset)).
% 8.72/1.65 thf(f857,plain,(
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% 8.72/1.65 inference(definition_unfolding,[],[f639,f812])).
% 8.72/1.65 thf(f812,plain,(
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% 8.72/1.65 inference(cnf_transformation,[],[f383])).
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% 8.72/1.65 thf(f382,plain,(
% 8.72/1.65 ((^[X0 : $i, X1 : $i, X2 : $i, X3 : $i] : (setunion @ (dsetconstr @ X1 @ (^[X4 : $i] : (in @ (kpair @ X3 @ X4) @ X2))))) = ap)),
% 8.72/1.65 inference(rectify,[],[f197])).
% 8.72/1.65 thf(f197,axiom,(
% 8.72/1.65 ((^[X3 : $i, X4 : $i, X13 : $i, X1 : $i] : (setunion @ (dsetconstr @ X4 @ (^[X2 : $i] : (in @ (kpair @ X1 @ X2) @ X13))))) = ap)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap)).
% 8.72/1.65 thf(f639,plain,(
% 8.72/1.65 (ap2p = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (funcSet @ Y2 @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (ap @ Y2 @ Y0 @ Y1 @ Y3) @ Y0))))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f583])).
% 8.72/1.65 thf(f583,plain,(
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% 8.72/1.65 inference(rectify,[],[f200])).
% 8.72/1.65 thf(f200,axiom,(
% 8.72/1.65 (! [X3,X13,X4] : ((in @ X13 @ (funcSet @ X3 @ X4)) => ! [X1] : ((in @ X1 @ X3) => (in @ (ap @ X3 @ X4 @ X13 @ X1) @ X4))) = ap2p)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap2p)).
% 8.72/1.65 thf(f856,plain,(
% 8.72/1.65 (infuncsetfunc = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (funcSet @ Y2 @ Y1)) => ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (subset @ Y8 @ (cartprod @ Y6 @ Y7))))))) @ Y3 @ Y4 @ Y5) & (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y3) => ((^[Y7 : $i]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: (?? @ $i @ (^[Y10 : $i]: ((in @ Y10 @ Y9) & ((setadjoin @ Y10 @ emptyset) = Y9))))) @ (dsetconstr @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y4 @ (^[Y7 : $i]: (in @ (kpair @ Y6 @ Y7) @ Y5)))))))))))) @ Y2 @ Y1 @ Y0)))))))))),
% 8.72/1.65 inference(definition_unfolding,[],[f683,f852])).
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% 8.72/1.65 (infuncsetfunc = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (funcSet @ Y2 @ Y1)) => (func @ Y2 @ Y1 @ Y0)))))))))),
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% 8.72/1.65 thf(f489,plain,(
% 8.72/1.65 (! [X0,X1,X2] : ((in @ X2 @ (funcSet @ X0 @ X1)) => (func @ X0 @ X1 @ X2)) = infuncsetfunc)),
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% 8.72/1.65 thf(f199,axiom,(
% 8.72/1.65 (! [X3,X4,X13] : ((in @ X13 @ (funcSet @ X3 @ X4)) => (func @ X3 @ X4 @ X13)) = infuncsetfunc)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infuncsetfunc)).
% 8.72/1.65 thf(f855,plain,(
% 8.72/1.65 (app = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (subset @ Y8 @ (cartprod @ Y6 @ Y7))))))) @ Y3 @ Y4 @ Y5) & (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y3) => ((^[Y7 : $i]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: (?? @ $i @ (^[Y10 : $i]: ((in @ Y10 @ Y9) & ((setadjoin @ Y10 @ emptyset) = Y9))))) @ (dsetconstr @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y4 @ (^[Y7 : $i]: (in @ (kpair @ Y6 @ Y7) @ Y5)))))))))))) @ Y0 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (setunion @ (dsetconstr @ Y5 @ (^[Y8 : $i]: (in @ (kpair @ Y7 @ Y8) @ Y6))))))))))) @ Y0 @ Y1 @ Y2 @ Y3) @ Y1))))))))))))),
% 8.72/1.65 inference(definition_unfolding,[],[f696,f852,f812])).
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% 8.72/1.65 thf(f198,axiom,(
% 8.72/1.65 (! [X13,X4,X3] : ((func @ X3 @ X4 @ X13) => ! [X1] : ((in @ X1 @ X3) => (in @ (ap @ X3 @ X4 @ X13 @ X1) @ X4))) = app)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',app)).
% 8.72/1.65 thf(f854,plain,(
% 8.72/1.65 (apProp = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (subset @ Y8 @ (cartprod @ Y6 @ Y7))))))) @ Y3 @ Y4 @ Y5) & (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y3) => ((^[Y7 : $i]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: (?? @ $i @ (^[Y10 : $i]: ((in @ Y10 @ Y9) & ((setadjoin @ Y10 @ emptyset) = Y9))))) @ (dsetconstr @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y4 @ (^[Y7 : $i]: (in @ (kpair @ Y6 @ Y7) @ Y5)))))))))))) @ Y1 @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setunion @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))) @ Y0))))))))))))),
% 8.72/1.65 inference(definition_unfolding,[],[f712,f852])).
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% 8.72/1.65 thf(f503,plain,(
% 8.72/1.65 (! [X0,X1,X2] : ((func @ X1 @ X2 @ X0) => ! [X3] : ((in @ X3 @ X1) => (in @ (setunion @ (dsetconstr @ X2 @ (^[X4 : $i] : (in @ (kpair @ X3 @ X4) @ X0)))) @ X2))) = apProp)),
% 8.72/1.65 inference(rectify,[],[f196])).
% 8.72/1.65 thf(f196,axiom,(
% 8.72/1.65 (! [X13,X3,X4] : ((func @ X3 @ X4 @ X13) => ! [X1] : ((in @ X1 @ X3) => (in @ (setunion @ (dsetconstr @ X4 @ (^[X2 : $i] : (in @ (kpair @ X1 @ X2) @ X13)))) @ X4))) = apProp)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apProp)).
% 8.72/1.65 thf(f853,plain,(
% 8.72/1.65 (funcImageSingleton = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (subset @ Y8 @ (cartprod @ Y6 @ Y7))))))) @ Y3 @ Y4 @ Y5) & (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y3) => ((^[Y7 : $i]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: (?? @ $i @ (^[Y10 : $i]: ((in @ Y10 @ Y9) & ((setadjoin @ Y10 @ emptyset) = Y9))))) @ (dsetconstr @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y4 @ (^[Y7 : $i]: (in @ (kpair @ Y6 @ Y7) @ Y5)))))))))))) @ Y0 @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & ((setadjoin @ Y5 @ emptyset) = Y4))))) @ (dsetconstr @ Y2 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y1)))))))))))))))),
% 8.72/1.65 inference(definition_unfolding,[],[f756,f852,f765])).
% 8.72/1.65 thf(f756,plain,(
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% 8.72/1.65 inference(cnf_transformation,[],[f345])).
% 8.72/1.65 thf(f345,plain,(
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% 8.72/1.65 inference(fool_elimination,[],[f344])).
% 8.72/1.65 thf(f344,plain,(
% 8.72/1.65 (! [X0,X1,X2] : ((func @ X2 @ X0 @ X1) => ! [X3] : ((in @ X3 @ X2) => (singleton @ (dsetconstr @ X0 @ (^[X4 : $i] : (in @ (kpair @ X3 @ X4) @ X1)))))) = funcImageSingleton)),
% 8.72/1.65 inference(rectify,[],[f195])).
% 8.72/1.65 thf(f195,axiom,(
% 8.72/1.65 (! [X4,X13,X3] : ((func @ X3 @ X4 @ X13) => ! [X1] : ((in @ X1 @ X3) => (singleton @ (dsetconstr @ X4 @ (^[X2 : $i] : (in @ (kpair @ X1 @ X2) @ X13)))))) = funcImageSingleton)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcImageSingleton)).
% 8.72/1.65 thf(f795,plain,(
% 8.72/1.65 (dpsetconstrER = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y3) @ (dpsetconstr @ Y2 @ Y1 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y0 @ Y5 @ Y6)))))) => (Y0 @ Y4 @ Y3)))))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f219])).
% 8.72/1.65 thf(f219,plain,(
% 8.72/1.65 (dpsetconstrER = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y3) @ (dpsetconstr @ Y2 @ Y1 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y0 @ Y5 @ Y6)))))) => (Y0 @ Y4 @ Y3)))))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f218])).
% 8.72/1.65 thf(f218,plain,(
% 8.72/1.65 (dpsetconstrER = ! [X0,X1,X2,X3,X4 : $i > $i > $o] : ((in @ (kpair @ X0 @ X1) @ (dpsetconstr @ X2 @ X3 @ (^[X5 : $i, X6 : $i] : (X4 @ X5 @ X6)))) => (X4 @ X0 @ X1)))),
% 8.72/1.65 inference(rectify,[],[f193])).
% 8.72/1.65 thf(f193,axiom,(
% 8.72/1.65 (dpsetconstrER = ! [X1,X2,X3,X4,X0 : $i > $i > $o] : ((in @ (kpair @ X1 @ X2) @ (dpsetconstr @ X3 @ X4 @ (^[X8 : $i, X10 : $i] : (X0 @ X8 @ X10)))) => (X0 @ X1 @ X2)))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrER)).
% 8.72/1.65 thf(f620,plain,(
% 8.72/1.65 (dpsetconstrEL2 = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y2) @ (dpsetconstr @ Y3 @ Y1 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y0 @ Y5 @ Y6)))))) => (in @ Y2 @ Y1)))))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f609])).
% 8.72/1.65 thf(f609,plain,(
% 8.72/1.65 (dpsetconstrEL2 = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y2) @ (dpsetconstr @ Y3 @ Y1 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y0 @ Y5 @ Y6)))))) => (in @ Y2 @ Y1)))))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f608])).
% 8.72/1.65 thf(f608,plain,(
% 8.72/1.65 (! [X0,X1,X2,X3,X4 : $i > $i > $o] : ((in @ (kpair @ X0 @ X2) @ (dpsetconstr @ X1 @ X3 @ (^[X5 : $i, X6 : $i] : (X4 @ X5 @ X6)))) => (in @ X2 @ X3)) = dpsetconstrEL2)),
% 8.72/1.65 inference(rectify,[],[f192])).
% 8.72/1.65 thf(f192,axiom,(
% 8.72/1.65 (! [X1,X3,X2,X4,X0 : $i > $i > $o] : ((in @ (kpair @ X1 @ X2) @ (dpsetconstr @ X3 @ X4 @ (^[X8 : $i, X10 : $i] : (X0 @ X8 @ X10)))) => (in @ X2 @ X4)) = dpsetconstrEL2)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrEL2)).
% 8.72/1.65 thf(f821,plain,(
% 8.72/1.65 (dpsetconstrEL1 = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y0) @ (dpsetconstr @ Y2 @ Y3 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y1 @ Y5 @ Y6)))))) => (in @ Y4 @ Y2)))))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f404])).
% 8.72/1.65 thf(f404,plain,(
% 8.72/1.65 (dpsetconstrEL1 = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y0) @ (dpsetconstr @ Y2 @ Y3 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y1 @ Y5 @ Y6)))))) => (in @ Y4 @ Y2)))))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f403])).
% 8.72/1.65 thf(f403,plain,(
% 8.72/1.65 (! [X0,X1,X2,X3 : $i > $i > $o,X4] : ((in @ (kpair @ X0 @ X4) @ (dpsetconstr @ X2 @ X1 @ (^[X5 : $i, X6 : $i] : (X3 @ X5 @ X6)))) => (in @ X0 @ X2)) = dpsetconstrEL1)),
% 8.72/1.65 inference(rectify,[],[f191])).
% 8.72/1.65 thf(f191,axiom,(
% 8.72/1.65 (! [X1,X4,X3,X0 : $i > $i > $o,X2] : ((in @ (kpair @ X1 @ X2) @ (dpsetconstr @ X3 @ X4 @ (^[X8 : $i, X10 : $i] : (X0 @ X8 @ X10)))) => (in @ X1 @ X3)) = dpsetconstrEL1)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrEL1)).
