TSTP Solution File: SEU674^1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU674^1 : 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n009.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 03:50:30 EDT 2024
% Result : Theorem 31.73s 4.40s
% Output : Refutation 31.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU674^1 : TPTP v8.2.0. Released v3.7.0.
% 0.06/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.34 % Computer : n009.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun May 19 16:55:23 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.14/0.34 This is a TH0_THM_EQU_NAR problem
% 0.14/0.34 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/sandbox/benchmark/theBenchmark.p
% 0.14/0.37 % (31996)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)
% 0.14/0.37 % (31997)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.37 % (31991)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.38 % (31998)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)
% 0.14/0.38 % (31995)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)
% 0.14/0.38 % (31998)Instruction limit reached!
% 0.14/0.38 % (31998)------------------------------
% 0.14/0.38 % (31998)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (31998)Termination reason: Unknown
% 0.14/0.38 % (31998)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (31995)Instruction limit reached!
% 0.14/0.38 % (31995)------------------------------
% 0.14/0.38 % (31995)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (31995)Termination reason: Unknown
% 0.14/0.38 % (31995)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (31995)Memory used [KB]: 1279
% 0.14/0.38 % (31995)Time elapsed: 0.003 s
% 0.14/0.38 % (31995)Instructions burned: 3 (million)
% 0.14/0.38 % (31995)------------------------------
% 0.14/0.38 % (31995)------------------------------
% 0.14/0.38 % (31998)Memory used [KB]: 1407
% 0.14/0.38 % (31998)Time elapsed: 0.005 s
% 0.14/0.38 % (31998)Instructions burned: 4 (million)
% 0.14/0.38 % (31998)------------------------------
% 0.14/0.38 % (31998)------------------------------
% 0.14/0.38 % (31997)Instruction limit reached!
% 0.14/0.38 % (31997)------------------------------
% 0.14/0.38 % (31997)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (31997)Termination reason: Unknown
% 0.14/0.38 % (31997)Termination phase: Property scanning
% 0.14/0.38
% 0.14/0.38 % (31997)Memory used [KB]: 1663
% 0.14/0.38 % (31997)Time elapsed: 0.010 s
% 0.14/0.38 % (31997)Instructions burned: 18 (million)
% 0.14/0.38 % (31997)------------------------------
% 0.14/0.38 % (31997)------------------------------
% 0.14/0.38 % (31994)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.38 % (31992)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)
% 0.14/0.38 % (31994)Instruction limit reached!
% 0.14/0.38 % (31994)------------------------------
% 0.14/0.38 % (31994)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (31994)Termination reason: Unknown
% 0.14/0.38 % (31994)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (31994)Memory used [KB]: 1279
% 0.14/0.38 % (31994)Time elapsed: 0.004 s
% 0.14/0.38 % (31994)Instructions burned: 3 (million)
% 0.14/0.38 % (31994)------------------------------
% 0.14/0.38 % (31994)------------------------------
% 0.14/0.38 % (31992)Instruction limit reached!
% 0.14/0.38 % (31992)------------------------------
% 0.14/0.38 % (31992)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (31992)Termination reason: Unknown
% 0.14/0.38 % (31992)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (31992)Memory used [KB]: 1407
% 0.14/0.38 % (31992)Time elapsed: 0.004 s
% 0.14/0.38 % (31992)Instructions burned: 5 (million)
% 0.14/0.38 % (31992)------------------------------
% 0.14/0.38 % (31992)------------------------------
% 0.20/0.39 % (31993)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)
% 0.20/0.39 % (31999)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)
% 0.20/0.40 % (32001)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)
% 0.20/0.40 % (32001)Instruction limit reached!
% 0.20/0.40 % (32001)------------------------------
% 0.20/0.40 % (32001)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.40 % (32001)Termination reason: Unknown
% 0.20/0.40 % (32001)Termination phase: shuffling
% 0.20/0.40
% 0.20/0.40 % (32001)Memory used [KB]: 1279
% 0.20/0.40 % (32001)Time elapsed: 0.003 s
% 0.20/0.40 % (32001)Instructions burned: 3 (million)
% 0.20/0.40 % (32001)------------------------------
% 0.20/0.40 % (32001)------------------------------
% 0.20/0.40 % (32000)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)
% 0.20/0.40 % (32002)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)
% 0.20/0.40 % (32003)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.40 % (31993)Instruction limit reached!
% 0.20/0.40 % (31993)------------------------------
% 0.20/0.40 % (31993)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.40 % (31993)Termination reason: Unknown
% 0.20/0.40 % (31993)Termination phase: shuffling
% 0.20/0.40
% 0.20/0.40 % (31993)Memory used [KB]: 1791
% 0.20/0.40 % (31993)Time elapsed: 0.016 s
% 0.20/0.40 % (31993)Instructions burned: 28 (million)
% 0.20/0.40 % (31993)------------------------------
% 0.20/0.40 % (31993)------------------------------
% 0.20/0.40 % (32003)Instruction limit reached!
% 0.20/0.40 % (32003)------------------------------
% 0.20/0.40 % (32003)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.40 % (32003)Termination reason: Unknown
% 0.20/0.40 % (32003)Termination phase: shuffling
% 0.20/0.40
% 0.20/0.40 % (32003)Memory used [KB]: 1407
% 0.20/0.40 % (32003)Time elapsed: 0.005 s
% 0.20/0.40 % (32003)Instructions burned: 7 (million)
% 0.20/0.40 % (32003)------------------------------
% 0.20/0.40 % (32003)------------------------------
% 0.20/0.40 % (32000)Instruction limit reached!
% 0.20/0.40 % (32000)------------------------------
% 0.20/0.40 % (32000)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.40 % (32000)Termination reason: Unknown
% 0.20/0.40 % (32000)Termination phase: shuffling
% 0.20/0.40
% 0.20/0.40 % (32000)Memory used [KB]: 1663
% 0.20/0.40 % (32000)Time elapsed: 0.009 s
% 0.20/0.40 % (32000)Instructions burned: 15 (million)
% 0.20/0.40 % (32000)------------------------------
% 0.20/0.40 % (32000)------------------------------
% 0.20/0.41 % (31999)Instruction limit reached!
% 0.20/0.41 % (31999)------------------------------
% 0.20/0.41 % (31999)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.41 % (31999)Termination reason: Unknown
% 0.20/0.41 % (31999)Termination phase: Property scanning
% 0.20/0.41
% 0.20/0.41 % (31999)Memory used [KB]: 2046
% 0.20/0.41 % (31999)Time elapsed: 0.018 s
% 0.20/0.41 % (31999)Instructions burned: 37 (million)
% 0.20/0.41 % (31999)------------------------------
% 0.20/0.41 % (31999)------------------------------
% 0.20/0.41 % (32004)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 % (32005)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)
% 0.20/0.42 % (32005)Instruction limit reached!
% 0.20/0.42 % (32005)------------------------------
% 0.20/0.42 % (32005)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.42 % (32005)Termination reason: Unknown
% 0.20/0.42 % (32005)Termination phase: shuffling
% 0.20/0.42
% 0.20/0.42 % (32005)Memory used [KB]: 1279
% 0.20/0.42 % (32005)Time elapsed: 0.004 s
% 0.20/0.42 % (32007)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)
% 0.20/0.42 % (32005)Instructions burned: 4 (million)
% 0.20/0.42 % (32005)------------------------------
% 0.20/0.42 % (32005)------------------------------
% 0.20/0.42 % (32006)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)
% 0.20/0.42 % (32004)Instruction limit reached!
% 0.20/0.42 % (32004)------------------------------
% 0.20/0.42 % (32004)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.42 % (32004)Termination reason: Unknown
% 0.20/0.42 % (32004)Termination phase: shuffling
% 0.20/0.42
% 0.20/0.42 % (32004)Memory used [KB]: 1663
% 0.20/0.42 % (32004)Time elapsed: 0.009 s
% 0.20/0.42 % (32004)Instructions burned: 17 (million)
% 0.20/0.42 % (32004)------------------------------
% 0.20/0.42 % (32004)------------------------------
% 0.20/0.42 % (32006)Instruction limit reached!
% 0.20/0.42 % (32006)------------------------------
% 0.20/0.42 % (32006)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.42 % (32006)Termination reason: Unknown
% 0.20/0.42 % (32006)Termination phase: shuffling
% 0.20/0.42
% 0.20/0.42 % (32006)Memory used [KB]: 1279
% 0.20/0.42 % (32006)Time elapsed: 0.003 s
% 0.20/0.42 % (32006)Instructions burned: 3 (million)
% 0.20/0.42 % (32006)------------------------------
% 0.20/0.42 % (32006)------------------------------
% 0.20/0.42 % (32007)Instruction limit reached!
% 0.20/0.42 % (32007)------------------------------
% 0.20/0.42 % (32007)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.42 % (32007)Termination reason: Unknown
% 0.20/0.42 % (32007)Termination phase: shuffling
% 0.20/0.42
% 0.20/0.42 % (32007)Memory used [KB]: 1407
% 0.20/0.42 % (32007)Time elapsed: 0.005 s
% 0.20/0.42 % (32007)Instructions burned: 8 (million)
% 0.20/0.42 % (32007)------------------------------
% 0.20/0.42 % (32007)------------------------------
% 0.20/0.43 % (32008)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)
% 0.20/0.43 % (32008)Instruction limit reached!
% 0.20/0.43 % (32008)------------------------------
% 0.20/0.43 % (32008)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.43 % (32008)Termination reason: Unknown
% 0.20/0.43 % (32008)Termination phase: shuffling
% 0.20/0.43
% 0.20/0.43 % (32008)Memory used [KB]: 1279
% 0.20/0.43 % (32008)Time elapsed: 0.003 s
% 0.20/0.43 % (32008)Instructions burned: 3 (million)
% 0.20/0.43 % (32008)------------------------------
% 0.20/0.43 % (32008)------------------------------
% 0.20/0.43 % (32009)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.20/0.43 % (32011)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.20/0.43 % (32009)Instruction limit reached!
% 0.20/0.43 % (32009)------------------------------
% 0.20/0.43 % (32009)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.43 % (32009)Termination reason: Unknown
% 0.20/0.43 % (32009)Termination phase: shuffling
% 0.20/0.43
% 0.20/0.43 % (32009)Memory used [KB]: 1407
% 0.20/0.43 % (32009)Time elapsed: 0.004 s
% 0.20/0.43 % (32009)Instructions burned: 4 (million)
% 0.20/0.43 % (32009)------------------------------
% 0.20/0.43 % (32009)------------------------------
% 0.20/0.43 % (32010)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 % (32012)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.20/0.44 % (32010)Instruction limit reached!
% 0.20/0.44 % (32010)------------------------------
% 0.20/0.44 % (32010)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.44 % (32010)Termination reason: Unknown
% 0.20/0.44 % (32010)Termination phase: shuffling
% 0.20/0.44
% 0.20/0.44 % (32010)Memory used [KB]: 1791
% 0.20/0.44 % (32010)Time elapsed: 0.010 s
% 0.20/0.44 % (32010)Instructions burned: 19 (million)
% 0.20/0.44 % (32010)------------------------------
% 0.20/0.44 % (32010)------------------------------
% 0.20/0.44 % (32012)Instruction limit reached!
% 0.20/0.44 % (32012)------------------------------
% 0.20/0.44 % (32012)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.44 % (32012)Termination reason: Unknown
% 0.20/0.44 % (32012)Termination phase: shuffling
% 0.20/0.44
% 0.20/0.44 % (32012)Memory used [KB]: 1407
% 0.20/0.44 % (32012)Time elapsed: 0.005 s
% 0.20/0.44 % (32012)Instructions burned: 7 (million)
% 0.20/0.44 % (32012)------------------------------
% 0.20/0.44 % (32012)------------------------------
% 0.20/0.45 % (32013)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 % (32015)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 % (32016)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)
% 0.20/0.46 % (32014)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 % (32015)Instruction limit reached!
% 0.20/0.46 % (32015)------------------------------
% 0.20/0.46 % (32015)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.46 % (32015)Termination reason: Unknown
% 0.20/0.46 % (32015)Termination phase: shuffling
% 0.20/0.46
% 0.20/0.46 % (32015)Memory used [KB]: 1407
% 0.20/0.46 % (32015)Time elapsed: 0.004 s
% 0.20/0.46 % (32015)Instructions burned: 5 (million)
% 0.20/0.46 % (32015)------------------------------
% 0.20/0.46 % (32015)------------------------------
% 0.20/0.46 % (32016)Instruction limit reached!
% 0.20/0.46 % (32016)------------------------------
% 0.20/0.46 % (32016)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.46 % (32016)Termination reason: Unknown
% 0.20/0.46 % (32016)Termination phase: shuffling
% 0.20/0.46
% 0.20/0.46 % (32016)Memory used [KB]: 1407
% 0.20/0.46 % (32016)Time elapsed: 0.005 s
% 0.20/0.46 % (32016)Instructions burned: 8 (million)
% 0.20/0.46 % (32016)------------------------------
% 0.20/0.46 % (32016)------------------------------
% 0.20/0.46 % (31991)Instruction limit reached!