% 8.72/1.65 thf(f700,plain,(
% 8.72/1.65 (dpsetconstrERa = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y3 @ Y1 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y2 @ Y5 @ Y6)))))) => (Y2 @ Y0 @ Y4)))))))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f452])).
% 8.72/1.65 thf(f452,plain,(
% 8.72/1.65 (dpsetconstrERa = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y3 @ Y1 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y2 @ Y5 @ Y6)))))) => (Y2 @ Y0 @ Y4)))))))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f451])).
% 8.72/1.65 thf(f451,plain,(
% 8.72/1.65 (dpsetconstrERa = ! [X0,X1 : $i > $i > $o,X2,X3] : ((in @ X3 @ X0) => ! [X4] : ((in @ X4 @ X2) => ((in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X0 @ X2 @ (^[X5 : $i, X6 : $i] : (X1 @ X5 @ X6)))) => (X1 @ X3 @ X4)))))),
% 8.72/1.65 inference(rectify,[],[f190])).
% 8.72/1.65 thf(f190,axiom,(
% 8.72/1.65 (dpsetconstrERa = ! [X3,X0 : $i > $i > $o,X4,X1] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => ((in @ (kpair @ X1 @ X2) @ (dpsetconstr @ X3 @ X4 @ (^[X8 : $i, X10 : $i] : (X0 @ X8 @ X10)))) => (X0 @ X1 @ X2)))))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrERa)).
% 8.72/1.65 thf(f851,plain,(
% 8.72/1.65 (setOfPairsIsBReln = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y0 @ Y1 @ (dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y2 @ Y3 @ Y4)))))))))))))),
% 8.72/1.65 inference(definition_unfolding,[],[f751,f634])).
% 8.72/1.65 thf(f751,plain,(
% 8.72/1.65 (setOfPairsIsBReln = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (breln @ Y0 @ Y1 @ (dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y2 @ Y3 @ Y4)))))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f615])).
% 8.72/1.65 thf(f615,plain,(
% 8.72/1.65 (setOfPairsIsBReln = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (breln @ Y0 @ Y1 @ (dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y2 @ Y3 @ Y4)))))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f614])).
% 8.72/1.65 thf(f614,plain,(
% 8.72/1.65 (! [X0 : $i > $i > $o,X1,X2] : (breln @ X2 @ X1 @ (dpsetconstr @ X2 @ X1 @ (^[X3 : $i, X4 : $i] : (X0 @ X3 @ X4)))) = setOfPairsIsBReln)),
% 8.72/1.65 inference(rectify,[],[f189])).
% 8.72/1.65 thf(f189,axiom,(
% 8.72/1.65 (! [X0 : $i > $i > $o,X4,X3] : (breln @ X3 @ X4 @ (dpsetconstr @ X3 @ X4 @ (^[X1 : $i, X2 : $i] : (X0 @ X1 @ X2)))) = setOfPairsIsBReln)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setOfPairsIsBReln)).
% 8.72/1.65 thf(f741,plain,(
% 8.72/1.65 (dpsetconstrSub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y1 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y2 @ Y3 @ Y4))))) @ (cartprod @ Y1 @ Y0)))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f502])).
% 8.72/1.65 thf(f502,plain,(
% 8.72/1.65 (dpsetconstrSub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y1 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y2 @ Y3 @ Y4))))) @ (cartprod @ Y1 @ Y0)))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f501])).
% 8.72/1.65 thf(f501,plain,(
% 8.72/1.65 (dpsetconstrSub = ! [X0 : $i > $i > $o,X1,X2] : (subset @ (dpsetconstr @ X1 @ X2 @ (^[X3 : $i, X4 : $i] : (X0 @ X3 @ X4))) @ (cartprod @ X1 @ X2)))),
% 8.72/1.65 inference(rectify,[],[f188])).
% 8.72/1.65 thf(f188,axiom,(
% 8.72/1.65 (dpsetconstrSub = ! [X0 : $i > $i > $o,X3,X4] : (subset @ (dpsetconstr @ X3 @ X4 @ (^[X1 : $i, X2 : $i] : (X0 @ X1 @ X2))) @ (cartprod @ X3 @ X4)))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrSub)).
% 8.72/1.65 thf(f816,plain,(
% 8.72/1.65 (dpsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((Y2 @ Y1 @ Y4) => (in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y0 @ Y3 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y2 @ Y5 @ Y6))))))))))))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f557])).
% 8.72/1.65 thf(f557,plain,(
% 8.72/1.65 (dpsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((Y2 @ Y1 @ Y4) => (in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y0 @ Y3 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y2 @ Y5 @ Y6))))))))))))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f556])).
% 8.72/1.65 thf(f556,plain,(
% 8.72/1.65 (dpsetconstrI = ! [X0,X1 : $i > $i > $o,X2,X3] : ((in @ X2 @ X3) => ! [X4] : ((in @ X4 @ X0) => ((X1 @ X2 @ X4) => (in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X3 @ X0 @ (^[X5 : $i, X6 : $i] : (X1 @ X5 @ X6))))))))),
% 8.72/1.65 inference(rectify,[],[f187])).
% 8.72/1.65 thf(f187,axiom,(
% 8.72/1.65 (dpsetconstrI = ! [X4,X0 : $i > $i > $o,X1,X3] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => ((X0 @ X1 @ X2) => (in @ (kpair @ X1 @ X2) @ (dpsetconstr @ X3 @ X4 @ (^[X8 : $i, X10 : $i] : (X0 @ X8 @ X10))))))))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrI)).
% 8.72/1.65 thf(f623,plain,(
% 8.72/1.65 (cartprodpairsurjEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => ((kpair @ (kfst @ Y2) @ (ksnd @ Y2)) = Y2)))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f329])).
% 8.72/1.65 thf(f329,plain,(
% 8.72/1.65 (cartprodpairsurjEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => ((kpair @ (kfst @ Y2) @ (ksnd @ Y2)) = Y2)))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f328])).
% 8.72/1.65 thf(f328,plain,(
% 8.72/1.65 (! [X0,X1,X2] : ((in @ X0 @ (cartprod @ X1 @ X2)) => ((kpair @ (kfst @ X0) @ (ksnd @ X0)) = X0)) = cartprodpairsurjEq)),
% 8.72/1.65 inference(rectify,[],[f185])).
% 8.72/1.65 thf(f185,axiom,(
% 8.72/1.65 (! [X10,X3,X4] : ((in @ X10 @ (cartprod @ X3 @ X4)) => ((kpair @ (kfst @ X10) @ (ksnd @ X10)) = X10)) = cartprodpairsurjEq)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairsurjEq)).
% 8.72/1.65 thf(f729,plain,(
% 8.72/1.65 (cartprodsndpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((ksnd @ (kpair @ Y0 @ Y3)) = Y3))))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f241])).
% 8.72/1.65 thf(f241,plain,(
% 8.72/1.65 (cartprodsndpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((ksnd @ (kpair @ Y0 @ Y3)) = Y3))))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f240])).
% 8.72/1.65 thf(f240,plain,(
% 8.72/1.65 (cartprodsndpairEq = ! [X0,X1,X2] : ((in @ X2 @ X0) => ! [X3] : ((in @ X3 @ X1) => ((ksnd @ (kpair @ X2 @ X3)) = X3))))),
% 8.72/1.65 inference(rectify,[],[f184])).
% 8.72/1.65 thf(f184,axiom,(
% 8.72/1.65 (cartprodsndpairEq = ! [X3,X4,X1] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => ((ksnd @ (kpair @ X1 @ X2)) = X2))))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodsndpairEq)).
% 8.72/1.65 thf(f825,plain,(
% 8.72/1.65 (cartprodfstpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kfst @ (kpair @ Y0 @ Y3)) = Y0))))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f607])).
% 8.72/1.65 thf(f607,plain,(
% 8.72/1.65 (cartprodfstpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kfst @ (kpair @ Y0 @ Y3)) = Y0))))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f606])).
% 8.72/1.65 thf(f606,plain,(
% 8.72/1.65 (cartprodfstpairEq = ! [X0,X1,X2] : ((in @ X2 @ X0) => ! [X3] : ((in @ X3 @ X1) => ((kfst @ (kpair @ X2 @ X3)) = X2))))),
% 8.72/1.65 inference(rectify,[],[f183])).
% 8.72/1.65 thf(f183,axiom,(
% 8.72/1.65 (cartprodfstpairEq = ! [X3,X4,X1] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => ((kfst @ (kpair @ X1 @ X2)) = X1))))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodfstpairEq)).
% 8.72/1.65 thf(f762,plain,(
% 8.72/1.65 (cartprodmempaircEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kpair @ Y2 @ Y3) = (kpair @ Y2 @ Y3)))))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f611])).
% 8.72/1.65 thf(f611,plain,(
% 8.72/1.65 (cartprodmempaircEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kpair @ Y2 @ Y3) = (kpair @ Y2 @ Y3)))))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f610])).
% 8.72/1.65 thf(f610,plain,(
% 8.72/1.65 (! [X0,X1,X2] : ((in @ X0 @ X2) => ! [X3] : ((in @ X3 @ X1) => ((kpair @ X0 @ X3) = (kpair @ X0 @ X3)))) = cartprodmempaircEq)),
% 8.72/1.65 inference(rectify,[],[f182])).
% 8.72/1.65 thf(f182,axiom,(
% 8.72/1.65 (! [X1,X4,X3] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => ((kpair @ X1 @ X2) = (kpair @ X1 @ X2)))) = cartprodmempaircEq)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempaircEq)).
% 8.72/1.65 thf(f677,plain,(
% 8.72/1.65 (cartprodpairmemER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y0 @ Y2)) => (in @ Y3 @ Y2)))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f247])).
% 8.72/1.65 thf(f247,plain,(
% 8.72/1.65 (cartprodpairmemER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y0 @ Y2)) => (in @ Y3 @ Y2)))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f246])).
% 8.72/1.65 thf(f246,plain,(
% 8.72/1.65 (cartprodpairmemER = ! [X0,X1,X2,X3] : ((in @ (kpair @ X2 @ X0) @ (cartprod @ X3 @ X1)) => (in @ X0 @ X1)))),
% 8.72/1.65 inference(rectify,[],[f181])).
% 8.72/1.65 thf(f181,axiom,(
% 8.72/1.65 (cartprodpairmemER = ! [X2,X4,X1,X3] : ((in @ (kpair @ X1 @ X2) @ (cartprod @ X3 @ X4)) => (in @ X2 @ X4)))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairmemER)).
% 8.72/1.65 thf(f727,plain,(
% 8.72/1.65 (cartprodpairmemEL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y2) @ (cartprod @ Y0 @ Y1)) => (in @ Y3 @ Y0)))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f569])).
% 8.72/1.65 thf(f569,plain,(
% 8.72/1.65 (cartprodpairmemEL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y2) @ (cartprod @ Y0 @ Y1)) => (in @ Y3 @ Y0)))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f568])).
% 8.72/1.65 thf(f568,plain,(
% 8.72/1.65 (cartprodpairmemEL = ! [X0,X1,X2,X3] : ((in @ (kpair @ X0 @ X1) @ (cartprod @ X3 @ X2)) => (in @ X0 @ X3)))),
% 8.72/1.65 inference(rectify,[],[f180])).
% 8.72/1.65 thf(f180,axiom,(
% 8.72/1.65 (cartprodpairmemEL = ! [X1,X2,X4,X3] : ((in @ (kpair @ X1 @ X2) @ (cartprod @ X3 @ X4)) => (in @ X1 @ X3)))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairmemEL)).
% 8.72/1.65 thf(f758,plain,(
% 8.72/1.65 (cartprodsndin = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (in @ (ksnd @ Y2) @ Y0)))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f466])).
% 8.72/1.65 thf(f466,plain,(
% 8.72/1.65 (cartprodsndin = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (in @ (ksnd @ Y2) @ Y0)))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f465])).
% 8.72/1.65 thf(f465,plain,(
% 8.72/1.65 (cartprodsndin = ! [X0,X1,X2] : ((in @ X0 @ (cartprod @ X1 @ X2)) => (in @ (ksnd @ X0) @ X2)))),
% 8.72/1.65 inference(rectify,[],[f179])).
% 8.72/1.65 thf(f179,axiom,(
% 8.72/1.65 (cartprodsndin = ! [X10,X3,X4] : ((in @ X10 @ (cartprod @ X3 @ X4)) => (in @ (ksnd @ X10) @ X4)))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodsndin)).
% 8.72/1.65 thf(f754,plain,(
% 8.72/1.65 (kpairsurjEq = (!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => ((kpair @ (kfst @ Y0) @ (ksnd @ Y0)) = Y0)))))),
% 8.72/1.65 inference(cnf_transformation,[],[f458])).
% 8.72/1.65 thf(f458,plain,(
% 8.72/1.65 (kpairsurjEq = (!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => ((kpair @ (kfst @ Y0) @ (ksnd @ Y0)) = Y0)))))),
% 8.72/1.65 inference(fool_elimination,[],[f457])).
% 8.72/1.65 thf(f457,plain,(
% 8.72/1.65 (! [X0] : ((iskpair @ X0) => ((kpair @ (kfst @ X0) @ (ksnd @ X0)) = X0)) = kpairsurjEq)),
% 8.72/1.65 inference(rectify,[],[f178])).
% 8.72/1.65 thf(f178,axiom,(
% 8.72/1.65 (! [X10] : ((iskpair @ X10) => ((kpair @ (kfst @ X10) @ (ksnd @ X10)) = X10)) = kpairsurjEq)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairsurjEq)).
% 8.72/1.65 thf(f822,plain,(
% 8.72/1.65 (ksndpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y1 @ Y0)) = Y0))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f428])).
% 8.72/1.65 thf(f428,plain,(
% 8.72/1.65 (ksndpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y1 @ Y0)) = Y0))))))),
% 8.72/1.65 inference(fool_elimination,[],[f427])).
% 8.72/1.65 thf(f427,plain,(
% 8.72/1.65 (! [X0,X1] : ((ksnd @ (kpair @ X0 @ X1)) = X1) = ksndpairEq)),
% 8.72/1.65 inference(rectify,[],[f177])).
% 8.72/1.65 thf(f177,axiom,(
% 8.72/1.65 (! [X1,X2] : ((ksnd @ (kpair @ X1 @ X2)) = X2) = ksndpairEq)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ksndpairEq)).
% 8.72/1.65 thf(f850,plain,(
% 8.72/1.65 (ksndsingleton = (!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & ((setadjoin @ Y2 @ emptyset) = Y1))))) @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: ((kpair @ (kfst @ Y0) @ Y1) = Y0))))))))),
% 8.72/1.65 inference(definition_unfolding,[],[f711,f765])).
% 8.72/1.65 thf(f711,plain,(
% 8.72/1.65 (ksndsingleton = (!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (singleton @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: ((kpair @ (kfst @ Y0) @ Y1) = Y0))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f553])).
% 8.72/1.65 thf(f553,plain,(
% 8.72/1.65 (ksndsingleton = (!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (singleton @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: ((kpair @ (kfst @ Y0) @ Y1) = Y0))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f552])).
% 8.72/1.65 thf(f552,plain,(
% 8.72/1.65 (ksndsingleton = ! [X0] : ((iskpair @ X0) => (singleton @ (dsetconstr @ (setunion @ X0) @ (^[X1 : $i] : (((kpair @ (kfst @ X0) @ X1) = X0)))))))),
% 8.72/1.65 inference(rectify,[],[f176])).
% 8.72/1.65 thf(f176,axiom,(
% 8.72/1.65 (ksndsingleton = ! [X10] : ((iskpair @ X10) => (singleton @ (dsetconstr @ (setunion @ X10) @ (^[X1 : $i] : (((kpair @ (kfst @ X10) @ X1) = X10)))))))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ksndsingleton)).
% 8.72/1.65 thf(f659,plain,(
% 8.72/1.65 (setukpairinjR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y3 = Y2)))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f565])).
% 8.72/1.65 thf(f565,plain,(
% 8.72/1.65 (setukpairinjR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y3 = Y2)))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f564])).
% 8.72/1.65 thf(f564,plain,(
% 8.72/1.65 (setukpairinjR = ! [X0,X1,X2,X3] : (((kpair @ X2 @ X0) = (kpair @ X3 @ X1)) => (X0 = X1)))),
% 8.72/1.65 inference(rectify,[],[f175])).
% 8.72/1.65 thf(f175,axiom,(
% 8.72/1.65 (setukpairinjR = ! [X10,X2,X8,X1] : (((kpair @ X1 @ X2) = (kpair @ X8 @ X10)) => (X2 = X10)))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR)).
% 8.72/1.65 thf(f632,plain,(
% 8.72/1.65 (setukpairinjR2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y3 = Y0)))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f530])).
% 8.72/1.65 thf(f530,plain,(
% 8.72/1.65 (setukpairinjR2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y3 = Y0)))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f529])).
% 8.72/1.65 thf(f529,plain,(
% 8.72/1.65 (! [X0,X1,X2,X3] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset)) @ emptyset))) => (X0 = X3)) = setukpairinjR2)),
% 8.72/1.65 inference(rectify,[],[f174])).
% 8.72/1.65 thf(f174,axiom,(
% 8.72/1.65 (! [X2,X8,X1,X10] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X8 @ emptyset) @ (setadjoin @ (setadjoin @ X8 @ (setadjoin @ X10 @ emptyset)) @ emptyset))) => (X2 = X10)) = setukpairinjR2)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR2)).
% 8.72/1.65 thf(f724,plain,(
% 8.72/1.65 (upairequniteq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y1 @ emptyset) = (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset))) => (Y2 = Y0)))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f524])).
% 8.72/1.65 thf(f524,plain,(
% 8.72/1.65 (upairequniteq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y1 @ emptyset) = (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset))) => (Y2 = Y0)))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f523])).
% 8.72/1.65 thf(f523,plain,(
% 8.72/1.65 (upairequniteq = ! [X0,X1,X2] : (((setadjoin @ X1 @ emptyset) = (setadjoin @ X0 @ (setadjoin @ X2 @ emptyset))) => (X0 = X2)))),
% 8.72/1.65 inference(rectify,[],[f173])).
% 8.72/1.65 thf(f173,axiom,(
% 8.72/1.65 (upairequniteq = ! [X1,X8,X2] : (((setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) = (setadjoin @ X8 @ emptyset)) => (X1 = X2)))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairequniteq)).
% 8.72/1.65 thf(f798,plain,(
% 8.72/1.65 (setukpairinjR1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y3 = Y0))))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f303])).
% 8.72/1.65 thf(f303,plain,(
% 8.72/1.65 (setukpairinjR1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y3 = Y0))))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f302])).
% 8.72/1.65 thf(f302,plain,(
% 8.72/1.65 (setukpairinjR1 = ! [X0,X1,X2,X3] : (((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset))) => ((X0 = X1) => (X0 = X3))))),
% 8.72/1.65 inference(rectify,[],[f172])).
% 8.72/1.65 thf(f172,axiom,(
% 8.72/1.65 (setukpairinjR1 = ! [X10,X8,X1,X2] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X8 @ emptyset) @ (setadjoin @ (setadjoin @ X8 @ (setadjoin @ X10 @ emptyset)) @ emptyset))) => ((X8 = X10) => (X2 = X10))))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR1)).
% 8.72/1.65 thf(f692,plain,(
% 8.72/1.65 (setukpairinjR12 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ emptyset))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f577])).
% 8.72/1.65 thf(f577,plain,(
% 8.72/1.65 (setukpairinjR12 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ emptyset))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f576])).
% 8.72/1.65 thf(f576,plain,(
% 8.72/1.65 (setukpairinjR12 = ! [X0,X1] : ((X0 = X1) => ((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X0 @ emptyset) @ emptyset))))),
% 8.72/1.65 inference(rectify,[],[f171])).
% 8.72/1.65 thf(f171,axiom,(
% 8.72/1.65 (setukpairinjR12 = ! [X1,X2] : ((X1 = X2) => ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X1 @ emptyset) @ emptyset))))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR12)).
% 8.72/1.65 thf(f745,plain,(
% 8.72/1.65 (setukpairinjR11 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f351])).
% 8.72/1.65 thf(f351,plain,(
% 8.72/1.65 (setukpairinjR11 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f350])).
% 8.72/1.65 thf(f350,plain,(
% 8.72/1.65 (setukpairinjR11 = ! [X0,X1] : ((X0 = X1) => ((setadjoin @ X1 @ emptyset) = (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)))))),
% 8.72/1.65 inference(rectify,[],[f170])).
% 8.72/1.65 thf(f170,axiom,(
% 8.72/1.65 (setukpairinjR11 = ! [X2,X1] : ((X1 = X2) => ((setadjoin @ X1 @ emptyset) = (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)))))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjR11)).
% 8.72/1.65 thf(f713,plain,(
% 8.72/1.65 (setukpairinjL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y3 @ Y1) = (kpair @ Y0 @ Y2)) => (Y3 = Y0)))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f269])).
% 8.72/1.65 thf(f269,plain,(
% 8.72/1.65 (setukpairinjL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y3 @ Y1) = (kpair @ Y0 @ Y2)) => (Y3 = Y0)))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f268])).
% 8.72/1.65 thf(f268,plain,(
% 8.72/1.65 (setukpairinjL = ! [X0,X1,X2,X3] : (((kpair @ X0 @ X2) = (kpair @ X3 @ X1)) => (X0 = X3)))),
% 8.72/1.65 inference(rectify,[],[f169])).
% 8.72/1.65 thf(f169,axiom,(
% 8.72/1.65 (setukpairinjL = ! [X8,X2,X10,X1] : (((kpair @ X1 @ X2) = (kpair @ X8 @ X10)) => (X1 = X8)))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL)).
% 8.72/1.65 thf(f673,plain,(
% 8.72/1.65 (setukpairinjL2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y1)))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f271])).
% 8.72/1.65 thf(f271,plain,(
% 8.72/1.65 (setukpairinjL2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y1)))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f270])).
% 8.72/1.65 thf(f270,plain,(
% 8.72/1.65 (! [X0,X1,X2,X3] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset)) @ emptyset))) => (X1 = X2)) = setukpairinjL2)),
% 8.72/1.65 inference(rectify,[],[f168])).
% 8.72/1.65 thf(f168,axiom,(
% 8.72/1.65 (! [X2,X8,X1,X10] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X8 @ emptyset) @ (setadjoin @ (setadjoin @ X8 @ (setadjoin @ X10 @ emptyset)) @ emptyset))) => (X1 = X8)) = setukpairinjL2)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL2)).
% 8.72/1.65 thf(f800,plain,(
% 8.72/1.65 (cartprodfstin = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (in @ (kfst @ Y1) @ Y0)))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f549])).
% 8.72/1.65 thf(f549,plain,(
% 8.72/1.65 (cartprodfstin = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (in @ (kfst @ Y1) @ Y0)))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f548])).
% 8.72/1.65 thf(f548,plain,(
% 8.72/1.65 (cartprodfstin = ! [X0,X1,X2] : ((in @ X1 @ (cartprod @ X2 @ X0)) => (in @ (kfst @ X1) @ X2)))),
% 8.72/1.65 inference(rectify,[],[f167])).
% 8.72/1.65 thf(f167,axiom,(
% 8.72/1.65 (cartprodfstin = ! [X4,X10,X3] : ((in @ X10 @ (cartprod @ X3 @ X4)) => (in @ (kfst @ X10) @ X3)))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodfstin)).