% 0.20/0.46 % (31991)------------------------------
% 0.20/0.46 % (31991)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.46 % (31991)Termination reason: Unknown
% 0.20/0.46 % (31991)Termination phase: Saturation
% 0.20/0.46
% 0.20/0.46 % (31991)Memory used [KB]: 7419
% 0.20/0.46 % (31991)Time elapsed: 0.092 s
% 0.20/0.46 % (31991)Instructions burned: 183 (million)
% 0.20/0.46 % (31991)------------------------------
% 0.20/0.46 % (31991)------------------------------
% 0.20/0.47 % (32014)Instruction limit reached!
% 0.20/0.47 % (32014)------------------------------
% 0.20/0.47 % (32014)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.47 % (32014)Termination reason: Unknown
% 0.20/0.47 % (32014)Termination phase: shuffling
% 0.20/0.47
% 0.20/0.47 % (32014)Memory used [KB]: 1791
% 0.20/0.47 % (32014)Time elapsed: 0.012 s
% 0.20/0.47 % (32014)Instructions burned: 23 (million)
% 0.20/0.47 % (32014)------------------------------
% 0.20/0.47 % (32014)------------------------------
% 0.20/0.47 % (32017)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2998ds/377Mi)
% 0.20/0.48 % (32019)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 (2998ds/19Mi)
% 0.20/0.48 % (32018)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 (2998ds/779Mi)
% 0.20/0.48 % (32019)Instruction limit reached!
% 0.20/0.48 % (32019)------------------------------
% 0.20/0.48 % (32019)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.48 % (32019)Termination reason: Unknown
% 0.20/0.48 % (32019)Termination phase: shuffling
% 0.20/0.48
% 0.20/0.48 % (32019)Memory used [KB]: 1663
% 0.20/0.48 % (32019)Time elapsed: 0.008 s
% 0.20/0.48 % (32019)Instructions burned: 21 (million)
% 0.20/0.48 % (32019)------------------------------
% 0.20/0.48 % (32019)------------------------------
% 0.20/0.49 % (32020)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)
% 0.20/0.49 % (32021)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2998ds/17Mi)
% 0.20/0.50 % (32021)Instruction limit reached!
% 0.20/0.50 % (32021)------------------------------
% 0.20/0.50 % (32021)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.50 % (32021)Termination reason: Unknown
% 0.20/0.50 % (32021)Termination phase: shuffling
% 0.20/0.50
% 0.20/0.50 % (32021)Memory used [KB]: 1663
% 0.20/0.50 % (32021)Time elapsed: 0.007 s
% 0.20/0.50 % (32021)Instructions burned: 20 (million)
% 0.20/0.50 % (32021)------------------------------
% 0.20/0.50 % (32021)------------------------------
% 0.20/0.50 % (31996)Instruction limit reached!
% 0.20/0.50 % (31996)------------------------------
% 0.20/0.50 % (31996)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.50 % (31996)Termination reason: Unknown
% 0.20/0.50 % (31996)Termination phase: Saturation
% 0.20/0.50
% 0.20/0.50 % (31996)Memory used [KB]: 8443
% 0.20/0.50 % (31996)Time elapsed: 0.133 s
% 0.20/0.51 % (31996)Instructions burned: 275 (million)
% 0.20/0.51 % (31996)------------------------------
% 0.20/0.51 % (31996)------------------------------
% 0.20/0.51 % (32022)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi)
% 0.20/0.51 % (32022)Instruction limit reached!
% 0.20/0.51 % (32022)------------------------------
% 0.20/0.51 % (32022)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.51 % (32022)Termination reason: Unknown
% 0.20/0.51 % (32022)Termination phase: shuffling
% 0.20/0.51
% 0.20/0.51 % (32022)Memory used [KB]: 1279
% 0.20/0.51 % (32022)Time elapsed: 0.002 s
% 0.20/0.51 % (32022)Instructions burned: 3 (million)
% 0.20/0.51 % (32022)------------------------------
% 0.20/0.51 % (32022)------------------------------
% 0.20/0.52 % (32023)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on theBenchmark for (2998ds/30Mi)
% 0.20/0.53 % (32024)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)
% 1.29/0.54 % (32023)Instruction limit reached!
% 1.29/0.54 % (32023)------------------------------
% 1.29/0.54 % (32023)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.29/0.54 % (32023)Termination reason: Unknown
% 1.29/0.54 % (32023)Termination phase: shuffling
% 1.29/0.54
% 1.29/0.54 % (32023)Memory used [KB]: 1918
% 1.29/0.54 % (32023)Time elapsed: 0.011 s
% 1.29/0.54 % (32023)Instructions burned: 31 (million)
% 1.29/0.54 % (32023)------------------------------
% 1.29/0.54 % (32023)------------------------------
% 1.39/0.56 % (32025)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)
% 1.39/0.57 % (32024)Instruction limit reached!
% 1.39/0.57 % (32024)------------------------------
% 1.39/0.57 % (32024)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.39/0.57 % (32024)Termination reason: Unknown
% 1.39/0.57 % (32024)Termination phase: Saturation
% 1.39/0.57
% 1.39/0.57 % (32024)Memory used [KB]: 6908
% 1.39/0.57 % (32024)Time elapsed: 0.036 s
% 1.39/0.57 % (32024)Instructions burned: 127 (million)
% 1.39/0.57 % (32024)------------------------------
% 1.39/0.57 % (32024)------------------------------
% 1.39/0.59 % (32026)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)
% 1.39/0.59 % (32026)Instruction limit reached!
% 1.39/0.59 % (32026)------------------------------
% 1.39/0.59 % (32026)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.39/0.59 % (32026)Termination reason: Unknown
% 1.39/0.59 % (32026)Termination phase: shuffling
% 1.39/0.59
% 1.39/0.59 % (32026)Memory used [KB]: 1279
% 1.39/0.59 % (32026)Time elapsed: 0.003 s
% 1.39/0.59 % (32026)Instructions burned: 3 (million)
% 1.39/0.59 % (32026)------------------------------
% 1.39/0.59 % (32026)------------------------------
% 1.39/0.59 % (32025)Instruction limit reached!
% 1.39/0.59 % (32025)------------------------------
% 1.39/0.59 % (32025)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.39/0.59 % (32025)Termination reason: Unknown
% 1.39/0.59 % (32025)Termination phase: Saturation
% 1.39/0.59
% 1.39/0.59 % (32025)Memory used [KB]: 6780
% 1.39/0.59 % (32025)Time elapsed: 0.029 s
% 1.39/0.59 % (32025)Instructions burned: 102 (million)
% 1.39/0.59 % (32025)------------------------------
% 1.39/0.59 % (32025)------------------------------
% 1.39/0.60 % (32028)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)
% 1.39/0.60 % (32027)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)
% 1.39/0.61 % (32027)Instruction limit reached!
% 1.39/0.61 % (32027)------------------------------
% 1.39/0.61 % (32027)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.39/0.61 % (32027)Termination reason: Unknown
% 1.39/0.61 % (32027)Termination phase: Property scanning
% 1.39/0.61
% 1.39/0.61 % (32027)Memory used [KB]: 1663
% 1.39/0.61 % (32027)Time elapsed: 0.012 s
% 1.39/0.61 % (32027)Instructions burned: 22 (million)
% 1.39/0.61 % (32027)------------------------------
% 1.39/0.61 % (32027)------------------------------
% 1.39/0.62 % (32028)Instruction limit reached!
% 1.39/0.62 % (32028)------------------------------
% 1.39/0.62 % (32028)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 1.39/0.62 % (32028)Termination reason: Unknown
% 1.39/0.62 % (32028)Termination phase: Property scanning
% 1.39/0.62
% 1.39/0.62 % (32028)Memory used [KB]: 2174
% 1.39/0.62 % (32028)Time elapsed: 0.025 s
% 1.39/0.62 % (32028)Instructions burned: 88 (million)
% 1.39/0.62 % (32028)------------------------------
% 1.39/0.62 % (32028)------------------------------
% 2.06/0.63 % (32030)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)
% 2.06/0.64 % (32029)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)
% 2.06/0.64 % (32030)Instruction limit reached!
% 2.06/0.64 % (32030)------------------------------
% 2.06/0.64 % (32030)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.06/0.64 % (32030)Termination reason: Unknown
% 2.06/0.64 % (32030)Termination phase: Property scanning
% 2.06/0.64
% 2.06/0.64 % (32030)Memory used [KB]: 2046
% 2.06/0.64 % (32030)Time elapsed: 0.013 s
% 2.06/0.64 % (32030)Instructions burned: 41 (million)
% 2.06/0.64 % (32030)------------------------------
% 2.06/0.64 % (32030)------------------------------
% 2.06/0.65 % (32017)Instruction limit reached!
% 2.06/0.65 % (32017)------------------------------
% 2.06/0.65 % (32017)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.06/0.65 % (32017)Termination reason: Unknown
% 2.06/0.65 % (32017)Termination phase: Saturation
% 2.06/0.65
% 2.06/0.65 % (32017)Memory used [KB]: 8315
% 2.06/0.65 % (32017)Time elapsed: 0.176 s
% 2.06/0.65 % (32017)Instructions burned: 377 (million)
% 2.06/0.65 % (32017)------------------------------
% 2.06/0.65 % (32017)------------------------------
% 2.06/0.65 % (32031)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 (2996ds/448Mi)
% 2.06/0.66 % (32032)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)
% 2.06/0.68 % (32029)Instruction limit reached!
% 2.06/0.68 % (32029)------------------------------
% 2.06/0.68 % (32029)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.06/0.68 % (32029)Termination reason: Unknown
% 2.06/0.68 % (32029)Termination phase: Saturation
% 2.06/0.68
% 2.06/0.68 % (32029)Memory used [KB]: 6652
% 2.06/0.68 % (32029)Time elapsed: 0.047 s
% 2.06/0.68 % (32029)Instructions burned: 109 (million)
% 2.06/0.68 % (32029)------------------------------
% 2.06/0.68 % (32029)------------------------------
% 2.06/0.68 % (32032)Instruction limit reached!
% 2.06/0.68 % (32032)------------------------------
% 2.06/0.68 % (32032)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.06/0.68 % (32032)Termination reason: Unknown
% 2.06/0.68 % (32032)Termination phase: Property scanning
% 2.06/0.68
% 2.06/0.68 % (32032)Memory used [KB]: 1918
% 2.06/0.68 % (32032)Time elapsed: 0.023 s
% 2.06/0.68 % (32032)Instructions burned: 48 (million)
% 2.06/0.68 % (32032)------------------------------
% 2.06/0.68 % (32032)------------------------------
% 2.48/0.70 % (32033)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)
% 2.48/0.70 % (32034)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)
% 2.48/0.71 % (32002)Instruction limit reached!
% 2.48/0.71 % (32002)------------------------------
% 2.48/0.71 % (32002)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.48/0.71 % (32002)Termination reason: Unknown
% 2.48/0.71 % (32002)Termination phase: Saturation
% 2.48/0.71
% 2.48/0.71 % (32002)Memory used [KB]: 11257
% 2.48/0.71 % (32002)Time elapsed: 0.324 s
% 2.48/0.71 % (32002)Instructions burned: 1041 (million)
% 2.48/0.71 % (32002)------------------------------
% 2.48/0.71 % (32002)------------------------------
% 2.48/0.72 % (32035)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)
% 2.48/0.74 % (32033)Instruction limit reached!
% 2.48/0.74 % (32033)------------------------------
% 2.48/0.74 % (32033)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.48/0.74 % (32033)Termination reason: Unknown
% 2.48/0.74 % (32033)Termination phase: Saturation
% 2.48/0.74
% 2.48/0.74 % (32033)Memory used [KB]: 2174
% 2.48/0.74 % (32033)Time elapsed: 0.042 s
% 2.48/0.74 % (32033)Instructions burned: 98 (million)
% 2.48/0.74 % (32033)------------------------------
% 2.48/0.74 % (32033)------------------------------
% 2.82/0.75 % (32018)Instruction limit reached!
% 2.82/0.75 % (32018)------------------------------
% 2.82/0.75 % (32018)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.82/0.75 % (32018)Termination reason: Unknown
% 2.82/0.75 % (32018)Termination phase: Saturation
% 2.82/0.75
% 2.82/0.75 % (32018)Memory used [KB]: 6908
% 2.82/0.75 % (32018)Time elapsed: 0.271 s
% 2.82/0.75 % (32018)Instructions burned: 780 (million)
% 2.82/0.75 % (32018)------------------------------
% 2.82/0.75 % (32018)------------------------------
% 2.82/0.75 % (32036)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on theBenchmark for (2996ds/39Mi)
% 2.86/0.76 % (32031)Instruction limit reached!
% 2.86/0.76 % (32031)------------------------------
% 2.86/0.76 % (32031)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.86/0.76 % (32031)Termination reason: Unknown
% 2.86/0.76 % (32031)Termination phase: Saturation
% 2.86/0.76
% 2.86/0.76 % (32031)Memory used [KB]: 6908
% 2.86/0.76 % (32031)Time elapsed: 0.112 s
% 2.86/0.76 % (32031)Instructions burned: 451 (million)
% 2.86/0.76 % (32031)------------------------------
% 2.86/0.76 % (32031)------------------------------
% 2.86/0.76 % (32035)Instruction limit reached!
% 2.86/0.76 % (32035)------------------------------
% 2.86/0.76 % (32035)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.86/0.76 % (32035)Termination reason: Unknown
% 2.86/0.76 % (32035)Termination phase: Saturation
% 2.86/0.76
% 2.86/0.76 % (32035)Memory used [KB]: 7419
% 2.86/0.76 % (32035)Time elapsed: 0.045 s
% 2.86/0.76 % (32035)Instructions burned: 149 (million)
% 2.86/0.76 % (32035)------------------------------
% 2.86/0.76 % (32035)------------------------------
% 2.86/0.77 % (32037)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 (2995ds/6Mi)
% 2.86/0.77 % (32037)Instruction limit reached!