% 8.72/1.65 thf(f740,plain,(
% 8.72/1.65 (kfstpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y0 @ Y1)) = Y0))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f571])).
% 8.72/1.65 thf(f571,plain,(
% 8.72/1.65 (kfstpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y0 @ Y1)) = Y0))))))),
% 8.72/1.65 inference(fool_elimination,[],[f570])).
% 8.72/1.65 thf(f570,plain,(
% 8.72/1.65 (kfstpairEq = ! [X0,X1] : ((kfst @ (kpair @ X1 @ X0)) = X1))),
% 8.72/1.65 inference(rectify,[],[f166])).
% 8.72/1.65 thf(f166,axiom,(
% 8.72/1.65 (kfstpairEq = ! [X2,X1] : ((kfst @ (kpair @ X1 @ X2)) = X1))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kfstpairEq)).
% 8.72/1.65 thf(f849,plain,(
% 8.72/1.65 (theprop = (!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & ((setadjoin @ Y2 @ emptyset) = Y1))))) @ Y0) => (in @ (setunion @ Y0) @ Y0)))))),
% 8.72/1.65 inference(definition_unfolding,[],[f648,f765])).
% 8.72/1.65 thf(f648,plain,(
% 8.72/1.65 (theprop = (!! @ $i @ (^[Y0 : $i]: ((singleton @ Y0) => (in @ (setunion @ Y0) @ Y0)))))),
% 8.72/1.65 inference(cnf_transformation,[],[f389])).
% 8.72/1.65 thf(f389,plain,(
% 8.72/1.65 (theprop = (!! @ $i @ (^[Y0 : $i]: ((singleton @ Y0) => (in @ (setunion @ Y0) @ Y0)))))),
% 8.72/1.65 inference(fool_elimination,[],[f388])).
% 8.72/1.65 thf(f388,plain,(
% 8.72/1.65 (theprop = ! [X0] : ((singleton @ X0) => (in @ (setunion @ X0) @ X0)))),
% 8.72/1.65 inference(rectify,[],[f165])).
% 8.72/1.65 thf(f165,axiom,(
% 8.72/1.65 (theprop = ! [X11] : ((singleton @ X11) => (in @ (setunion @ X11) @ X11)))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theprop)).
% 8.72/1.65 thf(f848,plain,(
% 8.72/1.65 (kfstsingleton = (!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & ((setadjoin @ Y2 @ emptyset) = Y1))))) @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: (in @ (setadjoin @ Y1 @ emptyset) @ Y0))))))))),
% 8.72/1.65 inference(definition_unfolding,[],[f787,f765])).
% 8.72/1.65 thf(f787,plain,(
% 8.72/1.65 (kfstsingleton = (!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (singleton @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: (in @ (setadjoin @ Y1 @ emptyset) @ Y0))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f231])).
% 8.72/1.65 thf(f231,plain,(
% 8.72/1.65 (kfstsingleton = (!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (singleton @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: (in @ (setadjoin @ Y1 @ emptyset) @ Y0))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f230])).
% 8.72/1.65 thf(f230,plain,(
% 8.72/1.65 (! [X0] : ((iskpair @ X0) => (singleton @ (dsetconstr @ (setunion @ X0) @ (^[X1 : $i] : (in @ (setadjoin @ X1 @ emptyset) @ X0))))) = kfstsingleton)),
% 8.72/1.65 inference(rectify,[],[f164])).
% 8.72/1.65 thf(f164,axiom,(
% 8.72/1.65 (! [X10] : ((iskpair @ X10) => (singleton @ (dsetconstr @ (setunion @ X10) @ (^[X1 : $i] : (in @ (setadjoin @ X1 @ emptyset) @ X10))))) = kfstsingleton)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kfstsingleton)).
% 8.72/1.65 thf(f772,plain,(
% 8.72/1.65 (setukpairinjL1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f464])).
% 8.72/1.65 thf(f464,plain,(
% 8.72/1.65 (setukpairinjL1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f463])).
% 8.72/1.65 thf(f463,plain,(
% 8.72/1.65 (setukpairinjL1 = ! [X0,X1,X2] : ((in @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) => (X0 = X2)))),
% 8.72/1.65 inference(rectify,[],[f163])).
% 8.72/1.65 thf(f163,axiom,(
% 8.72/1.65 (setukpairinjL1 = ! [X1,X2,X8] : ((in @ (setadjoin @ X8 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset))) => (X1 = X8)))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL1)).
% 8.72/1.65 thf(f653,plain,(
% 8.72/1.65 (singletonsuniq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f518])).
% 8.72/1.65 thf(f518,plain,(
% 8.72/1.65 (singletonsuniq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))))),
% 8.72/1.65 inference(fool_elimination,[],[f517])).
% 8.72/1.65 thf(f517,plain,(
% 8.72/1.65 (singletonsuniq = ! [X0,X1] : (((setadjoin @ X1 @ emptyset) = (setadjoin @ X0 @ emptyset)) => (X0 = X1)))),
% 8.72/1.65 inference(rectify,[],[f162])).
% 8.72/1.65 thf(f162,axiom,(
% 8.72/1.65 (singletonsuniq = ! [X2,X1] : (((setadjoin @ X2 @ emptyset) = (setadjoin @ X1 @ emptyset)) => (X1 = X2)))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsuniq)).
% 8.72/1.65 thf(f847,plain,(
% 8.72/1.65 (ex1I2 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => ((^[Y2 : $i]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & ((setadjoin @ Y5 @ emptyset) = Y4))))) @ (dsetconstr @ Y2 @ (^[Y4 : $i]: (Y3 @ Y4))))))) @ Y1 @ (^[Y2 : $i]: (Y0 @ Y2))))))))))),
% 8.72/1.65 inference(definition_unfolding,[],[f747,f844])).
% 8.72/1.65 thf(f747,plain,(
% 8.72/1.65 (ex1I2 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (ex1 @ Y1 @ (^[Y2 : $i]: (Y0 @ Y2))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f520])).
% 8.72/1.65 thf(f520,plain,(
% 8.72/1.65 (ex1I2 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y2) => ((Y0 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (ex1 @ Y1 @ (^[Y2 : $i]: (Y0 @ Y2))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f519])).
% 8.72/1.65 thf(f519,plain,(
% 8.72/1.65 (ex1I2 = ! [X0,X1 : $i > $o] : (! [X2] : ((in @ X2 @ X0) => ! [X3] : ((in @ X3 @ X0) => ((X1 @ X2) => ((X1 @ X3) => (X2 = X3))))) => (? [X4] : ((X1 @ X4) & (in @ X4 @ X0)) => (ex1 @ X0 @ (^[X5 : $i] : (X1 @ X5))))))),
% 8.72/1.65 inference(rectify,[],[f161])).
% 8.72/1.65 thf(f161,axiom,(
% 8.72/1.65 (ex1I2 = ! [X3,X0 : $i > $o] : (! [X1] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X3) => ((X0 @ X1) => ((X0 @ X2) => (X1 = X2))))) => (? [X1] : ((X0 @ X1) & (in @ X1 @ X3)) => (ex1 @ X3 @ (^[X1 : $i] : (X0 @ X1))))))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1I2)).
% 8.72/1.65 thf(f846,plain,(
% 8.72/1.65 (ex1I = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => ((^[Y3 : $i]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) & ((setadjoin @ Y6 @ emptyset) = Y5))))) @ (dsetconstr @ Y3 @ (^[Y5 : $i]: (Y4 @ Y5))))))) @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))),
% 8.72/1.65 inference(definition_unfolding,[],[f714,f844])).
% 8.72/1.65 thf(f714,plain,(
% 8.72/1.65 (ex1I = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (ex1 @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f432])).
% 8.72/1.65 thf(f432,plain,(
% 8.72/1.65 (ex1I = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (ex1 @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f431])).
% 8.72/1.65 thf(f431,plain,(
% 8.72/1.65 (! [X0,X1,X2 : $i > $o] : ((in @ X0 @ X1) => ((X2 @ X0) => (! [X3] : ((in @ X3 @ X1) => ((X2 @ X3) => (X0 = X3))) => (ex1 @ X1 @ (^[X4 : $i] : (X2 @ X4)))))) = ex1I)),
% 8.72/1.65 inference(rectify,[],[f160])).
% 8.72/1.65 thf(f160,axiom,(
% 8.72/1.65 (! [X1,X3,X0 : $i > $o] : ((in @ X1 @ X3) => ((X0 @ X1) => (! [X2] : ((in @ X2 @ X3) => ((X0 @ X2) => (X1 = X2))) => (ex1 @ X3 @ (^[X2 : $i] : (X0 @ X2)))))) = ex1I)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1I)).
% 8.72/1.65 thf(f845,plain,(
% 8.72/1.65 (ex1E1 = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((^[Y2 : $i]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & ((setadjoin @ Y5 @ emptyset) = Y4))))) @ (dsetconstr @ Y2 @ (^[Y4 : $i]: (Y3 @ Y4))))))) @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) => (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))))))))),
% 8.72/1.65 inference(definition_unfolding,[],[f690,f844])).
% 8.72/1.65 thf(f690,plain,(
% 8.72/1.65 (ex1E1 = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((ex1 @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) => (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f391])).
% 8.72/1.65 thf(f391,plain,(
% 8.72/1.65 (ex1E1 = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((ex1 @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) => (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f390])).
% 8.72/1.65 thf(f390,plain,(
% 8.72/1.65 (ex1E1 = ! [X0 : $i > $o,X1] : ((ex1 @ X1 @ (^[X2 : $i] : (X0 @ X2))) => ? [X3] : ((in @ X3 @ X1) & (X0 @ X3))))),
% 8.72/1.65 inference(rectify,[],[f159])).
% 8.72/1.65 thf(f159,axiom,(
% 8.72/1.65 (ex1E1 = ! [X0 : $i > $o,X3] : ((ex1 @ X3 @ (^[X1 : $i] : (X0 @ X1))) => ? [X1] : ((in @ X1 @ X3) & (X0 @ X1))))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1E1)).
% 8.72/1.65 thf(f843,plain,(
% 8.72/1.65 (singletonprop = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) & ((setadjoin @ Y3 @ emptyset) = Y2))))) @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2)))))))))))),
% 8.72/1.65 inference(definition_unfolding,[],[f814,f765])).
% 8.72/1.65 thf(f814,plain,(
% 8.72/1.65 (singletonprop = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2)))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f543])).
% 8.72/1.65 thf(f543,plain,(
% 8.72/1.65 (singletonprop = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2)))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f542])).
% 8.72/1.65 thf(f542,plain,(
% 8.72/1.65 (! [X0 : $i > $o,X1] : (! [X2] : ((in @ X2 @ X1) => ! [X3] : ((in @ X3 @ X1) => ((X0 @ X2) => ((X0 @ X3) => (X2 = X3))))) => (? [X4] : ((X0 @ X4) & (in @ X4 @ X1)) => (singleton @ (dsetconstr @ X1 @ (^[X5 : $i] : (X0 @ X5)))))) = singletonprop)),
% 8.72/1.65 inference(rectify,[],[f157])).
% 8.72/1.65 thf(f157,axiom,(
% 8.72/1.65 (! [X0 : $i > $o,X3] : (! [X1] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X3) => ((X0 @ X1) => ((X0 @ X2) => (X1 = X2))))) => (? [X1] : ((X0 @ X1) & (in @ X1 @ X3)) => (singleton @ (dsetconstr @ X3 @ (^[X1 : $i] : (X0 @ X1)))))) = singletonprop)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonprop)).
% 8.72/1.65 thf(f715,plain,(
% 8.72/1.65 (setunionsingleton = (!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))))),
% 8.72/1.65 inference(cnf_transformation,[],[f454])).
% 8.72/1.65 thf(f454,plain,(
% 8.72/1.65 (setunionsingleton = (!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))))),
% 8.72/1.65 inference(fool_elimination,[],[f453])).
% 8.72/1.65 thf(f453,plain,(
% 8.72/1.65 (! [X0] : ((setunion @ (setadjoin @ X0 @ emptyset)) = X0) = setunionsingleton)),
% 8.72/1.65 inference(rectify,[],[f155])).
% 8.72/1.65 thf(f155,axiom,(
% 8.72/1.65 (! [X1] : ((setunion @ (setadjoin @ X1 @ emptyset)) = X1) = setunionsingleton)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton)).
% 8.72/1.65 thf(f626,plain,(
% 8.72/1.65 (setunionsingleton2 = (!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f559])).
% 8.72/1.65 thf(f559,plain,(
% 8.72/1.65 (setunionsingleton2 = (!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))))),
% 8.72/1.65 inference(fool_elimination,[],[f558])).
% 8.72/1.65 thf(f558,plain,(
% 8.72/1.65 (! [X0] : (subset @ X0 @ (setunion @ (setadjoin @ X0 @ emptyset))) = setunionsingleton2)),
% 8.72/1.65 inference(rectify,[],[f154])).
% 8.72/1.65 thf(f154,axiom,(
% 8.72/1.65 (! [X3] : (subset @ X3 @ (setunion @ (setadjoin @ X3 @ emptyset))) = setunionsingleton2)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton2)).
% 8.72/1.65 thf(f704,plain,(
% 8.72/1.65 (setunionsingleton1 = (!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))))),
% 8.72/1.65 inference(cnf_transformation,[],[f237])).
% 8.72/1.65 thf(f237,plain,(
% 8.72/1.65 (setunionsingleton1 = (!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))))),
% 8.72/1.65 inference(fool_elimination,[],[f236])).
% 8.72/1.65 thf(f236,plain,(
% 8.72/1.65 (setunionsingleton1 = ! [X0] : (subset @ (setunion @ (setadjoin @ X0 @ emptyset)) @ X0))),
% 8.72/1.65 inference(rectify,[],[f153])).
% 8.72/1.65 thf(f153,axiom,(
% 8.72/1.65 (setunionsingleton1 = ! [X3] : (subset @ (setunion @ (setadjoin @ X3 @ emptyset)) @ X3))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton1)).
% 8.72/1.65 thf(f642,plain,(
% 8.72/1.65 (setunionE2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f416])).
% 8.72/1.65 thf(f416,plain,(
% 8.72/1.65 (setunionE2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f415])).
% 8.72/1.65 thf(f415,plain,(
% 8.72/1.65 (setunionE2 = ! [X0,X1] : ((in @ X0 @ (setunion @ X1)) => ? [X2] : ((in @ X0 @ X2) & (in @ X2 @ X1))))),
% 8.72/1.65 inference(rectify,[],[f152])).
% 8.72/1.65 thf(f152,axiom,(
% 8.72/1.65 (setunionE2 = ! [X1,X3] : ((in @ X1 @ (setunion @ X3)) => ? [X11] : ((in @ X1 @ X11) & (in @ X11 @ X3))))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE2)).
% 8.72/1.65 thf(f824,plain,(
% 8.72/1.65 (cartprodmempair = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (iskpair @ Y0)))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f522])).
% 8.72/1.65 thf(f522,plain,(
% 8.72/1.65 (cartprodmempair = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (iskpair @ Y0)))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f521])).
% 8.72/1.65 thf(f521,plain,(
% 8.72/1.65 (! [X0,X1,X2] : ((in @ X2 @ (cartprod @ X1 @ X0)) => (iskpair @ X2)) = cartprodmempair)),
% 8.72/1.65 inference(rectify,[],[f151])).
% 8.72/1.65 thf(f151,axiom,(
% 8.72/1.65 (! [X4,X3,X10] : ((in @ X10 @ (cartprod @ X3 @ X4)) => (iskpair @ X10)) = cartprodmempair)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair)).
% 8.72/1.65 thf(f705,plain,(
% 8.72/1.65 (cartprodmempair1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y2)))))))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f253])).
% 8.72/1.65 thf(f253,plain,(
% 8.72/1.65 (cartprodmempair1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y2)))))))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f252])).
% 8.72/1.65 thf(f252,plain,(
% 8.72/1.65 (cartprodmempair1 = ! [X0,X1,X2] : ((in @ X0 @ (cartprod @ X1 @ X2)) => ? [X3] : (? [X4] : (((kpair @ X3 @ X4) = X0) & (in @ X4 @ X2)) & (in @ X3 @ X1))))),
% 8.72/1.65 inference(rectify,[],[f150])).
% 8.72/1.65 thf(f150,axiom,(
% 8.72/1.65 (cartprodmempair1 = ! [X10,X3,X4] : ((in @ X10 @ (cartprod @ X3 @ X4)) => ? [X1] : (? [X2] : (((kpair @ X1 @ X2) = X10) & (in @ X2 @ X4)) & (in @ X1 @ X3))))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair1)).
% 8.72/1.65 thf(f781,plain,(
% 8.72/1.65 (cartprodpairin = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y2 @ Y0)))))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f305])).
% 8.72/1.65 thf(f305,plain,(
% 8.72/1.65 (cartprodpairin = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (cartprod @ Y2 @ Y0)))))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f304])).
% 8.72/1.65 thf(f304,plain,(
% 8.72/1.65 (cartprodpairin = ! [X0,X1,X2] : ((in @ X1 @ X0) => ! [X3] : ((in @ X3 @ X2) => (in @ (kpair @ X1 @ X3) @ (cartprod @ X0 @ X2)))))),
% 8.72/1.65 inference(rectify,[],[f149])).
% 8.72/1.65 thf(f149,axiom,(
% 8.72/1.65 (cartprodpairin = ! [X3,X1,X4] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => (in @ (kpair @ X1 @ X2) @ (cartprod @ X3 @ X4)))))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairin)).
% 8.72/1.65 thf(f826,plain,(
% 8.72/1.65 (ubforcartprodlem3 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f267])).
% 8.72/1.65 thf(f267,plain,(
% 8.72/1.65 (ubforcartprodlem3 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f266])).
% 8.72/1.65 thf(f266,plain,(
% 8.72/1.65 (ubforcartprodlem3 = ! [X0,X1,X2] : ((in @ X2 @ X1) => ! [X3] : ((in @ X3 @ X0) => (in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X1 @ X0)))))))),
% 8.72/1.65 inference(rectify,[],[f148])).
% 8.72/1.65 thf(f148,axiom,(
% 8.72/1.65 (ubforcartprodlem3 = ! [X4,X3,X1] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => (in @ (kpair @ X1 @ X2) @ (powerset @ (powerset @ (binunion @ X3 @ X4)))))))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem3)).
% 8.72/1.65 thf(f720,plain,(
% 8.72/1.65 (ubforcartprodlem2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f367])).
% 8.72/1.65 thf(f367,plain,(
% 8.72/1.65 (ubforcartprodlem2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y2)))))))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f366])).
% 8.72/1.65 thf(f366,plain,(
% 8.72/1.65 (! [X0,X1,X2] : ((in @ X1 @ X2) => ! [X3] : ((in @ X3 @ X0) => (in @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X2 @ X0)))))) = ubforcartprodlem2)),
% 8.72/1.65 inference(rectify,[],[f147])).
% 8.72/1.65 thf(f147,axiom,(
% 8.72/1.65 (! [X4,X1,X3] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => (in @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X3 @ X4)))))) = ubforcartprodlem2)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem2)).
% 8.72/1.65 thf(f805,plain,(
% 8.72/1.65 (ubforcartprodlem1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f424])).
% 8.72/1.65 thf(f424,plain,(
% 8.72/1.65 (ubforcartprodlem1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f423])).
% 8.72/1.65 thf(f423,plain,(
% 8.72/1.65 (! [X0,X1,X2] : ((in @ X1 @ X0) => ! [X3] : ((in @ X3 @ X2) => (subset @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X0 @ X2))))) = ubforcartprodlem1)),
% 8.72/1.65 inference(rectify,[],[f146])).
% 8.72/1.65 thf(f146,axiom,(
% 8.72/1.65 (! [X3,X1,X4] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => (subset @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X3 @ X4))))) = ubforcartprodlem1)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem1)).
% 8.72/1.65 thf(f699,plain,(
% 8.72/1.65 (upairinpowunion = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f450])).
% 8.72/1.65 thf(f450,plain,(
% 8.72/1.65 (upairinpowunion = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f449])).
% 8.72/1.65 thf(f449,plain,(
% 8.72/1.65 (! [X0,X1,X2] : ((in @ X1 @ X0) => ! [X3] : ((in @ X3 @ X2) => (in @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X0 @ X2))))) = upairinpowunion)),
% 8.72/1.65 inference(rectify,[],[f145])).
% 8.72/1.65 thf(f145,axiom,(
% 8.72/1.65 (! [X3,X1,X4] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => (in @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ (powerset @ (binunion @ X3 @ X4))))) = upairinpowunion)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairinpowunion)).
% 8.72/1.65 thf(f669,plain,(
% 8.72/1.65 (upairsubunion = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y2)))))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f337])).
% 8.72/1.65 thf(f337,plain,(
% 8.72/1.65 (upairsubunion = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y2)))))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f336])).
% 8.72/1.65 thf(f336,plain,(
% 8.72/1.65 (! [X0,X1,X2] : ((in @ X2 @ X1) => ! [X3] : ((in @ X3 @ X0) => (subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X1 @ X0)))) = upairsubunion)),
% 8.72/1.65 inference(rectify,[],[f144])).
% 8.72/1.65 thf(f144,axiom,(
% 8.72/1.65 (! [X4,X3,X1] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => (subset @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ (binunion @ X3 @ X4)))) = upairsubunion)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsubunion)).
% 8.72/1.65 thf(f702,plain,(
% 8.72/1.65 (upairset2E = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f408])).
% 8.72/1.65 thf(f408,plain,(
% 8.72/1.65 (upairset2E = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f407])).
% 8.72/1.65 thf(f407,plain,(
% 8.72/1.65 (upairset2E = ! [X0,X1,X2] : ((in @ X1 @ (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset))) => ((X0 = X1) | (X1 = X2))))),
% 8.72/1.65 inference(rectify,[],[f143])).
% 8.72/1.65 thf(f143,axiom,(
% 8.72/1.65 (upairset2E = ! [X2,X8,X1] : ((in @ X8 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset))) => ((X2 = X8) | (X1 = X8))))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2E)).
% 8.72/1.65 thf(f746,plain,(
% 8.72/1.65 (singletoninpowunion = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y1)))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f494])).
% 8.72/1.65 thf(f494,plain,(
% 8.72/1.65 (singletoninpowunion = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y1)))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f493])).
% 8.72/1.65 thf(f493,plain,(
% 8.72/1.65 (singletoninpowunion = ! [X0,X1,X2] : ((in @ X2 @ X0) => (in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X0 @ X1)))))),
% 8.72/1.65 inference(rectify,[],[f142])).
% 8.72/1.65 thf(f142,axiom,(
% 8.72/1.65 (singletoninpowunion = ! [X3,X4,X1] : ((in @ X1 @ X3) => (in @ (setadjoin @ X1 @ emptyset) @ (powerset @ (binunion @ X3 @ X4)))))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletoninpowunion)).
% 8.72/1.65 thf(f755,plain,(
% 8.72/1.65 (singletoninpowerset = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ Y0))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f442])).
% 8.72/1.65 thf(f442,plain,(
% 8.72/1.65 (singletoninpowerset = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ Y0))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f441])).
% 8.72/1.65 thf(f441,plain,(
% 8.72/1.65 (singletoninpowerset = ! [X0,X1] : ((in @ X0 @ X1) => (in @ (setadjoin @ X0 @ emptyset) @ (powerset @ X1))))),
% 8.72/1.65 inference(rectify,[],[f141])).
% 8.72/1.65 thf(f141,axiom,(
% 8.72/1.65 (singletoninpowerset = ! [X1,X3] : ((in @ X1 @ X3) => (in @ (setadjoin @ X1 @ emptyset) @ (powerset @ X3))))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletoninpowerset)).