% 2.86/0.77 % (32037)------------------------------
% 2.86/0.77 % (32037)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.86/0.77 % (32037)Termination reason: Unknown
% 2.86/0.77 % (32037)Termination phase: shuffling
% 2.86/0.77
% 2.86/0.77 % (32037)Memory used [KB]: 1407
% 2.86/0.77 % (32037)Time elapsed: 0.005 s
% 2.86/0.77 % (32037)Instructions burned: 7 (million)
% 2.86/0.77 % (32037)------------------------------
% 2.86/0.77 % (32037)------------------------------
% 2.86/0.77 % (32038)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 (2995ds/1087Mi)
% 2.86/0.77 % (32036)Instruction limit reached!
% 2.86/0.77 % (32036)------------------------------
% 2.86/0.77 % (32036)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.86/0.77 % (32036)Termination reason: Unknown
% 2.86/0.77 % (32036)Termination phase: Property scanning
% 2.86/0.77
% 2.86/0.77 % (32036)Memory used [KB]: 1918
% 2.86/0.77 % (32036)Time elapsed: 0.019 s
% 2.86/0.77 % (32036)Instructions burned: 39 (million)
% 2.86/0.77 % (32036)------------------------------
% 2.86/0.77 % (32036)------------------------------
% 2.86/0.77 % (32039)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on theBenchmark for (2995ds/47Mi)
% 2.86/0.78 % (32011)Instruction limit reached!
% 2.86/0.78 % (32011)------------------------------
% 2.86/0.78 % (32011)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.86/0.78 % (32011)Termination reason: Unknown
% 2.86/0.78 % (32011)Termination phase: Saturation
% 2.86/0.78
% 2.86/0.78 % (32011)Memory used [KB]: 9594
% 2.86/0.78 % (32011)Time elapsed: 0.353 s
% 2.86/0.78 % (32011)Instructions burned: 710 (million)
% 2.86/0.78 % (32011)------------------------------
% 2.86/0.78 % (32011)------------------------------
% 2.86/0.78 % (32040)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)
% 2.86/0.79 % (32039)Instruction limit reached!
% 2.86/0.79 % (32039)------------------------------
% 2.86/0.79 % (32039)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.86/0.79 % (32039)Termination reason: Unknown
% 2.86/0.79 % (32039)Termination phase: Property scanning
% 2.86/0.79
% 2.86/0.79 % (32039)Memory used [KB]: 1918
% 2.86/0.79 % (32039)Time elapsed: 0.014 s
% 2.86/0.79 % (32039)Instructions burned: 47 (million)
% 2.86/0.79 % (32039)------------------------------
% 2.86/0.79 % (32039)------------------------------
% 2.86/0.79 % (32041)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)
% 2.86/0.79 % (32013)Instruction limit reached!
% 2.86/0.79 % (32013)------------------------------
% 2.86/0.79 % (32013)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.86/0.79 % (32013)Termination reason: Unknown
% 2.86/0.79 % (32013)Termination phase: Saturation
% 2.86/0.79
% 2.86/0.79 % (32013)Memory used [KB]: 10362
% 2.86/0.79 % (32013)Time elapsed: 0.351 s
% 2.86/0.79 % (32013)Instructions burned: 904 (million)
% 2.86/0.79 % (32013)------------------------------
% 2.86/0.79 % (32013)------------------------------
% 2.86/0.79 % (32043)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)
% 2.86/0.80 % (32044)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on theBenchmark for (2995ds/96Mi)
% 2.86/0.80 % (32042)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)
% 2.86/0.80 % (32043)Instruction limit reached!
% 2.86/0.80 % (32043)------------------------------
% 2.86/0.80 % (32043)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.86/0.80 % (32043)Termination reason: Unknown
% 2.86/0.80 % (32043)Termination phase: shuffling
% 2.86/0.80
% 2.86/0.80 % (32040)Instruction limit reached!
% 2.86/0.80 % (32040)------------------------------
% 2.86/0.80 % (32040)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 2.86/0.80 % (32040)Termination reason: Unknown
% 2.86/0.80 % (32040)Termination phase: Property scanning
% 2.86/0.80
% 2.86/0.80 % (32040)Memory used [KB]: 2046
% 2.86/0.80 % (32040)Time elapsed: 0.021 s
% 2.86/0.80 % (32040)Instructions burned: 45 (million)
% 2.86/0.80 % (32040)------------------------------
% 2.86/0.80 % (32040)------------------------------
% 2.86/0.80 % (32043)Memory used [KB]: 1918
% 2.86/0.80 % (32043)Time elapsed: 0.010 s
% 2.86/0.80 % (32043)Instructions burned: 31 (million)
% 2.86/0.80 % (32043)------------------------------
% 2.86/0.80 % (32043)------------------------------
% 3.27/0.81 % (32045)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)
% 3.27/0.82 % (32046)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)
% 3.27/0.82 % (32044)Instruction limit reached!
% 3.27/0.82 % (32044)------------------------------
% 3.27/0.82 % (32044)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.27/0.82 % (32044)Termination reason: Unknown
% 3.27/0.82 % (32044)Termination phase: Saturation
% 3.27/0.82
% 3.27/0.82 % (32044)Memory used [KB]: 6652
% 3.27/0.82 % (32044)Time elapsed: 0.027 s
% 3.27/0.82 % (32044)Instructions burned: 96 (million)
% 3.27/0.82 % (32044)------------------------------
% 3.27/0.82 % (32044)------------------------------
% 3.27/0.83 % (32042)Instruction limit reached!
% 3.27/0.83 % (32042)------------------------------
% 3.27/0.83 % (32042)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.27/0.83 % (32042)Termination reason: Unknown
% 3.27/0.83 % (32042)Termination phase: Property scanning
% 3.27/0.83
% 3.27/0.83 % (32042)Memory used [KB]: 2046
% 3.27/0.83 % (32042)Time elapsed: 0.028 s
% 3.27/0.83 % (32042)Instructions burned: 62 (million)
% 3.27/0.83 % (32042)------------------------------
% 3.27/0.83 % (32042)------------------------------
% 3.27/0.83 % (32047)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)
% 3.38/0.84 % (32048)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on theBenchmark for (2995ds/11Mi)
% 3.38/0.84 % (32046)Instruction limit reached!
% 3.38/0.84 % (32046)------------------------------
% 3.38/0.84 % (32046)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.38/0.84 % (32046)Termination reason: Unknown
% 3.38/0.84 % (32046)Termination phase: Function definition elimination
% 3.38/0.84
% 3.38/0.84 % (32046)Memory used [KB]: 2046
% 3.38/0.84 % (32046)Time elapsed: 0.021 s
% 3.38/0.84 % (32046)Instructions burned: 72 (million)
% 3.38/0.84 % (32046)------------------------------
% 3.38/0.84 % (32046)------------------------------
% 3.38/0.85 % (32048)Instruction limit reached!
% 3.38/0.85 % (32048)------------------------------
% 3.38/0.85 % (32048)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.38/0.85 % (32048)Termination reason: Unknown
% 3.38/0.85 % (32048)Termination phase: shuffling
% 3.38/0.85
% 3.38/0.85 % (32048)Memory used [KB]: 1535
% 3.38/0.85 % (32048)Time elapsed: 0.007 s
% 3.38/0.85 % (32048)Instructions burned: 12 (million)
% 3.38/0.85 % (32048)------------------------------
% 3.38/0.85 % (32048)------------------------------
% 3.38/0.85 % (32049)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 (2995ds/41Mi)
% 3.38/0.86 % (32047)Instruction limit reached!
% 3.38/0.86 % (32047)------------------------------
% 3.38/0.86 % (32047)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.38/0.86 % (32047)Termination reason: Unknown
% 3.38/0.86 % (32047)Termination phase: Function definition elimination
% 3.38/0.86
% 3.38/0.86 % (32047)Memory used [KB]: 2046
% 3.38/0.86 % (32047)Time elapsed: 0.024 s
% 3.38/0.86 % (32047)Instructions burned: 85 (million)
% 3.38/0.86 % (32047)------------------------------
% 3.38/0.86 % (32047)------------------------------
% 3.38/0.86 % (32050)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2995ds/6Mi)
% 3.38/0.86 % (32049)Instruction limit reached!
% 3.38/0.86 % (32049)------------------------------
% 3.38/0.86 % (32049)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.38/0.86 % (32049)Termination reason: Unknown
% 3.38/0.86 % (32049)Termination phase: Property scanning
% 3.38/0.86
% 3.38/0.86 % (32049)Memory used [KB]: 1918
% 3.38/0.86 % (32049)Time elapsed: 0.013 s
% 3.38/0.86 % (32049)Instructions burned: 44 (million)
% 3.38/0.86 % (32049)------------------------------
% 3.38/0.86 % (32049)------------------------------
% 3.38/0.86 % (32051)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on theBenchmark for (2994ds/150Mi)
% 3.38/0.87 % (32050)Instruction limit reached!
% 3.38/0.87 % (32050)------------------------------
% 3.38/0.87 % (32050)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.38/0.87 % (32050)Termination reason: Unknown
% 3.38/0.87 % (32050)Termination phase: shuffling
% 3.38/0.87
% 3.38/0.87 % (32050)Memory used [KB]: 1407
% 3.38/0.87 % (32050)Time elapsed: 0.005 s
% 3.38/0.87 % (32050)Instructions burned: 8 (million)
% 3.38/0.87 % (32050)------------------------------
% 3.38/0.87 % (32050)------------------------------
% 3.38/0.87 % (32052)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)
% 3.38/0.88 % (32053)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)
% 3.38/0.91 % (32051)Instruction limit reached!
% 3.38/0.91 % (32051)------------------------------
% 3.38/0.91 % (32051)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.38/0.91 % (32051)Termination reason: Unknown
% 3.38/0.91 % (32051)Termination phase: Saturation
% 3.38/0.91
% 3.38/0.91 % (32051)Memory used [KB]: 8059
% 3.38/0.91 % (32051)Time elapsed: 0.044 s
% 3.38/0.91 % (32051)Instructions burned: 152 (million)
% 3.38/0.91 % (32051)------------------------------
% 3.38/0.91 % (32051)------------------------------
% 3.38/0.92 % (32054)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)
% 3.38/0.92 % (32045)Instruction limit reached!
% 3.38/0.92 % (32045)------------------------------
% 3.38/0.92 % (32045)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.38/0.92 % (32045)Termination reason: Unknown
% 3.38/0.92 % (32045)Termination phase: Saturation
% 3.38/0.92
% 3.38/0.92 % (32045)Memory used [KB]: 8059
% 3.38/0.92 % (32045)Time elapsed: 0.109 s
% 3.38/0.92 % (32045)Instructions burned: 453 (million)
% 3.38/0.92 % (32045)------------------------------
% 3.38/0.92 % (32045)------------------------------
% 3.38/0.92 % (32020)Instruction limit reached!
% 3.38/0.92 % (32020)------------------------------
% 3.38/0.92 % (32020)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.38/0.92 % (32020)Termination reason: Unknown
% 3.38/0.92 % (32020)Termination phase: Saturation
% 3.38/0.92
% 3.38/0.92 % (32020)Memory used [KB]: 8443
% 3.38/0.92 % (32020)Time elapsed: 0.466 s
% 3.38/0.92 % (32020)Instructions burned: 879 (million)
% 3.38/0.92 % (32020)------------------------------
% 3.38/0.92 % (32020)------------------------------
% 3.38/0.93 % (32053)Instruction limit reached!
% 3.38/0.93 % (32053)------------------------------
% 3.38/0.93 % (32053)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.38/0.93 % (32053)Termination reason: Unknown
% 3.38/0.93 % (32053)Termination phase: Saturation
% 3.38/0.93
% 3.38/0.93 % (32053)Memory used [KB]: 6780
% 3.38/0.93 % (32053)Time elapsed: 0.048 s
% 3.38/0.93 % (32053)Instructions burned: 110 (million)
% 3.38/0.93 % (32053)------------------------------
% 3.38/0.93 % (32053)------------------------------
% 3.38/0.93 % (32055)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)
% 3.83/0.94 % (32034)Instruction limit reached!
% 3.83/0.94 % (32034)------------------------------
% 3.83/0.94 % (32034)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.83/0.94 % (32034)Termination reason: Unknown
% 3.83/0.94 % (32034)Termination phase: Saturation
% 3.83/0.94
% 3.83/0.94 % (32034)Memory used [KB]: 7547
% 3.83/0.94 % (32034)Time elapsed: 0.238 s
% 3.83/0.94 % (32034)Instructions burned: 507 (million)
% 3.83/0.94 % (32034)------------------------------
% 3.83/0.94 % (32034)------------------------------
% 3.83/0.94 % (32056)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)
% 3.83/0.94 % (32057)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)
% 3.83/0.95 % (32041)Instruction limit reached!