% 8.72/1.65 thf(f719,plain,(
% 8.72/1.65 (singletonsubset = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f265])).
% 8.72/1.65 thf(f265,plain,(
% 8.72/1.65 (singletonsubset = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))))),
% 8.72/1.65 inference(fool_elimination,[],[f264])).
% 8.72/1.65 thf(f264,plain,(
% 8.72/1.65 (! [X0,X1] : ((in @ X0 @ X1) => (subset @ (setadjoin @ X0 @ emptyset) @ X1)) = singletonsubset)),
% 8.72/1.65 inference(rectify,[],[f140])).
% 8.72/1.65 thf(f140,axiom,(
% 8.72/1.65 (! [X1,X3] : ((in @ X1 @ X3) => (subset @ (setadjoin @ X1 @ emptyset) @ X3)) = singletonsubset)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsubset)).
% 8.72/1.65 thf(f656,plain,(
% 8.72/1.65 (kpairp = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y0 @ Y1)))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f563])).
% 8.72/1.65 thf(f563,plain,(
% 8.72/1.65 (kpairp = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y0 @ Y1)))))))),
% 8.72/1.65 inference(fool_elimination,[],[f562])).
% 8.72/1.65 thf(f562,plain,(
% 8.72/1.65 (kpairp = ! [X0,X1] : (iskpair @ (kpair @ X1 @ X0)))),
% 8.72/1.65 inference(rectify,[],[f139])).
% 8.72/1.65 thf(f139,axiom,(
% 8.72/1.65 (kpairp = ! [X2,X1] : (iskpair @ (kpair @ X1 @ X2)))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairp)).
% 8.72/1.65 thf(f706,plain,(
% 8.72/1.65 (kpairiskpair = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f514])).
% 8.72/1.65 thf(f514,plain,(
% 8.72/1.65 (kpairiskpair = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f513])).
% 8.72/1.65 thf(f513,plain,(
% 8.72/1.65 (kpairiskpair = ! [X0,X1] : (iskpair @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))))),
% 8.72/1.65 inference(rectify,[],[f138])).
% 8.72/1.65 thf(f138,axiom,(
% 8.72/1.65 (kpairiskpair = ! [X1,X2] : (iskpair @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset))))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairiskpair)).
% 8.72/1.65 thf(f627,plain,(
% 8.72/1.65 (setukpairIR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f398])).
% 8.72/1.65 thf(f398,plain,(
% 8.72/1.65 (setukpairIR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f397])).
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% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairIL)).
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% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffE)).
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% 8.72/1.65 inference(fool_elimination,[],[f392])).
% 8.72/1.65 thf(f392,plain,(
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% 8.72/1.65 thf(f120,axiom,(
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% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusI)).
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% 8.72/1.65 thf(f119,axiom,(
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% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bs114d)).
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% 8.72/1.65 thf(f118,axiom,(
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% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset1)).
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% 8.72/1.65 thf(f117,axiom,(
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% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset4)).
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% 8.72/1.65 thf(f785,plain,(
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% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjointsetsI1)).
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% 8.72/1.65 thf(f114,axiom,(
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% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectER)).
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% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset3)).
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% 8.72/1.65 thf(f112,axiom,(
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% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset2)).
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% 8.72/1.65 thf(f111,axiom,(
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% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectLsub)).
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% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectEL)).
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% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset5)).
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% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionRsub)).
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% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionLsub)).
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% 8.72/1.65 thf(f105,axiom,(
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% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionE)).
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% 8.72/1.65 inference(rectify,[],[f104])).
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% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionEcases)).
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% 8.72/1.65 inference(fool_elimination,[],[f212])).
% 8.72/1.65 thf(f212,plain,(
% 8.72/1.65 (! [X0,X1,X2] : ((subset @ X1 @ X2) => (~(in @ X0 @ X2) => ~(in @ X0 @ X1))) = subsetE2)),
% 8.72/1.65 inference(rectify,[],[f84])).
% 8.72/1.65 thf(f84,axiom,(
% 8.72/1.65 (! [X1,X3,X4] : ((subset @ X3 @ X4) => (~(in @ X1 @ X4) => ~(in @ X1 @ X3))) = subsetE2)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE2)).
% 8.72/1.65 thf(f802,plain,(
% 8.72/1.65 (subsetE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f278])).
% 8.72/1.65 thf(f278,plain,(
% 8.72/1.65 (subsetE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f277])).
% 8.72/1.65 thf(f277,plain,(
% 8.72/1.65 (! [X0,X1,X2] : ((subset @ X2 @ X0) => ((in @ X1 @ X2) => (in @ X1 @ X0))) = subsetE)),
% 8.72/1.65 inference(rectify,[],[f83])).
% 8.72/1.65 thf(f83,axiom,(
% 8.72/1.65 (! [X4,X1,X3] : ((subset @ X3 @ X4) => ((in @ X1 @ X3) => (in @ X1 @ X4))) = subsetE)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE)).
% 8.72/1.65 thf(f742,plain,(
% 8.72/1.65 (emptysetsubset = (!! @ $i @ (^[Y0 : $i]: (subset @ emptyset @ Y0))))),
% 8.72/1.65 inference(cnf_transformation,[],[f492])).
% 8.72/1.65 thf(f492,plain,(
% 8.72/1.65 (emptysetsubset = (!! @ $i @ (^[Y0 : $i]: (subset @ emptyset @ Y0))))),
% 8.72/1.65 inference(fool_elimination,[],[f491])).
% 8.72/1.65 thf(f491,plain,(
% 8.72/1.65 (emptysetsubset = ! [X0] : (subset @ emptyset @ X0))),
% 8.72/1.65 inference(rectify,[],[f82])).
% 8.72/1.65 thf(f82,axiom,(
% 8.72/1.65 (emptysetsubset = ! [X3] : (subset @ emptyset @ X3))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetsubset)).
% 8.72/1.65 thf(f685,plain,(
% 8.72/1.65 (subsetI2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f257])).
% 8.72/1.65 thf(f257,plain,(
% 8.72/1.65 (subsetI2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))))),
% 8.72/1.65 inference(fool_elimination,[],[f256])).
% 8.72/1.65 thf(f256,plain,(
% 8.72/1.65 (! [X0,X1] : (! [X2] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI2)),
% 8.72/1.65 inference(rectify,[],[f81])).
% 8.72/1.65 thf(f81,axiom,(
% 8.72/1.65 (! [X3,X4] : (! [X1] : ((in @ X1 @ X3) => (in @ X1 @ X4)) => (subset @ X3 @ X4)) = subsetI2)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2)).
% 8.72/1.65 thf(f794,plain,(
% 8.72/1.65 (eqimpsubset1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f369])).
% 8.72/1.65 thf(f369,plain,(
% 8.72/1.65 (eqimpsubset1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))))),
% 8.72/1.65 inference(fool_elimination,[],[f368])).
% 8.72/1.65 thf(f368,plain,(
% 8.72/1.65 (eqimpsubset1 = ! [X0,X1] : ((X0 = X1) => (subset @ X1 @ X0)))),
% 8.72/1.65 inference(rectify,[],[f80])).
% 8.72/1.65 thf(f80,axiom,(
% 8.72/1.65 (eqimpsubset1 = ! [X4,X3] : ((X3 = X4) => (subset @ X3 @ X4)))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset1)).
% 8.72/1.65 thf(f636,plain,(
% 8.72/1.65 (eqimpsubset2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f215])).
% 8.72/1.65 thf(f215,plain,(
% 8.72/1.65 (eqimpsubset2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))))),
% 8.72/1.65 inference(fool_elimination,[],[f214])).
% 8.72/1.65 thf(f214,plain,(
% 8.72/1.65 (! [X0,X1] : ((X0 = X1) => (subset @ X1 @ X0)) = eqimpsubset2)),
% 8.72/1.65 inference(rectify,[],[f79])).
% 8.72/1.65 thf(f79,axiom,(
% 8.72/1.65 (! [X3,X4] : ((X3 = X4) => (subset @ X4 @ X3)) = eqimpsubset2)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset2)).
% 8.72/1.65 thf(f808,plain,(
% 8.72/1.65 (subsetI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f371])).
% 8.72/1.65 thf(f371,plain,(
% 8.72/1.65 (subsetI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))))),
% 8.72/1.65 inference(fool_elimination,[],[f370])).
% 8.72/1.65 thf(f370,plain,(
% 8.72/1.65 (subsetI1 = ! [X0,X1] : (! [X2] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)))),
% 8.72/1.65 inference(rectify,[],[f78])).
% 8.72/1.65 thf(f78,axiom,(
% 8.72/1.65 (subsetI1 = ! [X4,X3] : (! [X1] : ((in @ X1 @ X3) => (in @ X1 @ X4)) => (subset @ X3 @ X4)))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1)).
% 8.72/1.65 thf(f638,plain,(
% 8.72/1.65 (dsetconstr__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ (^[Y4 : $i]: (Y3 @ Y4))) = (dsetconstr @ Y1 @ (^[Y4 : $i]: (Y2 @ Y4)))))))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f482])).
% 8.72/1.65 thf(f482,plain,(
% 8.72/1.65 (dsetconstr__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y2 @ Y4) = (Y3 @ Y5))))))))) => ((dsetconstr @ Y0 @ (^[Y4 : $i]: (Y3 @ Y4))) = (dsetconstr @ Y1 @ (^[Y4 : $i]: (Y2 @ Y4)))))))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f481])).
% 8.72/1.65 thf(f481,plain,(
% 8.72/1.65 (! [X0,X1] : ((X0 = X1) => ! [X2 : $i > $o,X3 : $i > $o] : (! [X4] : ((in @ X4 @ X0) => ! [X5] : ((in @ X5 @ X1) => ((X4 = X5) => ((X3 @ X4) <=> (X2 @ X5))))) => ((dsetconstr @ X1 @ (^[X6 : $i] : (X2 @ X6))) = (dsetconstr @ X0 @ (^[X7 : $i] : (X3 @ X7)))))) = dsetconstr__Cong)),
% 8.72/1.65 inference(rectify,[],[f77])).
% 8.72/1.65 thf(f77,axiom,(
% 8.72/1.65 (! [X3,X4] : ((X3 = X4) => ! [X9 : $i > $o,X0 : $i > $o] : (! [X1] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => ((X1 = X2) => ((X0 @ X1) <=> (X9 @ X2))))) => ((dsetconstr @ X4 @ (^[X1 : $i] : (X9 @ X1))) = (dsetconstr @ X3 @ (^[X1 : $i] : (X0 @ X1)))))) = dsetconstr__Cong)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstr__Cong)).
% 8.72/1.65 thf(f842,plain,(
% 8.72/1.65 (descr__Cong = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => (((^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) => (Y3 = Y4)))))))) @ (^[Y2 : $i]: (Y0 @ Y2))) => (((^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) => (Y3 = Y4)))))))) @ (^[Y2 : $i]: (Y1 @ Y2))) => ((descr @ (^[Y2 : $i]: (Y0 @ Y2))) = (descr @ (^[Y2 : $i]: (Y1 @ Y2))))))))))))),
% 8.72/1.65 inference(definition_unfolding,[],[f759,f726,f726])).
% 8.72/1.65 thf(f726,plain,(
% 8.72/1.65 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f375])).
% 8.72/1.65 thf(f375,plain,(
% 8.72/1.65 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f374])).
% 8.72/1.65 thf(f374,plain,(
% 8.72/1.65 ((^[X0 : $i > $o] : (? [X1] : (! [X2] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))) = exu)),
% 8.72/1.65 inference(rectify,[],[f1])).
% 8.72/1.65 thf(f1,axiom,(
% 8.72/1.65 ((^[X0 : $i > $o] : (? [X1] : (! [X2] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))) = exu)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu)).
% 8.72/1.65 thf(f759,plain,(
% 8.72/1.65 (descr__Cong = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((exu @ (^[Y2 : $i]: (Y0 @ Y2))) => ((exu @ (^[Y2 : $i]: (Y1 @ Y2))) => ((descr @ (^[Y2 : $i]: (Y0 @ Y2))) = (descr @ (^[Y2 : $i]: (Y1 @ Y2))))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f251])).
% 8.72/1.65 thf(f251,plain,(
% 8.72/1.65 (descr__Cong = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((exu @ (^[Y2 : $i]: (Y0 @ Y2))) => ((exu @ (^[Y2 : $i]: (Y1 @ Y2))) => ((descr @ (^[Y2 : $i]: (Y0 @ Y2))) = (descr @ (^[Y2 : $i]: (Y1 @ Y2))))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f250])).
% 8.72/1.65 thf(f250,plain,(
% 8.72/1.65 (descr__Cong = ! [X0 : $i > $o,X1 : $i > $o] : (! [X2,X3] : ((X2 = X3) => ((X1 @ X2) <=> (X0 @ X3))) => ((exu @ (^[X4 : $i] : (X1 @ X4))) => ((exu @ (^[X5 : $i] : (X0 @ X5))) => ((descr @ (^[X6 : $i] : (X1 @ X6))) = (descr @ (^[X7 : $i] : (X0 @ X7))))))))),
% 8.72/1.65 inference(rectify,[],[f76])).
% 8.72/1.65 thf(f76,axiom,(
% 8.72/1.65 (descr__Cong = ! [X9 : $i > $o,X0 : $i > $o] : (! [X1,X2] : ((X1 = X2) => ((X0 @ X1) <=> (X9 @ X2))) => ((exu @ (^[X1 : $i] : (X0 @ X1))) => ((exu @ (^[X1 : $i] : (X9 @ X1))) => ((descr @ (^[X1 : $i] : (X0 @ X1))) = (descr @ (^[X1 : $i] : (X9 @ X1))))))))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',descr__Cong)).
% 8.72/1.65 thf(f841,plain,(
% 8.72/1.65 (exuEu = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))))))) @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))))),
% 8.72/1.65 inference(definition_unfolding,[],[f718,f726])).
% 8.72/1.65 thf(f718,plain,(
% 8.72/1.65 (exuEu = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f478])).
% 8.72/1.65 thf(f478,plain,(
% 8.72/1.65 (exuEu = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f477])).
% 8.72/1.65 thf(f477,plain,(
% 8.72/1.65 (! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ! [X2,X3] : ((X0 @ X2) => ((X0 @ X3) => (X2 = X3)))) = exuEu)),
% 8.72/1.65 inference(rectify,[],[f75])).
% 8.72/1.65 thf(f75,axiom,(
% 8.72/1.65 (! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ! [X1,X2] : ((X0 @ X1) => ((X0 @ X2) => (X1 = X2)))) = exuEu)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuEu)).
% 8.72/1.65 thf(f809,plain,(
% 8.72/1.65 (omega__Cong = (omega = omega))),
% 8.72/1.65 inference(cnf_transformation,[],[f394])).
% 8.72/1.65 thf(f394,plain,(
% 8.72/1.65 (omega__Cong = (omega = omega))),
% 8.72/1.65 inference(fool_elimination,[],[f74])).
% 8.72/1.65 thf(f74,axiom,(
% 8.72/1.65 ((omega = omega) = omega__Cong)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega__Cong)).
% 8.72/1.65 thf(f666,plain,(
% 8.72/1.65 (setunion__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f506])).
% 8.72/1.65 thf(f506,plain,(
% 8.72/1.65 (setunion__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f505])).
% 8.72/1.65 thf(f505,plain,(
% 8.72/1.65 (setunion__Cong = ! [X0,X1] : ((X0 = X1) => ((setunion @ X1) = (setunion @ X0))))),
% 8.72/1.65 inference(rectify,[],[f73])).
% 8.72/1.65 thf(f73,axiom,(
% 8.72/1.65 (setunion__Cong = ! [X4,X3] : ((X3 = X4) => ((setunion @ X3) = (setunion @ X4))))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunion__Cong)).
% 8.72/1.65 thf(f708,plain,(
% 8.72/1.65 (powerset__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f460])).
% 8.72/1.65 thf(f460,plain,(
% 8.72/1.65 (powerset__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f459])).
% 8.72/1.65 thf(f459,plain,(
% 8.72/1.65 (powerset__Cong = ! [X0,X1] : ((X0 = X1) => ((powerset @ X0) = (powerset @ X1))))),
% 8.72/1.65 inference(rectify,[],[f72])).
% 8.72/1.65 thf(f72,axiom,(
% 8.72/1.65 (powerset__Cong = ! [X3,X4] : ((X3 = X4) => ((powerset @ X3) = (powerset @ X4))))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powerset__Cong)).
% 8.72/1.65 thf(f701,plain,(
% 8.72/1.65 (setadjoin__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f355])).
% 8.72/1.65 thf(f355,plain,(
% 8.72/1.65 (setadjoin__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f354])).
% 8.72/1.65 thf(f354,plain,(
% 8.72/1.65 (! [X0,X1] : ((X0 = X1) => ! [X2,X3] : ((X2 = X3) => ((setadjoin @ X1 @ X2) = (setadjoin @ X0 @ X3)))) = setadjoin__Cong)),
% 8.72/1.65 inference(rectify,[],[f71])).
% 8.72/1.65 thf(f71,axiom,(
% 8.72/1.65 (! [X1,X2] : ((X1 = X2) => ! [X10,X8] : ((X8 = X10) => ((setadjoin @ X1 @ X8) = (setadjoin @ X2 @ X10)))) = setadjoin__Cong)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoin__Cong)).
% 8.72/1.65 thf(f738,plain,(
% 8.72/1.65 (emptyset__Cong = (emptyset = emptyset))),
% 8.72/1.65 inference(cnf_transformation,[],[f539])).
% 8.72/1.65 thf(f539,plain,(
% 8.72/1.65 (emptyset__Cong = (emptyset = emptyset))),
% 8.72/1.65 inference(fool_elimination,[],[f70])).
% 8.72/1.65 thf(f70,axiom,(
% 8.72/1.65 (emptyset__Cong = (emptyset = emptyset))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyset__Cong)).
% 8.72/1.65 thf(f840,plain,(
% 8.72/1.65 (exu__Cong = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => (((^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) => (Y3 = Y4)))))))) @ (^[Y2 : $i]: (Y0 @ Y2))) = ((^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) => (Y3 = Y4)))))))) @ (^[Y2 : $i]: (Y1 @ Y2))))))))))),
% 8.72/1.65 inference(definition_unfolding,[],[f625,f726,f726])).
% 8.72/1.65 thf(f625,plain,(
% 8.72/1.65 (exu__Cong = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((exu @ (^[Y2 : $i]: (Y0 @ Y2))) = (exu @ (^[Y2 : $i]: (Y1 @ Y2))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f496])).
% 8.72/1.65 thf(f496,plain,(
% 8.72/1.65 (exu__Cong = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y1 @ Y2) = (Y0 @ Y3))))))) => ((exu @ (^[Y2 : $i]: (Y0 @ Y2))) = (exu @ (^[Y2 : $i]: (Y1 @ Y2))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f495])).
% 8.72/1.65 thf(f495,plain,(
% 8.72/1.65 (exu__Cong = ! [X0 : $i > $o,X1 : $i > $o] : (! [X2,X3] : ((X2 = X3) => ((X0 @ X3) <=> (X1 @ X2))) => ((exu @ (^[X4 : $i] : (X1 @ X4))) <=> (exu @ (^[X5 : $i] : (X0 @ X5))))))),
% 8.72/1.65 inference(rectify,[],[f69])).
% 8.72/1.65 thf(f69,axiom,(
% 8.72/1.65 (exu__Cong = ! [X9 : $i > $o,X0 : $i > $o] : (! [X1,X2] : ((X1 = X2) => ((X9 @ X2) <=> (X0 @ X1))) => ((exu @ (^[X1 : $i] : (X0 @ X1))) <=> (exu @ (^[X1 : $i] : (X9 @ X1))))))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu__Cong)).
% 8.72/1.65 thf(f839,plain,(
% 8.72/1.65 (exuE3u = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))))))) @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))))),
% 8.72/1.65 inference(definition_unfolding,[],[f823,f726])).
% 8.72/1.65 thf(f823,plain,(
% 8.72/1.65 (exuE3u = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f341])).
% 8.72/1.65 thf(f341,plain,(
% 8.72/1.65 (exuE3u = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f340])).
% 8.72/1.65 thf(f340,plain,(
% 8.72/1.65 (! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ! [X2,X3] : ((X0 @ X2) => ((X0 @ X3) => (X2 = X3)))) = exuE3u)),
% 8.72/1.65 inference(rectify,[],[f68])).
% 8.72/1.65 thf(f68,axiom,(
% 8.72/1.65 (! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ! [X1,X2] : ((X0 @ X1) => ((X0 @ X2) => (X1 = X2)))) = exuE3u)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3u)).
% 8.72/1.65 thf(f769,plain,(
% 8.72/1.65 (in__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f619])).
% 8.72/1.65 thf(f619,plain,(
% 8.72/1.65 (in__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y2 @ Y0) = (in @ Y3 @ Y1)))))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f618])).
% 8.72/1.65 thf(f618,plain,(
% 8.72/1.65 (! [X0,X1] : ((X0 = X1) => ! [X2,X3] : ((X2 = X3) => ((in @ X3 @ X1) <=> (in @ X2 @ X0)))) = in__Cong)),
% 8.72/1.65 inference(rectify,[],[f67])).
% 8.72/1.65 thf(f67,axiom,(
% 8.72/1.65 (! [X4,X3] : ((X3 = X4) => ! [X2,X1] : ((X1 = X2) => ((in @ X1 @ X3) <=> (in @ X2 @ X4)))) = in__Cong)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in__Cong)).
% 8.72/1.65 thf(f645,plain,(
% 8.72/1.65 (inCongP = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f617])).
% 8.72/1.65 thf(f617,plain,(
% 8.72/1.65 (inCongP = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f616])).
% 8.72/1.65 thf(f616,plain,(
% 8.72/1.65 (! [X0,X1] : ((X0 = X1) => ! [X2,X3] : ((X2 = X3) => ((in @ X2 @ X0) => (in @ X3 @ X1)))) = inCongP)),
% 8.72/1.65 inference(rectify,[],[f66])).
% 8.72/1.65 thf(f66,axiom,(
% 8.72/1.65 (! [X3,X4] : ((X3 = X4) => ! [X1,X2] : ((X1 = X2) => ((in @ X1 @ X3) => (in @ X2 @ X4)))) = inCongP)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inCongP)).
% 8.72/1.65 thf(f838,plain,(
% 8.72/1.65 (exuI2 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))))))) @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 8.72/1.65 inference(definition_unfolding,[],[f728,f726])).
% 8.72/1.65 thf(f728,plain,(
% 8.72/1.65 (exuI2 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f406])).
% 8.72/1.65 thf(f406,plain,(
% 8.72/1.65 (exuI2 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 8.72/1.65 inference(fool_elimination,[],[f405])).
% 8.72/1.65 thf(f405,plain,(
% 8.72/1.65 (exuI2 = ! [X0 : $i > $o] : (? [X1] : ! [X2] : ((X0 @ X2) <=> (X1 = X2)) => (exu @ (^[X3 : $i] : (X0 @ X3)))))),
% 8.72/1.65 inference(rectify,[],[f65])).
% 8.72/1.65 thf(f65,axiom,(
% 8.72/1.65 (exuI2 = ! [X0 : $i > $o] : (? [X1] : ! [X2] : ((X0 @ X2) <=> (X1 = X2)) => (exu @ (^[X1 : $i] : (X0 @ X1)))))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI2)).
% 8.72/1.65 thf(f837,plain,(
% 8.72/1.65 (exuI3 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))))))) @ (^[Y1 : $i]: (Y0 @ Y1))))))))),
% 8.72/1.65 inference(definition_unfolding,[],[f770,f726])).