% 3.83/0.95 % (32041)------------------------------
% 3.83/0.95 % (32041)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.83/0.95 % (32041)Termination reason: Unknown
% 3.83/0.95 % (32041)Termination phase: Saturation
% 3.83/0.95
% 3.83/0.95 % (32041)Memory used [KB]: 3326
% 3.83/0.95 % (32041)Time elapsed: 0.162 s
% 3.83/0.95 % (32041)Instructions burned: 434 (million)
% 3.83/0.95 % (32041)------------------------------
% 3.83/0.95 % (32041)------------------------------
% 3.83/0.95 % (32058)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 (2994ds/339Mi)
% 3.83/0.96 % (32059)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 (2994ds/283Mi)
% 3.83/0.96 % (32055)Instruction limit reached!
% 3.83/0.96 % (32055)------------------------------
% 3.83/0.96 % (32055)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.83/0.96 % (32055)Termination reason: Unknown
% 3.83/0.96 % (32055)Termination phase: Saturation
% 3.83/0.96
% 3.83/0.96 % (32055)Memory used [KB]: 6908
% 3.83/0.96 % (32055)Time elapsed: 0.037 s
% 3.83/0.96 % (32055)Instructions burned: 140 (million)
% 3.83/0.96 % (32055)------------------------------
% 3.83/0.96 % (32055)------------------------------
% 3.83/0.97 % (32052)Instruction limit reached!
% 3.83/0.97 % (32052)------------------------------
% 3.83/0.97 % (32052)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 3.83/0.97 % (32052)Termination reason: Unknown
% 3.83/0.97 % (32052)Termination phase: Saturation
% 3.83/0.97
% 3.83/0.97 % (32052)Memory used [KB]: 8187
% 3.83/0.97 % (32052)Time elapsed: 0.097 s
% 3.83/0.97 % (32052)Instructions burned: 345 (million)
% 3.83/0.97 % (32052)------------------------------
% 3.83/0.97 % (32052)------------------------------
% 3.83/0.97 % (32060)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)
% 3.83/0.98 % (32061)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on theBenchmark for (2993ds/298Mi)
% 4.40/0.99 % (32054)Instruction limit reached!
% 4.40/0.99 % (32054)------------------------------
% 4.40/0.99 % (32054)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.40/0.99 % (32054)Termination reason: Unknown
% 4.40/0.99 % (32054)Termination phase: Saturation
% 4.40/0.99
% 4.40/0.99 % (32054)Memory used [KB]: 8571
% 4.40/0.99 % (32054)Time elapsed: 0.076 s
% 4.40/0.99 % (32054)Instructions burned: 253 (million)
% 4.40/0.99 % (32054)------------------------------
% 4.40/0.99 % (32054)------------------------------
% 4.40/1.00 % (32062)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)
% 4.40/1.01 % (32060)Instruction limit reached!
% 4.40/1.01 % (32060)------------------------------
% 4.40/1.01 % (32060)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.40/1.01 % (32060)Termination reason: Unknown
% 4.40/1.01 % (32060)Termination phase: Saturation
% 4.40/1.01
% 4.40/1.01 % (32060)Memory used [KB]: 7036
% 4.40/1.01 % (32060)Time elapsed: 0.035 s
% 4.40/1.01 % (32060)Instructions burned: 134 (million)
% 4.40/1.01 % (32060)------------------------------
% 4.40/1.01 % (32060)------------------------------
% 4.40/1.01 % (32063)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 (2993ds/258Mi)
% 4.40/1.04 % (32057)Instruction limit reached!
% 4.40/1.04 % (32057)------------------------------
% 4.40/1.04 % (32057)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.40/1.04 % (32057)Termination reason: Unknown
% 4.40/1.04 % (32057)Termination phase: Saturation
% 4.40/1.04
% 4.40/1.04 % (32057)Memory used [KB]: 9083
% 4.40/1.04 % (32057)Time elapsed: 0.099 s
% 4.40/1.04 % (32057)Instructions burned: 203 (million)
% 4.40/1.04 % (32057)------------------------------
% 4.40/1.04 % (32057)------------------------------
% 4.40/1.05 % (32061)Instruction limit reached!
% 4.40/1.05 % (32061)------------------------------
% 4.40/1.05 % (32061)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.40/1.05 % (32061)Termination reason: Unknown
% 4.40/1.05 % (32061)Termination phase: Saturation
% 4.40/1.05
% 4.40/1.05 % (32061)Memory used [KB]: 7164
% 4.40/1.05 % (32061)Time elapsed: 0.072 s
% 4.40/1.05 % (32061)Instructions burned: 301 (million)
% 4.40/1.05 % (32061)------------------------------
% 4.40/1.05 % (32061)------------------------------
% 4.40/1.05 % (32062)Instruction limit reached!
% 4.40/1.05 % (32062)------------------------------
% 4.40/1.05 % (32062)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.40/1.05 % (32062)Termination reason: Unknown
% 4.40/1.05 % (32062)Termination phase: Saturation
% 4.40/1.05
% 4.40/1.05 % (32062)Memory used [KB]: 7547
% 4.40/1.05 % (32062)Time elapsed: 0.051 s
% 4.40/1.05 % (32062)Instructions burned: 192 (million)
% 4.40/1.05 % (32062)------------------------------
% 4.40/1.05 % (32062)------------------------------
% 4.78/1.05 % (32065)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)
% 4.78/1.06 % (32064)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 (2993ds/90Mi)
% 4.78/1.06 % (32066)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)
% 4.78/1.07 % (32059)Instruction limit reached!
% 4.78/1.07 % (32059)------------------------------
% 4.78/1.07 % (32059)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 4.78/1.07 % (32059)Termination reason: Unknown
% 4.78/1.07 % (32059)Termination phase: Saturation
% 4.78/1.07
% 4.78/1.07 % (32059)Memory used [KB]: 6908
% 4.78/1.07 % (32059)Time elapsed: 0.109 s
% 4.78/1.07 % (32059)Instructions burned: 286 (million)
% 4.78/1.07 % (32059)------------------------------
% 4.78/1.07 % (32059)------------------------------
% 5.56/1.08 % (32067)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)
% 5.56/1.08 % (32063)Instruction limit reached!
% 5.56/1.08 % (32063)------------------------------
% 5.56/1.08 % (32063)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.56/1.08 % (32063)Termination reason: Unknown
% 5.56/1.08 % (32063)Termination phase: Saturation
% 5.56/1.08
% 5.56/1.08 % (32063)Memory used [KB]: 7803
% 5.56/1.08 % (32063)Time elapsed: 0.071 s
% 5.56/1.08 % (32063)Instructions burned: 259 (million)
% 5.56/1.08 % (32063)------------------------------
% 5.56/1.08 % (32063)------------------------------
% 5.56/1.09 % (32067)Instruction limit reached!
% 5.56/1.09 % (32067)------------------------------
% 5.56/1.09 % (32067)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.56/1.09 % (32067)Termination reason: Unknown
% 5.56/1.09 % (32067)Termination phase: Property scanning
% 5.56/1.09
% 5.56/1.09 % (32067)Memory used [KB]: 1918
% 5.56/1.09 % (32067)Time elapsed: 0.010 s
% 5.56/1.09 % (32067)Instructions burned: 31 (million)
% 5.56/1.09 % (32067)------------------------------
% 5.56/1.09 % (32067)------------------------------
% 5.56/1.09 % (32068)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)
% 5.56/1.09 % (32064)Instruction limit reached!
% 5.56/1.09 % (32064)------------------------------
% 5.56/1.09 % (32064)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.56/1.09 % (32064)Termination reason: Unknown
% 5.56/1.09 % (32064)Termination phase: Twee Goal Transformation
% 5.56/1.09
% 5.56/1.09 % (32064)Memory used [KB]: 2558
% 5.56/1.09 % (32064)Time elapsed: 0.041 s
% 5.56/1.09 % (32064)Instructions burned: 91 (million)
% 5.56/1.09 % (32064)------------------------------
% 5.56/1.09 % (32064)------------------------------
% 5.56/1.10 % (32069)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 (2992ds/987Mi)
% 5.56/1.11 % (32058)Instruction limit reached!
% 5.56/1.11 % (32058)------------------------------
% 5.56/1.11 % (32058)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.56/1.11 % (32058)Termination reason: Unknown
% 5.56/1.11 % (32058)Termination phase: Saturation
% 5.56/1.11
% 5.56/1.11 % (32058)Memory used [KB]: 8059
% 5.56/1.11 % (32058)Time elapsed: 0.156 s
% 5.56/1.11 % (32058)Instructions burned: 341 (million)
% 5.56/1.11 % (32058)------------------------------
% 5.56/1.11 % (32058)------------------------------
% 5.56/1.11 % (32070)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 (2992ds/182Mi)
% 5.84/1.12 % (32071)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 (2992ds/182Mi)
% 5.98/1.16 % (32068)Instruction limit reached!
% 5.98/1.16 % (32068)------------------------------
% 5.98/1.16 % (32068)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.98/1.16 % (32068)Termination reason: Unknown
% 5.98/1.16 % (32068)Termination phase: Saturation
% 5.98/1.16
% 5.98/1.16 % (32068)Memory used [KB]: 8187
% 5.98/1.16 % (32068)Time elapsed: 0.071 s
% 5.98/1.16 % (32068)Instructions burned: 299 (million)
% 5.98/1.16 % (32068)------------------------------
% 5.98/1.16 % (32068)------------------------------
% 5.98/1.17 % (32065)Instruction limit reached!
% 5.98/1.17 % (32065)------------------------------
% 5.98/1.17 % (32065)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.98/1.17 % (32065)Termination reason: Unknown
% 5.98/1.17 % (32065)Termination phase: Saturation
% 5.98/1.17
% 5.98/1.17 % (32065)Memory used [KB]: 12153
% 5.98/1.17 % (32065)Time elapsed: 0.104 s
% 5.98/1.17 % (32065)Instructions burned: 231 (million)
% 5.98/1.17 % (32065)------------------------------
% 5.98/1.17 % (32065)------------------------------
% 5.98/1.17 % (32072)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 (2991ds/154Mi)
% 5.98/1.19 % (32073)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 (2991ds/79Mi)
% 5.98/1.19 % (32066)Instruction limit reached!
% 5.98/1.19 % (32066)------------------------------
% 5.98/1.19 % (32066)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.98/1.19 % (32066)Termination reason: Unknown
% 5.98/1.19 % (32066)Termination phase: Saturation
% 5.98/1.19
% 5.98/1.19 % (32066)Memory used [KB]: 8315
% 5.98/1.19 % (32066)Time elapsed: 0.133 s
% 5.98/1.19 % (32066)Instructions burned: 458 (million)
% 5.98/1.19 % (32066)------------------------------
% 5.98/1.19 % (32066)------------------------------
% 5.98/1.19 % (32070)Instruction limit reached!
% 5.98/1.19 % (32070)------------------------------
% 5.98/1.19 % (32070)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.98/1.19 % (32070)Termination reason: Unknown
% 5.98/1.19 % (32070)Termination phase: Saturation
% 5.98/1.19
% 5.98/1.19 % (32070)Memory used [KB]: 7419
% 5.98/1.19 % (32070)Time elapsed: 0.081 s
% 5.98/1.19 % (32070)Instructions burned: 183 (million)
% 5.98/1.19 % (32070)------------------------------
% 5.98/1.19 % (32070)------------------------------
% 5.98/1.20 % (32074)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 (2991ds/216Mi)
% 5.98/1.20 % (32075)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 (2991ds/114Mi)
% 5.98/1.21 % (32072)Instruction limit reached!
% 5.98/1.21 % (32072)------------------------------
% 5.98/1.21 % (32072)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.98/1.21 % (32072)Termination reason: Unknown
% 5.98/1.21 % (32072)Termination phase: Saturation
% 5.98/1.21
% 5.98/1.21 % (32072)Memory used [KB]: 6780
% 5.98/1.21 % (32072)Time elapsed: 0.038 s
% 5.98/1.21 % (32072)Instructions burned: 154 (million)
% 5.98/1.21 % (32072)------------------------------
% 5.98/1.21 % (32072)------------------------------
% 5.98/1.21 % (32071)Instruction limit reached!
% 5.98/1.21 % (32071)------------------------------
% 5.98/1.21 % (32071)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.98/1.21 % (32071)Termination reason: Unknown
% 5.98/1.21 % (32071)Termination phase: Saturation
% 5.98/1.21
% 5.98/1.21 % (32071)Memory used [KB]: 10106
% 5.98/1.21 % (32071)Time elapsed: 0.088 s
% 5.98/1.21 % (32071)Instructions burned: 182 (million)
% 5.98/1.21 % (32071)------------------------------
% 5.98/1.21 % (32071)------------------------------
% 5.98/1.21 % (32076)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 (2991ds/922Mi)
% 5.98/1.22 % (32073)Instruction limit reached!
% 5.98/1.22 % (32073)------------------------------
% 5.98/1.22 % (32073)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.98/1.22 % (32073)Termination reason: Unknown
% 5.98/1.22 % (32073)Termination phase: Property scanning
% 5.98/1.22
% 5.98/1.22 % (32073)Memory used [KB]: 2174
% 5.98/1.22 % (32073)Time elapsed: 0.035 s
% 5.98/1.22 % (32073)Instructions burned: 79 (million)
% 5.98/1.22 % (32073)------------------------------
% 5.98/1.22 % (32073)------------------------------
% 5.98/1.22 % (32056)Instruction limit reached!