% 8.72/1.65 thf(f770,plain,(
% 8.72/1.65 (exuI3 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f297])).
% 8.72/1.65 thf(f297,plain,(
% 8.72/1.65 (exuI3 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1))))))))),
% 8.72/1.65 inference(fool_elimination,[],[f296])).
% 8.72/1.65 thf(f296,plain,(
% 8.72/1.65 (exuI3 = ! [X0 : $i > $o] : (? [X1] : (X0 @ X1) => (! [X2,X3] : ((X0 @ X3) => ((X0 @ X2) => (X2 = X3))) => (exu @ (^[X4 : $i] : (X0 @ X4))))))),
% 8.72/1.65 inference(rectify,[],[f64])).
% 8.72/1.65 thf(f64,axiom,(
% 8.72/1.65 (exuI3 = ! [X0 : $i > $o] : (? [X1] : (X0 @ X1) => (! [X2,X1] : ((X0 @ X1) => ((X0 @ X2) => (X1 = X2))) => (exu @ (^[X1 : $i] : (X0 @ X1))))))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI3)).
% 8.72/1.65 thf(f836,plain,(
% 8.72/1.65 (exuI1 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))))))) @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 8.72/1.65 inference(definition_unfolding,[],[f820,f726])).
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% 8.72/1.65 inference(cnf_transformation,[],[f361])).
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% 8.72/1.65 inference(fool_elimination,[],[f360])).
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% 8.72/1.65 (! [X0 : $i > $o] : (? [X1] : (! [X2] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)) => (exu @ (^[X3 : $i] : (X0 @ X3)))) = exuI1)),
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% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI1)).
% 8.72/1.65 thf(f637,plain,(
% 8.72/1.65 (notdallE = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f259])).
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% 8.72/1.65 inference(fool_elimination,[],[f258])).
% 8.72/1.65 thf(f258,plain,(
% 8.72/1.65 (notdallE = ! [X0,X1 : $i > $o] : (~! [X2] : ((in @ X2 @ X0) => (X1 @ X2)) => ? [X3] : ((in @ X3 @ X0) & ~(X1 @ X3))))),
% 8.72/1.65 inference(rectify,[],[f62])).
% 8.72/1.65 thf(f62,axiom,(
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% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notdallE)).
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% 8.72/1.65 (notdexE = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f295])).
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% 8.72/1.65 inference(fool_elimination,[],[f294])).
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% 8.72/1.65 (! [X0,X1 : $i > $o] : (~? [X2] : ((X1 @ X2) & (in @ X2 @ X0)) => ! [X3] : ((in @ X3 @ X0) => ~(X1 @ X3))) = notdexE)),
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% 8.72/1.65 (! [X3,X0 : $i > $o] : (~? [X1] : ((X0 @ X1) & (in @ X1 @ X3)) => ! [X1] : ((in @ X1 @ X3) => ~(X0 @ X1))) = notdexE)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notdexE)).
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% 8.72/1.65 (prop2set2propI = ! [X0 : $o] : (X0 => (set2prop @ (prop2set @ X0))))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2set2propI)).
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% 8.72/1.65 inference(rectify,[],[f59])).
% 8.72/1.65 thf(f59,axiom,(
% 8.72/1.65 (prop2setI = ! [X0 : $o] : (X0 => (in @ emptyset @ (prop2set @ X0))))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setI)).
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% 8.72/1.65 inference(cnf_transformation,[],[f555])).
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% 8.72/1.65 inference(fool_elimination,[],[f554])).
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% 8.72/1.65 (quantDeMorgan4 = ! [X0 : $i > $o,X1] : (? [X2] : (~(X0 @ X2) & (in @ X2 @ X1)) => ~! [X3] : ((in @ X3 @ X1) => (X0 @ X3))))),
% 8.72/1.65 inference(rectify,[],[f58])).
% 8.72/1.65 thf(f58,axiom,(
% 8.72/1.65 (quantDeMorgan4 = ! [X0 : $i > $o,X3] : (? [X1] : (~(X0 @ X1) & (in @ X1 @ X3)) => ~! [X1] : ((in @ X1 @ X3) => (X0 @ X1))))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan4)).
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% 8.72/1.65 inference(cnf_transformation,[],[f484])).
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% 8.72/1.65 inference(fool_elimination,[],[f483])).
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% 8.72/1.65 inference(rectify,[],[f57])).
% 8.72/1.65 thf(f57,axiom,(
% 8.72/1.65 (! [X0 : $i > $o,X3] : (~? [X1] : ((X0 @ X1) & (in @ X1 @ X3)) => ! [X1] : ((in @ X1 @ X3) => ~(X0 @ X1))) = quantDeMorgan3)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan3)).
% 8.72/1.65 thf(f665,plain,(
% 8.72/1.65 (quantDeMorgan2 = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))))))))))),
% 8.72/1.65 inference(cnf_transformation,[],[f385])).
% 8.72/1.65 thf(f385,plain,(
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% 8.72/1.65 inference(fool_elimination,[],[f384])).
% 8.72/1.65 thf(f384,plain,(
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% 8.72/1.65 inference(rectify,[],[f56])).
% 8.72/1.65 thf(f56,axiom,(
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% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan2)).
% 8.72/1.65 thf(f688,plain,(
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% 8.72/1.65 inference(fool_elimination,[],[f226])).
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% 8.72/1.65 inference(rectify,[],[f55])).
% 8.72/1.65 thf(f55,axiom,(
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% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan1)).
% 8.72/1.65 thf(f764,plain,(
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% 8.72/1.65 inference(cnf_transformation,[],[f335])).
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% 8.72/1.65 inference(fool_elimination,[],[f334])).
% 8.72/1.65 thf(f334,plain,(
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% 8.72/1.65 inference(rectify,[],[f54])).
% 8.72/1.65 thf(f54,axiom,(
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% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vacuousDall)).
% 8.72/1.65 thf(f810,plain,(
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% 8.72/1.65 inference(cnf_transformation,[],[f567])).
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% 8.72/1.65 inference(fool_elimination,[],[f566])).
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% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyE1)).
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% 8.72/1.65 thf(f52,axiom,(
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% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIR)).
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% 8.72/1.65 inference(cnf_transformation,[],[f589])).
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% 8.72/1.65 thf(f51,axiom,(
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% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIL)).
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% 8.72/1.65 thf(f50,axiom,(
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% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetE)).
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% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsswitch)).
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% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyImpWitness)).
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% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE2)).
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% 8.72/1.65 inference(cnf_transformation,[],[f426])).
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% 8.72/1.65 thf(f43,axiom,(
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% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subPowSU)).
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% 8.72/1.65 thf(f23,axiom,(
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% 8.72/1.65 inference(definition_unfolding,[],[f668,f726])).
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% 8.72/1.65 thf(f22,axiom,(
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% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3e)).
% 8.72/1.65 thf(f698,plain,(
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% 8.72/1.65 thf(f445,plain,(
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% 8.72/1.65 inference(rectify,[],[f21])).
% 8.72/1.65 thf(f21,axiom,(
% 8.72/1.65 (notinemptyset = ! [X1] : ~(in @ X1 @ emptyset))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinemptyset)).
% 8.72/1.65 thf(f779,plain,(
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% 8.72/1.65 inference(rectify,[],[f20])).
% 8.72/1.65 thf(f20,axiom,(
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% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetimpfalse)).
% 8.72/1.65 thf(f633,plain,(
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% 8.72/1.65 thf(f19,axiom,(
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% 8.72/1.65 thf(f332,plain,(
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% 8.72/1.65 thf(f18,axiom,(
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% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setE)).
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% 8.72/1.65 inference(cnf_transformation,[],[f365])).
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% 8.72/1.65 thf(f364,plain,(
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% 8.72/1.65 thf(f17,axiom,(
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% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE1)).
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% 8.72/1.65 (dsetconstrER = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3)))) => (Y1 @ Y0)))))))))),
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% 8.72/1.65 thf(f16,axiom,(
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% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER)).
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% 8.72/1.65 thf(f15,axiom,(
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% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrEL)).
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% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrI)).
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% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',descrp)).
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% 8.72/1.65 inference(rectify,[],[f12])).
% 8.72/1.65 thf(f12,axiom,(
% 8.72/1.65 (! [X3] : ? [X4] : (! [X1,X2] : (((in @ X1 @ X3) & (in @ X2 @ X3)) => (! [X5] : ((in @ X5 @ X4) => ((in @ X1 @ X5) <=> (in @ X2 @ X5))) => (X1 = X2))) & ! [X5,X6] : (((in @ X6 @ X4) & (in @ X5 @ X4)) => (! [X1] : ((in @ X1 @ X6) => (in @ X1 @ X5)) | ! [X1] : ((in @ X1 @ X5) => (in @ X1 @ X6)))) & ! [X5] : ((in @ X5 @ X4) => ! [X1] : ((in @ X1 @ X5) => (in @ X1 @ X3))) & ! [X5] : ((? [X1] : (in @ X1 @ X5) & ! [X1] : ((in @ X1 @ X5) => (in @ X1 @ X3))) => ? [X6,X1] : ((in @ X1 @ X5) & (in @ X6 @ X4) & ~? [X2] : ((in @ X2 @ X6) & (in @ X2 @ X5)) & ! [X7] : ((in @ X7 @ X4) => (! [X2] : ((in @ X2 @ X7) => (in @ X2 @ X6)) | (in @ X1 @ X7)))))) = wellorderingAx)),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wellorderingAx)).
% 8.72/1.65 thf(f681,plain,(
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% 8.72/1.65 inference(cnf_transformation,[],[f532])).
% 8.72/1.65 thf(f532,plain,(
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% 8.72/1.65 inference(fool_elimination,[],[f531])).
% 8.72/1.65 thf(f531,plain,(
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% 8.72/1.65 inference(fool_elimination,[],[f224])).
% 8.72/1.65 thf(f224,plain,(
% 8.72/1.65 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => ! [X0,X1,X2] : ((breln @ X2 @ X1 @ X0) => ! [X3 : $i > $o] : (! [X4] : ((in @ X4 @ X2) => ! [X5] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X0) => (X3 @ (kpair @ X4 @ X5))))) => ! [X6] : ((in @ X6 @ X0) => (X3 @ X6))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.65 inference(rectify,[],[f208])).
% 8.72/1.65 thf(f208,negated_conjecture,(
% 8.72/1.65 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => ! [X12,X4,X3] : ((breln @ X3 @ X4 @ X12) => ! [X0 : $i > $o] : (! [X1] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => ((in @ (kpair @ X1 @ X2) @ X12) => (X0 @ (kpair @ X1 @ X2))))) => ! [X1] : ((in @ X1 @ X12) => (X0 @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.65 inference(negated_conjecture,[],[f207])).
% 8.72/1.65 thf(f207,conjecture,(
% 8.72/1.65 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => ! [X12,X4,X3] : ((breln @ X3 @ X4 @ X12) => ! [X0 : $i > $o] : (! [X1] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => ((in @ (kpair @ X1 @ X2) @ X12) => (X0 @ (kpair @ X1 @ X2))))) => ! [X1] : ((in @ X1 @ X12) => (X0 @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.72/1.65 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',brelnall2)).
% 8.72/1.65 % SZS output end Proof for theBenchmark
% 8.72/1.65 % (27436)------------------------------
% 8.72/1.65 % (27436)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 8.72/1.65 % (27436)Termination reason: Refutation
% 8.72/1.65
% 8.72/1.65 % (27436)Memory used [KB]: 222725
% 8.72/1.65 % (27436)Time elapsed: 1.193 s
% 8.72/1.65 % (27436)Instructions burned: 846 (million)
% 8.72/1.65 % (27436)------------------------------
% 8.72/1.65 % (27436)------------------------------
% 8.72/1.65 % (27424)Success in time 1.276 s
% 8.72/1.65 % Vampire---4.8 exiting
%------------------------------------------------------------------------------