% 5.98/1.22 % (32056)------------------------------
% 5.98/1.22 % (32056)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 5.98/1.22 % (32056)Termination reason: Unknown
% 5.98/1.22 % (32056)Termination phase: Saturation
% 5.98/1.22
% 5.98/1.22 % (32056)Memory used [KB]: 8699
% 5.98/1.22 % (32056)Time elapsed: 0.305 s
% 5.98/1.22 % (32056)Instructions burned: 614 (million)
% 5.98/1.22 % (32056)------------------------------
% 5.98/1.22 % (32056)------------------------------
% 5.98/1.22 % (32077)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 (2991ds/182Mi)
% 6.57/1.23 % (32078)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 (2991ds/164Mi)
% 6.57/1.24 % (32079)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 (2991ds/50Mi)
% 6.57/1.25 % (32074)Instruction limit reached!
% 6.57/1.25 % (32074)------------------------------
% 6.57/1.25 % (32074)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.57/1.25 % (32074)Termination reason: Unknown
% 6.57/1.25 % (32074)Termination phase: Saturation
% 6.57/1.25
% 6.57/1.25 % (32074)Memory used [KB]: 6780
% 6.57/1.25 % (32074)Time elapsed: 0.053 s
% 6.57/1.25 % (32074)Instructions burned: 220 (million)
% 6.57/1.25 % (32074)------------------------------
% 6.57/1.25 % (32074)------------------------------
% 6.57/1.25 % (32075)Instruction limit reached!
% 6.57/1.25 % (32075)------------------------------
% 6.57/1.25 % (32075)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.57/1.25 % (32075)Termination reason: Unknown
% 6.57/1.25 % (32075)Termination phase: Saturation
% 6.57/1.25
% 6.57/1.25 % (32075)Memory used [KB]: 6908
% 6.57/1.25 % (32075)Time elapsed: 0.051 s
% 6.57/1.25 % (32075)Instructions burned: 116 (million)
% 6.57/1.25 % (32075)------------------------------
% 6.57/1.25 % (32075)------------------------------
% 6.57/1.26 % (32080)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 (2991ds/368Mi)
% 6.57/1.26 % (32079)Instruction limit reached!
% 6.57/1.26 % (32079)------------------------------
% 6.57/1.26 % (32079)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.57/1.26 % (32079)Termination reason: Unknown
% 6.57/1.26 % (32079)Termination phase: Property scanning
% 6.57/1.26
% 6.57/1.26 % (32079)Memory used [KB]: 1918
% 6.57/1.26 % (32079)Time elapsed: 0.023 s
% 6.57/1.26 % (32079)Instructions burned: 51 (million)
% 6.57/1.26 % (32079)------------------------------
% 6.57/1.26 % (32079)------------------------------
% 6.57/1.27 % (32081)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 (2990ds/1021Mi)
% 6.77/1.28 % (32082)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 (2990ds/267Mi)
% 6.77/1.29 % (32038)Instruction limit reached!
% 6.77/1.29 % (32038)------------------------------
% 6.77/1.29 % (32038)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.77/1.29 % (32038)Termination reason: Unknown
% 6.77/1.29 % (32038)Termination phase: Saturation
% 6.77/1.29
% 6.77/1.29 % (32038)Memory used [KB]: 10746
% 6.77/1.29 % (32038)Time elapsed: 0.517 s
% 6.77/1.29 % (32038)Instructions burned: 1087 (million)
% 6.77/1.29 % (32038)------------------------------
% 6.77/1.29 % (32038)------------------------------
% 6.77/1.30 % (32077)Instruction limit reached!
% 6.77/1.30 % (32077)------------------------------
% 6.77/1.30 % (32077)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.77/1.30 % (32077)Termination reason: Unknown
% 6.77/1.30 % (32077)Termination phase: Saturation
% 6.77/1.30
% 6.77/1.30 % (32077)Memory used [KB]: 6780
% 6.77/1.30 % (32077)Time elapsed: 0.074 s
% 6.77/1.30 % (32077)Instructions burned: 182 (million)
% 6.77/1.30 % (32077)------------------------------
% 6.77/1.30 % (32077)------------------------------
% 6.77/1.30 % (32078)Instruction limit reached!
% 6.77/1.30 % (32078)------------------------------
% 6.77/1.30 % (32078)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.77/1.30 % (32078)Termination reason: Unknown
% 6.77/1.30 % (32078)Termination phase: Saturation
% 6.77/1.30
% 6.77/1.30 % (32078)Memory used [KB]: 2558
% 6.77/1.30 % (32078)Time elapsed: 0.071 s
% 6.77/1.30 % (32078)Instructions burned: 164 (million)
% 6.77/1.30 % (32078)------------------------------
% 6.77/1.30 % (32078)------------------------------
% 6.77/1.31 % (32083)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 (2990ds/204Mi)
% 6.77/1.31 % (32084)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 (2990ds/26Mi)
% 6.77/1.32 % (32085)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 (2990ds/53Mi)
% 6.77/1.32 % (32084)Instruction limit reached!
% 6.77/1.32 % (32084)------------------------------
% 6.77/1.32 % (32084)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.77/1.32 % (32084)Termination reason: Unknown
% 6.77/1.32 % (32084)Termination phase: shuffling
% 6.77/1.32
% 6.77/1.32 % (32084)Memory used [KB]: 1791
% 6.77/1.32 % (32084)Time elapsed: 0.013 s
% 6.77/1.32 % (32084)Instructions burned: 26 (million)
% 6.77/1.32 % (32084)------------------------------
% 6.77/1.32 % (32084)------------------------------
% 6.77/1.33 % (32069)Instruction limit reached!
% 6.77/1.33 % (32069)------------------------------
% 6.77/1.33 % (32069)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 6.77/1.33 % (32069)Termination reason: Unknown
% 6.77/1.33 % (32069)Termination phase: Saturation
% 6.77/1.33
% 6.77/1.33 % (32069)Memory used [KB]: 11257
% 6.77/1.33 % (32069)Time elapsed: 0.238 s
% 6.77/1.33 % (32069)Instructions burned: 988 (million)
% 6.77/1.33 % (32069)------------------------------
% 6.77/1.33 % (32069)------------------------------
% 7.24/1.34 % (32086)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 (2990ds/4436Mi)
% 7.24/1.34 % (32085)Instruction limit reached!
% 7.24/1.34 % (32085)------------------------------
% 7.24/1.34 % (32085)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.24/1.34 % (32085)Termination reason: Unknown
% 7.24/1.34 % (32085)Termination phase: Property scanning
% 7.24/1.34
% 7.24/1.34 % (32085)Memory used [KB]: 2174
% 7.24/1.34 % (32085)Time elapsed: 0.025 s
% 7.24/1.34 % (32085)Instructions burned: 54 (million)
% 7.24/1.34 % (32085)------------------------------
% 7.24/1.34 % (32085)------------------------------
% 7.24/1.34 % (32087)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 (2990ds/1539Mi)
% 7.24/1.35 % (32080)Instruction limit reached!
% 7.24/1.35 % (32080)------------------------------
% 7.24/1.35 % (32080)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.24/1.35 % (32080)Termination reason: Unknown
% 7.24/1.35 % (32080)Termination phase: Saturation
% 7.24/1.35
% 7.24/1.35 % (32080)Memory used [KB]: 7931
% 7.24/1.35 % (32080)Time elapsed: 0.096 s
% 7.24/1.35 % (32080)Instructions burned: 372 (million)
% 7.24/1.35 % (32080)------------------------------
% 7.24/1.35 % (32080)------------------------------
% 7.24/1.36 % (32088)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 (2990ds/408Mi)
% 7.24/1.36 % (32089)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 (2990ds/5205Mi)
% 7.38/1.38 % (32082)Instruction limit reached!
% 7.38/1.38 % (32082)------------------------------
% 7.38/1.38 % (32082)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.38/1.38 % (32082)Termination reason: Unknown
% 7.38/1.38 % (32082)Termination phase: Saturation
% 7.38/1.38
% 7.38/1.38 % (32082)Memory used [KB]: 6908
% 7.38/1.38 % (32082)Time elapsed: 0.103 s
% 7.38/1.38 % (32082)Instructions burned: 267 (million)
% 7.38/1.38 % (32082)------------------------------
% 7.38/1.38 % (32082)------------------------------
% 7.38/1.39 % (32090)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 (2989ds/1913Mi)
% 7.38/1.40 % (32083)Instruction limit reached!
% 7.38/1.40 % (32083)------------------------------
% 7.38/1.40 % (32083)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.38/1.40 % (32083)Termination reason: Unknown
% 7.38/1.40 % (32083)Termination phase: Saturation
% 7.38/1.40
% 7.38/1.40 % (32083)Memory used [KB]: 7419
% 7.38/1.40 % (32083)Time elapsed: 0.089 s
% 7.38/1.40 % (32083)Instructions burned: 205 (million)
% 7.38/1.40 % (32083)------------------------------
% 7.38/1.40 % (32083)------------------------------
% 7.38/1.41 % (32091)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on theBenchmark for (2989ds/4350Mi)
% 7.59/1.51 % (32076)Instruction limit reached!
% 7.59/1.51 % (32076)------------------------------
% 7.59/1.51 % (32076)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.59/1.51 % (32076)Termination reason: Unknown
% 7.59/1.51 % (32076)Termination phase: Saturation
% 7.59/1.51
% 7.59/1.51 % (32076)Memory used [KB]: 10362
% 7.59/1.51 % (32076)Time elapsed: 0.294 s
% 7.59/1.51 % (32076)Instructions burned: 924 (million)
% 7.59/1.51 % (32076)------------------------------
% 7.59/1.51 % (32076)------------------------------
% 7.59/1.52 % (32092)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=68:si=on:rtra=on_0 on theBenchmark for (2988ds/68Mi)
% 7.89/1.53 % (32092)Instruction limit reached!
% 7.89/1.53 % (32092)------------------------------
% 7.89/1.53 % (32092)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.89/1.53 % (32092)Termination reason: Unknown
% 7.89/1.53 % (32092)Termination phase: Property scanning
% 7.89/1.53
% 7.89/1.53 % (32092)Memory used [KB]: 2046
% 7.89/1.53 % (32092)Time elapsed: 0.019 s
% 7.89/1.53 % (32092)Instructions burned: 71 (million)
% 7.89/1.53 % (32092)------------------------------
% 7.89/1.53 % (32092)------------------------------
% 7.89/1.54 % (32093)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on theBenchmark for (2988ds/358Mi)
% 7.89/1.56 % (32088)Instruction limit reached!
% 7.89/1.56 % (32088)------------------------------
% 7.89/1.56 % (32088)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 7.89/1.56 % (32088)Termination reason: Unknown
% 7.89/1.56 % (32088)Termination phase: Saturation
% 7.89/1.56
% 7.89/1.56 % (32088)Memory used [KB]: 9850
% 7.89/1.56 % (32088)Time elapsed: 0.209 s
% 7.89/1.56 % (32088)Instructions burned: 409 (million)
% 7.89/1.56 % (32088)------------------------------
% 7.89/1.56 % (32088)------------------------------
% 8.14/1.58 % (32094)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 (2987ds/31Mi)
% 8.14/1.59 % (32094)Instruction limit reached!
% 8.14/1.59 % (32094)------------------------------
% 8.14/1.59 % (32094)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 8.14/1.59 % (32094)Termination reason: Unknown
% 8.14/1.59 % (32094)Termination phase: Property scanning
% 8.14/1.59
% 8.14/1.59 % (32094)Memory used [KB]: 1918
% 8.14/1.59 % (32094)Time elapsed: 0.016 s
% 8.14/1.59 % (32094)Instructions burned: 31 (million)
% 8.14/1.59 % (32094)------------------------------
% 8.14/1.59 % (32094)------------------------------
% 8.14/1.61 % (32095)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on theBenchmark for (2987ds/279Mi)
% 8.14/1.64 % (32093)Instruction limit reached!
% 8.14/1.64 % (32093)------------------------------
% 8.14/1.64 % (32093)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 8.14/1.64 % (32093)Termination reason: Unknown
% 8.14/1.64 % (32093)Termination phase: Saturation
% 8.14/1.64
% 8.14/1.64 % (32093)Memory used [KB]: 8059
% 8.14/1.64 % (32093)Time elapsed: 0.103 s
% 8.14/1.64 % (32093)Instructions burned: 360 (million)
% 8.14/1.64 % (32093)------------------------------
% 8.14/1.64 % (32093)------------------------------
% 10.07/1.65 % (32096)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on theBenchmark for (2987ds/258Mi)
% 10.24/1.71 % (32095)Instruction limit reached!
% 10.24/1.71 % (32095)------------------------------
% 10.24/1.71 % (32095)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 10.24/1.71 % (32095)Termination reason: Unknown
% 10.24/1.71 % (32095)Termination phase: Saturation
% 10.24/1.71
% 10.24/1.71 % (32095)Memory used [KB]: 6908
% 10.24/1.71 % (32095)Time elapsed: 0.109 s
% 10.24/1.71 % (32095)Instructions burned: 282 (million)
% 10.24/1.71 % (32095)------------------------------
% 10.24/1.71 % (32095)------------------------------
% 10.24/1.72 % (32096)Instruction limit reached!
% 10.24/1.72 % (32096)------------------------------
% 10.24/1.72 % (32096)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 10.24/1.72 % (32096)Termination reason: Unknown
% 10.24/1.72 % (32096)Termination phase: Saturation
% 10.24/1.72
% 10.24/1.72 % (32096)Memory used [KB]: 7931
% 10.24/1.72 % (32096)Time elapsed: 0.072 s
% 10.24/1.72 % (32096)Instructions burned: 259 (million)
% 10.24/1.72 % (32096)------------------------------
% 10.24/1.72 % (32096)------------------------------
% 10.24/1.73 % (32097)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 (2986ds/26Mi)
% 10.24/1.73 % (32098)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on theBenchmark for (2986ds/995Mi)
% 10.73/1.74 % (32097)Instruction limit reached!
% 10.73/1.74 % (32097)------------------------------
% 10.73/1.74 % (32097)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 10.73/1.74 % (32097)Termination reason: Unknown
% 10.73/1.74 % (32097)Termination phase: shuffling
% 10.73/1.74
% 10.73/1.74 % (32097)Memory used [KB]: 1791
% 10.73/1.74 % (32097)Time elapsed: 0.013 s
% 10.73/1.74 % (32097)Instructions burned: 28 (million)
% 10.73/1.74 % (32097)------------------------------
% 10.73/1.74 % (32097)------------------------------
% 10.92/1.76 % (32099)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on theBenchmark for (2986ds/373Mi)
% 10.92/1.78 % (32081)Instruction limit reached!
% 10.92/1.78 % (32081)------------------------------
% 10.92/1.78 % (32081)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 10.92/1.78 % (32081)Termination reason: Unknown
% 10.92/1.78 % (32081)Termination phase: Saturation
% 10.92/1.78
% 10.92/1.78 % (32081)Memory used [KB]: 10618
% 10.92/1.78 % (32081)Time elapsed: 0.507 s
% 10.92/1.78 % (32081)Instructions burned: 1021 (million)
% 10.92/1.78 % (32081)------------------------------
% 10.92/1.78 % (32081)------------------------------
% 10.92/1.79 % (32100)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on theBenchmark for (2985ds/253Mi)
% 11.28/1.85 % (32087)Instruction limit reached!
% 11.28/1.85 % (32087)------------------------------
% 11.28/1.85 % (32087)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 11.28/1.85 % (32087)Termination reason: Unknown
% 11.28/1.85 % (32087)Termination phase: Saturation
% 11.28/1.85
% 11.28/1.85 % (32087)Memory used [KB]: 10106
% 11.28/1.85 % (32087)Time elapsed: 0.517 s
% 11.28/1.85 % (32087)Instructions burned: 1539 (million)
% 11.28/1.85 % (32087)------------------------------
% 11.28/1.85 % (32087)------------------------------
% 11.28/1.86 % (32101)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on theBenchmark for (2985ds/832Mi)
% 11.48/1.89 % (32100)Instruction limit reached!
% 11.48/1.89 % (32100)------------------------------
% 11.48/1.89 % (32100)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 11.48/1.89 % (32100)Termination reason: Unknown
% 11.48/1.89 % (32100)Termination phase: Saturation
% 11.48/1.89
% 11.48/1.89 % (32100)Memory used [KB]: 7036
% 11.48/1.89 % (32100)Time elapsed: 0.099 s
% 11.48/1.89 % (32100)Instructions burned: 254 (million)
% 11.48/1.89 % (32100)------------------------------
% 11.48/1.89 % (32100)------------------------------
% 11.48/1.91 % (32102)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on theBenchmark for (2984ds/668Mi)
% 11.48/1.93 % (32099)Instruction limit reached!
% 11.48/1.93 % (32099)------------------------------
% 11.48/1.93 % (32099)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 11.48/1.93 % (32099)Termination reason: Unknown
% 11.48/1.93 % (32099)Termination phase: Saturation
% 11.48/1.93
% 11.48/1.93 % (32099)Memory used [KB]: 8187
% 11.48/1.93 % (32099)Time elapsed: 0.197 s
% 11.48/1.93 % (32099)Instructions burned: 373 (million)
% 11.48/1.93 % (32099)------------------------------
% 11.48/1.93 % (32099)------------------------------
% 12.07/1.95 % (32103)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=40:si=on:rtra=on_0 on theBenchmark for (2984ds/40Mi)
% 12.07/1.96 % (32098)Instruction limit reached!
% 12.07/1.96 % (32098)------------------------------
% 12.07/1.96 % (32098)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 12.07/1.96 % (32098)Termination reason: Unknown
% 12.07/1.96 % (32098)Termination phase: Saturation
% 12.07/1.96
% 12.07/1.96 % (32098)Memory used [KB]: 10746
% 12.07/1.96 % (32098)Time elapsed: 0.227 s
% 12.07/1.96 % (32098)Instructions burned: 995 (million)
% 12.07/1.96 % (32098)------------------------------
% 12.07/1.96 % (32098)------------------------------
% 12.07/1.96 % (32103)Instruction limit reached!
% 12.07/1.96 % (32103)------------------------------
% 12.07/1.96 % (32103)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 12.07/1.96 % (32103)Termination reason: Unknown
% 12.07/1.96 % (32103)Termination phase: Property scanning
% 12.07/1.96
% 12.07/1.96 % (32103)Memory used [KB]: 2046
% 12.07/1.96 % (32103)Time elapsed: 0.019 s
% 12.07/1.96 % (32103)Instructions burned: 41 (million)
% 12.07/1.96 % (32103)------------------------------
% 12.07/1.96 % (32103)------------------------------
% 12.07/1.96 % (32104)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on theBenchmark for (2983ds/294Mi)
% 12.47/1.98 % (32105)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on theBenchmark for (2983ds/187Mi)
% 12.71/2.03 % (32104)Instruction limit reached!
% 12.71/2.03 % (32104)------------------------------
% 12.71/2.03 % (32104)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 12.71/2.03 % (32104)Termination reason: Unknown
% 12.71/2.03 % (32104)Termination phase: Saturation
% 12.71/2.03
% 12.71/2.03 % (32104)Memory used [KB]: 7164
% 12.71/2.03 % (32104)Time elapsed: 0.071 s
% 12.71/2.03 % (32104)Instructions burned: 296 (million)
% 12.71/2.03 % (32104)------------------------------
% 12.71/2.03 % (32104)------------------------------
% 12.71/2.04 % (32106)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on theBenchmark for (2983ds/371Mi)
% 12.90/2.06 % (32105)Instruction limit reached!
% 12.90/2.06 % (32105)------------------------------
% 12.90/2.06 % (32105)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 12.90/2.06 % (32105)Termination reason: Unknown
% 12.90/2.06 % (32105)Termination phase: Saturation
% 12.90/2.06
% 12.90/2.06 % (32105)Memory used [KB]: 7419
% 12.90/2.06 % (32105)Time elapsed: 0.083 s
% 12.90/2.06 % (32105)Instructions burned: 187 (million)
% 12.90/2.06 % (32105)------------------------------
% 12.90/2.06 % (32105)------------------------------
% 12.90/2.08 % (32107)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on theBenchmark for (2982ds/1827Mi)
% 13.26/2.15 % (32102)Instruction limit reached!
% 13.26/2.15 % (32102)------------------------------
% 13.26/2.15 % (32102)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 13.26/2.15 % (32102)Termination reason: Unknown
% 13.26/2.15 % (32102)Termination phase: Saturation
% 13.26/2.15
% 13.26/2.15 % (32102)Memory used [KB]: 15223
% 13.26/2.15 % (32102)Time elapsed: 0.240 s
% 13.26/2.15 % (32102)Instructions burned: 668 (million)
% 13.26/2.15 % (32102)------------------------------
% 13.26/2.15 % (32102)------------------------------
% 13.26/2.15 % (32106)Instruction limit reached!
% 13.26/2.15 % (32106)------------------------------
% 13.26/2.15 % (32106)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 13.26/2.15 % (32106)Termination reason: Unknown
% 13.26/2.15 % (32106)Termination phase: Saturation
% 13.26/2.15
% 13.26/2.15 % (32106)Memory used [KB]: 8315
% 13.26/2.15 % (32106)Time elapsed: 0.108 s
% 13.26/2.15 % (32106)Instructions burned: 373 (million)
% 13.26/2.15 % (32106)------------------------------
% 13.26/2.15 % (32106)------------------------------
% 13.26/2.16 % (32109)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on theBenchmark for (2981ds/316Mi)
% 13.26/2.16 % (32108)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on theBenchmark for (2981ds/70Mi)
% 14.29/2.19 % (32108)Instruction limit reached!
% 14.29/2.19 % (32108)------------------------------
% 14.29/2.19 % (32108)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 14.29/2.19 % (32108)Termination reason: Unknown
% 14.29/2.19 % (32108)Termination phase: Function definition elimination
% 14.29/2.19
% 14.29/2.19 % (32108)Memory used [KB]: 2174
% 14.29/2.19 % (32108)Time elapsed: 0.032 s
% 14.29/2.19 % (32108)Instructions burned: 71 (million)
% 14.29/2.19 % (32108)------------------------------
% 14.29/2.19 % (32108)------------------------------
% 14.29/2.19 % (32101)Instruction limit reached!
% 14.29/2.19 % (32101)------------------------------
% 14.29/2.19 % (32101)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 14.29/2.19 % (32101)Termination reason: Unknown
% 14.29/2.19 % (32101)Termination phase: Saturation
% 14.29/2.19
% 14.29/2.19 % (32101)Memory used [KB]: 9594
% 14.29/2.19 % (32101)Time elapsed: 0.347 s
% 14.29/2.19 % (32101)Instructions burned: 832 (million)
% 14.29/2.19 % (32101)------------------------------
% 14.29/2.19 % (32101)------------------------------
% 14.29/2.20 % (32111)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on theBenchmark for (2981ds/4714Mi)
% 14.29/2.22 % (32110)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on theBenchmark for (2981ds/932Mi)
% 14.29/2.24 % (32109)Instruction limit reached!
% 14.29/2.24 % (32109)------------------------------
% 14.29/2.24 % (32109)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 14.29/2.24 % (32109)Termination reason: Unknown
% 14.29/2.24 % (32109)Termination phase: Saturation
% 14.29/2.24
% 14.29/2.24 % (32109)Memory used [KB]: 7164
% 14.29/2.24 % (32109)Time elapsed: 0.086 s
% 14.29/2.24 % (32109)Instructions burned: 319 (million)
% 14.29/2.24 % (32109)------------------------------
% 14.29/2.24 % (32109)------------------------------
% 14.29/2.25 % (32112)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on theBenchmark for (2981ds/8250Mi)
% 14.96/2.32 % (32090)Instruction limit reached!
% 14.96/2.32 % (32090)------------------------------
% 14.96/2.32 % (32090)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 14.96/2.32 % (32090)Termination reason: Unknown
% 14.96/2.32 % (32090)Termination phase: Saturation
% 14.96/2.32
% 14.96/2.32 % (32090)Memory used [KB]: 4733
% 14.96/2.32 % (32090)Time elapsed: 0.925 s
% 14.96/2.32 % (32090)Instructions burned: 1914 (million)
% 14.96/2.32 % (32090)------------------------------
% 14.96/2.32 % (32090)------------------------------
% 15.16/2.33 % (32113)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on theBenchmark for (2980ds/770Mi)
% 16.07/2.57 % (32110)Instruction limit reached!
% 16.07/2.57 % (32110)------------------------------
% 16.07/2.57 % (32110)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 16.07/2.57 % (32110)Termination reason: Unknown
% 16.07/2.57 % (32110)Termination phase: Saturation
% 16.07/2.57
% 16.07/2.57 % (32110)Memory used [KB]: 12281
% 16.07/2.57 % (32110)Time elapsed: 0.353 s
% 16.07/2.57 % (32110)Instructions burned: 934 (million)
% 16.07/2.57 % (32110)------------------------------
% 16.07/2.57 % (32110)------------------------------
% 16.07/2.59 % (32114)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on theBenchmark for (2977ds/794Mi)
% 16.58/2.61 % (32089)Instruction limit reached!
% 16.58/2.61 % (32089)------------------------------
% 16.58/2.61 % (32089)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 16.58/2.61 % (32089)Termination reason: Unknown
% 16.58/2.61 % (32089)Termination phase: Saturation
% 16.58/2.61
% 16.58/2.61 % (32089)Memory used [KB]: 11641
% 16.58/2.61 % (32089)Time elapsed: 1.249 s
% 16.58/2.61 % (32089)Instructions burned: 5207 (million)
% 16.58/2.61 % (32089)------------------------------
% 16.58/2.61 % (32089)------------------------------
% 16.58/2.61 % (32115)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on theBenchmark for (2977ds/464Mi)
% 16.74/2.67 % (32113)Instruction limit reached!
% 16.74/2.67 % (32113)------------------------------
% 16.74/2.67 % (32113)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 16.74/2.67 % (32113)Termination reason: Unknown
% 16.74/2.67 % (32113)Termination phase: Saturation
% 16.74/2.67
% 16.74/2.67 % (32113)Memory used [KB]: 7164
% 16.74/2.67 % (32113)Time elapsed: 0.341 s
% 16.74/2.67 % (32113)Instructions burned: 770 (million)
% 16.74/2.67 % (32113)------------------------------
% 16.74/2.67 % (32113)------------------------------
% 16.74/2.69 % (32116)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on theBenchmark for (2976ds/1376Mi)
% 18.58/2.75 % (32115)Instruction limit reached!
% 18.58/2.75 % (32115)------------------------------
% 18.58/2.75 % (32115)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 18.58/2.75 % (32115)Termination reason: Unknown
% 18.58/2.75 % (32115)Termination phase: Saturation
% 18.58/2.75
% 18.58/2.75 % (32115)Memory used [KB]: 8315
% 18.58/2.75 % (32115)Time elapsed: 0.140 s
% 18.58/2.75 % (32115)Instructions burned: 465 (million)
% 18.58/2.75 % (32115)------------------------------
% 18.58/2.75 % (32115)------------------------------
% 18.58/2.76 % (32117)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on theBenchmark for (2975ds/906Mi)
% 19.98/2.92 % (32107)Instruction limit reached!
% 19.98/2.92 % (32107)------------------------------
% 19.98/2.92 % (32107)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 19.98/2.92 % (32107)Termination reason: Unknown
% 19.98/2.92 % (32107)Termination phase: Saturation
% 19.98/2.92
% 19.98/2.92 % (32107)Memory used [KB]: 18038
% 19.98/2.92 % (32107)Time elapsed: 0.843 s
% 19.98/2.92 % (32107)Instructions burned: 1828 (million)
% 19.98/2.92 % (32107)------------------------------
% 19.98/2.92 % (32107)------------------------------
% 20.06/2.94 % (32118)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on theBenchmark for (2974ds/434Mi)
% 20.06/2.97 % (32114)Instruction limit reached!
% 20.06/2.97 % (32114)------------------------------
% 20.06/2.97 % (32114)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 20.06/2.97 % (32114)Termination reason: Unknown
% 20.06/2.97 % (32114)Termination phase: Saturation
% 20.06/2.97
% 20.06/2.97 % (32114)Memory used [KB]: 4605
% 20.06/2.97 % (32114)Time elapsed: 0.385 s
% 20.06/2.97 % (32114)Instructions burned: 794 (million)
% 20.06/2.97 % (32114)------------------------------
% 20.06/2.97 % (32114)------------------------------
% 20.06/2.97 % (32091)Instruction limit reached!
% 20.06/2.97 % (32091)------------------------------
% 20.06/2.97 % (32091)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 20.06/2.97 % (32091)Termination reason: Unknown
% 20.06/2.97 % (32091)Termination phase: Saturation
% 20.06/2.97
% 20.06/2.97 % (32091)Memory used [KB]: 13176
% 20.06/2.97 % (32091)Time elapsed: 1.563 s
% 20.06/2.97 % (32091)Instructions burned: 4352 (million)
% 20.06/2.97 % (32091)------------------------------
% 20.06/2.97 % (32091)------------------------------
% 20.06/2.98 % (32119)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on theBenchmark for (2973ds/865Mi)
% 20.06/2.99 % (32120)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on theBenchmark for (2973ds/593Mi)
% 20.50/3.06 % (32117)Instruction limit reached!
% 20.50/3.06 % (32117)------------------------------
% 20.50/3.06 % (32117)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 20.50/3.06 % (32117)Termination reason: Unknown
% 20.50/3.06 % (32117)Termination phase: Saturation
% 20.50/3.06
% 20.50/3.06 % (32117)Memory used [KB]: 9850
% 20.50/3.06 % (32117)Time elapsed: 0.300 s
% 20.50/3.06 % (32117)Instructions burned: 907 (million)
% 20.50/3.06 % (32117)------------------------------
% 20.50/3.06 % (32117)------------------------------
% 20.50/3.07 % (32121)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on theBenchmark for (2972ds/443Mi)
% 21.08/3.14 % (32118)Instruction limit reached!
% 21.08/3.14 % (32118)------------------------------
% 21.08/3.14 % (32118)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 21.08/3.14 % (32118)Termination reason: Unknown
% 21.08/3.14 % (32118)Termination phase: Saturation
% 21.08/3.14
% 21.08/3.14 % (32118)Memory used [KB]: 9594
% 21.08/3.14 % (32118)Time elapsed: 0.210 s
% 21.08/3.14 % (32118)Instructions burned: 435 (million)
% 21.08/3.14 % (32118)------------------------------
% 21.08/3.14 % (32118)------------------------------
% 21.08/3.16 % (32122)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on theBenchmark for (2972ds/594Mi)
% 21.76/3.20 % (32120)Instruction limit reached!
% 21.76/3.20 % (32120)------------------------------
% 21.76/3.20 % (32120)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 21.76/3.20 % (32120)Termination reason: Unknown
% 21.76/3.20 % (32120)Termination phase: Saturation
% 21.76/3.20
% 21.76/3.20 % (32120)Memory used [KB]: 6908
% 21.76/3.20 % (32120)Time elapsed: 0.210 s
% 21.76/3.20 % (32120)Instructions burned: 596 (million)
% 21.76/3.20 % (32120)------------------------------
% 21.76/3.20 % (32120)------------------------------
% 21.76/3.20 % (32116)Instruction limit reached!
% 21.76/3.20 % (32116)------------------------------
% 21.76/3.20 % (32116)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 21.76/3.20 % (32116)Termination reason: Unknown
% 21.76/3.20 % (32116)Termination phase: Saturation
% 21.76/3.20
% 21.76/3.20 % (32116)Memory used [KB]: 8187
% 21.76/3.20 % (32116)Time elapsed: 0.513 s
% 21.76/3.20 % (32116)Instructions burned: 1377 (million)
% 21.76/3.20 % (32116)------------------------------
% 21.76/3.20 % (32116)------------------------------
% 21.76/3.21 % (32123)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on theBenchmark for (2971ds/327Mi)
% 22.08/3.22 % (32124)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on theBenchmark for (2971ds/5411Mi)
% 22.08/3.23 % (32121)Instruction limit reached!
% 22.08/3.23 % (32121)------------------------------
% 22.08/3.23 % (32121)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 22.08/3.23 % (32121)Termination reason: Unknown
% 22.08/3.23 % (32121)Termination phase: Saturation
% 22.08/3.23
% 22.08/3.23 % (32121)Memory used [KB]: 8315
% 22.08/3.23 % (32121)Time elapsed: 0.159 s
% 22.08/3.23 % (32121)Instructions burned: 443 (million)
% 22.08/3.23 % (32121)------------------------------
% 22.08/3.23 % (32121)------------------------------
% 22.65/3.24 % (32125)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on theBenchmark for (2971ds/1762Mi)
% 22.65/3.24 % (32119)Instruction limit reached!
% 22.65/3.24 % (32119)------------------------------
% 22.65/3.24 % (32119)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 22.65/3.24 % (32119)Termination reason: Unknown
% 22.65/3.24 % (32119)Termination phase: Saturation
% 22.65/3.24
% 22.65/3.24 % (32119)Memory used [KB]: 9594
% 22.65/3.24 % (32119)Time elapsed: 0.263 s
% 22.65/3.24 % (32119)Instructions burned: 866 (million)
% 22.65/3.24 % (32119)------------------------------
% 22.65/3.24 % (32119)------------------------------
% 22.65/3.25 % (32126)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on theBenchmark for (2971ds/96Mi)
% 22.65/3.28 % (32126)Instruction limit reached!
% 22.65/3.28 % (32126)------------------------------
% 22.65/3.28 % (32126)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 22.65/3.28 % (32126)Termination reason: Unknown
% 22.65/3.28 % (32126)Termination phase: Property scanning
% 22.65/3.28
% 22.65/3.28 % (32126)Memory used [KB]: 2174
% 22.65/3.28 % (32126)Time elapsed: 0.025 s
% 22.65/3.28 % (32126)Instructions burned: 97 (million)
% 22.65/3.28 % (32126)------------------------------
% 22.65/3.28 % (32126)------------------------------
% 22.65/3.28 % (32127)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on theBenchmark for (2970ds/503Mi)
% 23.20/3.38 % (32123)Instruction limit reached!
% 23.20/3.38 % (32123)------------------------------
% 23.20/3.38 % (32123)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 23.20/3.38 % (32123)Termination reason: Unknown
% 23.20/3.38 % (32123)Termination phase: Saturation
% 23.20/3.38
% 23.20/3.38 % (32123)Memory used [KB]: 9978
% 23.20/3.38 % (32123)Time elapsed: 0.165 s
% 23.20/3.38 % (32123)Instructions burned: 328 (million)
% 23.20/3.38 % (32123)------------------------------
% 23.20/3.38 % (32123)------------------------------
% 23.64/3.39 % (32128)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 (2969ds/90Mi)
% 23.64/3.43 % (32128)Instruction limit reached!
% 23.64/3.43 % (32128)------------------------------
% 23.64/3.43 % (32128)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 23.64/3.43 % (32128)Termination reason: Unknown
% 23.64/3.43 % (32128)Termination phase: Twee Goal Transformation
% 23.64/3.43
% 23.64/3.43 % (32128)Memory used [KB]: 2558
% 23.64/3.43 % (32128)Time elapsed: 0.041 s
% 23.64/3.43 % (32128)Instructions burned: 92 (million)
% 23.64/3.43 % (32128)------------------------------
% 23.64/3.43 % (32128)------------------------------
% 23.64/3.43 % (32127)Instruction limit reached!
% 23.64/3.43 % (32127)------------------------------
% 23.64/3.43 % (32127)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 23.64/3.43 % (32127)Termination reason: Unknown
% 23.64/3.43 % (32127)Termination phase: Saturation
% 23.64/3.43
% 23.64/3.43 % (32127)Memory used [KB]: 8315
% 23.64/3.43 % (32127)Time elapsed: 0.151 s
% 23.64/3.43 % (32127)Instructions burned: 505 (million)
% 23.64/3.43 % (32127)------------------------------
% 23.64/3.43 % (32127)------------------------------
% 23.64/3.44 % (32130)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on theBenchmark for (2969ds/1512Mi)
% 23.64/3.44 % (32122)Instruction limit reached!
% 23.64/3.44 % (32122)------------------------------
% 23.64/3.44 % (32122)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 23.64/3.44 % (32122)Termination reason: Unknown
% 23.64/3.44 % (32122)Termination phase: Saturation
% 23.64/3.44
% 23.64/3.44 % (32122)Memory used [KB]: 8315
% 23.64/3.44 % (32122)Time elapsed: 0.281 s
% 23.64/3.44 % (32122)Instructions burned: 595 (million)
% 23.64/3.44 % (32122)------------------------------
% 23.64/3.44 % (32122)------------------------------
% 23.64/3.45 % (32129)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on theBenchmark for (2969ds/593Mi)
% 23.64/3.46 % (32131)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on theBenchmark for (2969ds/569Mi)
% 24.45/3.54 % (32086)Instruction limit reached!
% 24.45/3.54 % (32086)------------------------------
% 24.45/3.54 % (32086)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 24.45/3.54 % (32086)Termination reason: Unknown
% 24.45/3.54 % (32086)Termination phase: Saturation
% 24.45/3.54
% 24.45/3.54 % (32086)Memory used [KB]: 17654
% 24.45/3.54 % (32086)Time elapsed: 2.202 s
% 24.45/3.54 % (32086)Instructions burned: 4436 (million)
% 24.45/3.54 % (32086)------------------------------
% 24.45/3.54 % (32086)------------------------------
% 24.45/3.55 % (32132)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on theBenchmark for (2968ds/501Mi)
% 24.45/3.58 % (32111)Refutation not found, non-redundant clauses discarded% (32111)------------------------------
% 24.45/3.58 % (32111)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 24.45/3.58 % (32111)Termination reason: Refutation not found, non-redundant clauses discarded
% 24.45/3.58
% 24.45/3.58 % (32111)Memory used [KB]: 7419
% 24.45/3.58 % (32111)Time elapsed: 1.375 s
% 24.45/3.58 % (32111)Instructions burned: 4494 (million)
% 24.45/3.58 % (32111)------------------------------
% 24.45/3.58 % (32111)------------------------------
% 24.45/3.59 % (32133)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on theBenchmark for (2967ds/562Mi)
% 24.45/3.59 % (32125)First to succeed.
% 24.73/3.66 % (32131)Instruction limit reached!
% 24.73/3.66 % (32131)------------------------------
% 24.73/3.66 % (32131)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 24.73/3.66 % (32131)Termination reason: Unknown
% 24.73/3.66 % (32131)Termination phase: Saturation
% 24.73/3.66
% 24.73/3.66 % (32131)Memory used [KB]: 10746
% 24.73/3.66 % (32131)Time elapsed: 0.209 s
% 24.73/3.66 % (32131)Instructions burned: 570 (million)
% 24.73/3.66 % (32131)------------------------------
% 24.73/3.66 % (32131)------------------------------
% 24.73/3.68 % (32134)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on theBenchmark for (2966ds/406Mi)
% 25.09/3.73 % (32129)Instruction limit reached!
% 25.09/3.73 % (32129)------------------------------
% 25.09/3.73 % (32129)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 25.09/3.73 % (32129)Termination reason: Unknown
% 25.09/3.73 % (32129)Termination phase: Saturation
% 25.09/3.73
% 25.09/3.73 % (32129)Memory used [KB]: 8443
% 25.09/3.73 % (32129)Time elapsed: 0.285 s
% 25.09/3.73 % (32129)Instructions burned: 594 (million)
% 25.09/3.73 % (32129)------------------------------
% 25.09/3.73 % (32129)------------------------------
% 25.09/3.75 % (32135)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on theBenchmark for (2966ds/582Mi)
% 25.09/3.75 % (32133)Instruction limit reached!
% 25.09/3.75 % (32133)------------------------------
% 25.09/3.75 % (32133)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 25.09/3.75 % (32133)Termination reason: Unknown
% 25.09/3.75 % (32133)Termination phase: Saturation
% 25.09/3.75
% 25.09/3.75 % (32133)Memory used [KB]: 8059
% 25.09/3.75 % (32133)Time elapsed: 0.163 s
% 25.09/3.75 % (32133)Instructions burned: 563 (million)
% 25.09/3.75 % (32133)------------------------------
% 25.09/3.75 % (32133)------------------------------
% 25.09/3.76 % (32136)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on theBenchmark for (2965ds/456Mi)
% 25.74/3.80 % (32132)Instruction limit reached!
% 25.74/3.80 % (32132)------------------------------
% 25.74/3.80 % (32132)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 25.74/3.80 % (32132)Termination reason: Unknown
% 25.74/3.80 % (32132)Termination phase: Saturation
% 25.74/3.80
% 25.74/3.80 % (32132)Memory used [KB]: 9210
% 25.74/3.80 % (32132)Time elapsed: 0.265 s
% 25.74/3.80 % (32132)Instructions burned: 501 (million)
% 25.74/3.80 % (32132)------------------------------
% 25.74/3.80 % (32132)------------------------------
% 25.74/3.81 % (32137)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on theBenchmark for (2965ds/393Mi)
% 27.43/3.85 % (32134)Refutation not found, incomplete strategy
% 27.43/3.85 % (32134)------------------------------
% 27.43/3.85 % (32134)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 27.43/3.85 % (32134)Termination reason: Refutation not found, incomplete strategy
% 27.43/3.85
% 27.43/3.85
% 27.43/3.85 % (32134)Memory used [KB]: 7164
% 27.43/3.85 % (32134)Time elapsed: 0.172 s
% 27.43/3.85 % (32134)Instructions burned: 377 (million)
% 27.43/3.85 % (32134)------------------------------
% 27.43/3.85 % (32134)------------------------------
% 27.43/3.87 % (32138)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on theBenchmark for (2964ds/1335Mi)
% 27.43/3.90 % (32136)Instruction limit reached!
% 27.43/3.90 % (32136)------------------------------
% 27.43/3.90 % (32136)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 27.43/3.90 % (32136)Termination reason: Unknown
% 27.43/3.90 % (32136)Termination phase: Saturation
% 27.43/3.90
% 27.43/3.90 % (32136)Memory used [KB]: 8315
% 27.43/3.90 % (32136)Time elapsed: 0.139 s
% 27.43/3.90 % (32136)Instructions burned: 458 (million)
% 27.43/3.90 % (32136)------------------------------
% 27.43/3.90 % (32136)------------------------------
% 27.43/3.91 % (32139)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on theBenchmark for (2964ds/3373Mi)
% 27.43/3.91 % (32130)Instruction limit reached!
% 27.43/3.91 % (32130)------------------------------
% 27.43/3.91 % (32130)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 27.43/3.91 % (32130)Termination reason: Unknown
% 27.43/3.91 % (32130)Termination phase: Saturation
% 27.43/3.91
% 27.43/3.91 % (32130)Memory used [KB]: 12665
% 27.43/3.91 % (32130)Time elapsed: 0.474 s
% 27.43/3.91 % (32130)Instructions burned: 1513 (million)
% 27.43/3.91 % (32130)------------------------------
% 27.43/3.91 % (32130)------------------------------
% 28.07/3.92 % (32140)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on theBenchmark for (2964ds/474Mi)
% 28.07/3.98 % (32137)Instruction limit reached!
% 28.07/3.98 % (32137)------------------------------
% 28.07/3.98 % (32137)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 28.07/3.98 % (32137)Termination reason: Unknown
% 28.07/3.98 % (32137)Termination phase: Saturation
% 28.07/3.98
% 28.07/3.98 % (32137)Memory used [KB]: 8827
% 28.07/3.98 % (32137)Time elapsed: 0.169 s
% 28.07/3.98 % (32137)Instructions burned: 393 (million)
% 28.07/3.98 % (32137)------------------------------
% 28.07/3.98 % (32137)------------------------------
% 28.40/4.00 % (32141)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on theBenchmark for (2963ds/157Mi)
% 28.40/4.03 % (32140)Instruction limit reached!
% 28.40/4.03 % (32140)------------------------------
% 28.40/4.03 % (32140)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 28.40/4.03 % (32140)Termination reason: Unknown
% 28.40/4.03 % (32140)Termination phase: Saturation
% 28.40/4.03
% 28.40/4.03 % (32140)Memory used [KB]: 10618
% 28.40/4.03 % (32135)Instruction limit reached!
% 28.40/4.03 % (32135)------------------------------
% 28.40/4.03 % (32135)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 28.40/4.03 % (32135)Termination reason: Unknown
% 28.40/4.03 % (32135)Termination phase: Saturation
% 28.40/4.03
% 28.40/4.03 % (32135)Memory used [KB]: 9594
% 28.40/4.03 % (32135)Time elapsed: 0.289 s
% 28.40/4.03 % (32135)Instructions burned: 582 (million)
% 28.40/4.03 % (32135)------------------------------
% 28.40/4.03 % (32135)------------------------------
% 28.40/4.03 % (32140)Time elapsed: 0.113 s
% 28.40/4.03 % (32140)Instructions burned: 474 (million)
% 28.40/4.03 % (32140)------------------------------
% 28.40/4.03 % (32140)------------------------------
% 28.40/4.04 % (32142)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on theBenchmark for (2963ds/590Mi)
% 28.40/4.05 % (32143)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on theBenchmark for (2963ds/104Mi)
% 28.40/4.06 % (32141)Instruction limit reached!
% 28.40/4.06 % (32141)------------------------------
% 28.40/4.06 % (32141)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 28.40/4.06 % (32141)Termination reason: Unknown
% 28.40/4.06 % (32141)Termination phase: Saturation
% 28.40/4.06
% 28.40/4.06 % (32141)Memory used [KB]: 6780
% 28.40/4.06 % (32141)Time elapsed: 0.066 s
% 28.40/4.06 % (32141)Instructions burned: 157 (million)
% 28.40/4.06 % (32141)------------------------------
% 28.40/4.06 % (32141)------------------------------
% 28.90/4.07 % (32144)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on theBenchmark for (2962ds/414Mi)
% 28.90/4.08 % (32143)Instruction limit reached!
% 28.90/4.08 % (32143)------------------------------
% 28.90/4.08 % (32143)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 28.90/4.08 % (32143)Termination reason: Unknown
% 28.90/4.08 % (32143)Termination phase: Saturation
% 28.90/4.08
% 28.90/4.08 % (32143)Memory used [KB]: 6780
% 28.90/4.08 % (32143)Time elapsed: 0.028 s
% 28.90/4.08 % (32143)Instructions burned: 107 (million)
% 28.90/4.08 % (32143)------------------------------
% 28.90/4.08 % (32143)------------------------------
% 28.90/4.09 % (32145)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on theBenchmark for (2962ds/715Mi)
% 29.40/4.22 % (32144)Instruction limit reached!
% 29.40/4.22 % (32144)------------------------------
% 29.40/4.22 % (32144)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 29.40/4.22 % (32144)Termination reason: Unknown
% 29.40/4.22 % (32144)Termination phase: Saturation
% 29.40/4.22
% 29.40/4.22 % (32144)Memory used [KB]: 6908
% 29.40/4.22 % (32144)Time elapsed: 0.151 s
% 29.40/4.22 % (32144)Instructions burned: 416 (million)
% 29.40/4.22 % (32144)------------------------------
% 29.40/4.22 % (32144)------------------------------
% 29.40/4.24 % (32146)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on theBenchmark for (2961ds/961Mi)
% 29.75/4.31 % (32145)Instruction limit reached!
% 29.75/4.31 % (32145)------------------------------
% 29.75/4.31 % (32145)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 29.75/4.31 % (32145)Termination reason: Unknown
% 29.75/4.31 % (32145)Termination phase: Saturation
% 29.75/4.31
% 29.75/4.31 % (32145)Memory used [KB]: 4093
% 29.75/4.31 % (32145)Time elapsed: 0.223 s
% 29.75/4.31 % (32145)Instructions burned: 715 (million)
% 29.75/4.31 % (32145)------------------------------
% 29.75/4.31 % (32145)------------------------------
% 29.75/4.31 % (32142)Instruction limit reached!
% 29.75/4.31 % (32142)------------------------------
% 29.75/4.31 % (32142)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 29.75/4.31 % (32142)Termination reason: Unknown
% 29.75/4.31 % (32142)Termination phase: Saturation
% 29.75/4.31
% 29.75/4.31 % (32142)Memory used [KB]: 8571
% 29.75/4.31 % (32142)Time elapsed: 0.272 s
% 29.75/4.31 % (32142)Instructions burned: 590 (million)
% 29.75/4.31 % (32142)------------------------------
% 29.75/4.31 % (32142)------------------------------
% 29.75/4.32 % (32147)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on theBenchmark for (2960ds/1213Mi)
% 29.75/4.33 % (32148)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on theBenchmark for (2960ds/1979Mi)
% 31.73/4.40 % (32125)Refutation found. Thanks to Tanya!
% 31.73/4.40 % SZS status Theorem for theBenchmark
% 31.73/4.40 % SZS output start Proof for theBenchmark
% 31.73/4.40 thf(func_def_0, type, in: $i > $i > $o).
% 31.73/4.40 thf(func_def_1, type, exu: ($i > $o) > $o).
% 31.73/4.40 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 31.73/4.40 thf(func_def_8, type, powerset: $i > $i).
% 31.73/4.40 thf(func_def_10, type, setunion: $i > $i).
% 31.73/4.40 thf(func_def_19, type, descr: ($i > $o) > $i).
% 31.73/4.40 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 31.73/4.40 thf(func_def_26, type, prop2set: $o > $i).
% 31.73/4.40 thf(func_def_36, type, nonempty: $i > $o).
% 31.73/4.40 thf(func_def_69, type, set2prop: $i > $o).
% 31.73/4.40 thf(func_def_88, type, subset: $i > $i > $o).
% 31.73/4.40 thf(func_def_89, type, disjoint: $i > $i > $o).
% 31.73/4.40 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 31.73/4.40 thf(func_def_114, type, binunion: $i > $i > $i).
% 31.73/4.40 thf(func_def_122, type, binintersect: $i > $i > $i).
% 31.73/4.40 thf(func_def_135, type, regular: $i > $o).
% 31.73/4.40 thf(func_def_136, type, setminus: $i > $i > $i).
% 31.73/4.40 thf(func_def_147, type, symdiff: $i > $i > $i).
% 31.73/4.40 thf(func_def_153, type, iskpair: $i > $o).
% 31.73/4.40 thf(func_def_158, type, kpair: $i > $i > $i).
% 31.73/4.40 thf(func_def_160, type, cartprod: $i > $i > $i).
% 31.73/4.40 thf(func_def_177, type, singleton: $i > $o).
% 31.73/4.40 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 31.73/4.40 thf(func_def_184, type, atmost1p: $i > $o).
% 31.73/4.40 thf(func_def_185, type, atleast2p: $i > $o).
% 31.73/4.40 thf(func_def_186, type, atmost2p: $i > $o).
% 31.73/4.40 thf(func_def_187, type, upairsetp: $i > $o).
% 31.73/4.40 thf(func_def_191, type, kfst: $i > $i).
% 31.73/4.40 thf(func_def_203, type, ksnd: $i > $i).
% 31.73/4.40 thf(func_def_213, type, breln: $i > $i > $i > $o).
% 31.73/4.40 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 31.73/4.40 thf(func_def_222, type, func: $i > $i > $i > $o).
% 31.73/4.40 thf(func_def_223, type, funcSet: $i > $i > $i).
% 31.73/4.40 thf(func_def_226, type, ap: $i > $i > $i > $i > $i).
% 31.73/4.40 thf(func_def_245, type, sP0: $o > $o).
% 31.73/4.40 thf(f1019,plain,(
% 31.73/4.40 $false),
% 31.73/4.40 inference(trivial_inequality_removal,[],[f1018])).
% 31.73/4.40 thf(f1018,plain,(
% 31.73/4.40 ($true = $false)),
% 31.73/4.40 inference(boolean_simplification,[],[f1017])).
% 31.73/4.40 thf(f1017,plain,(
% 31.73/4.40 ($true = (~ $true))),
% 31.73/4.40 inference(boolean_simplification,[],[f1016])).
% 31.73/4.40 thf(f1016,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => $true)) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f1015])).
% 31.73/4.40 thf(f1015,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => $true))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f1014])).
% 31.73/4.40 thf(f1014,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => $true)))))),
% 31.73/4.40 inference(boolean_simplification,[],[f1013])).
% 31.73/4.40 thf(f1013,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => $true))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f1012])).
% 31.73/4.40 thf(f1012,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => $true)))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f1011])).
% 31.73/4.40 thf(f1011,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => $true))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f1010])).
% 31.73/4.40 thf(f1010,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => $true)))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f1009])).
% 31.73/4.40 thf(f1009,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => $true))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f1008])).
% 31.73/4.40 thf(f1008,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => $true)))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f1007])).
% 31.73/4.40 thf(f1007,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => $true))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f1006])).
% 31.73/4.40 thf(f1006,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => $true)))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f1005])).
% 31.73/4.40 thf(f1005,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => $true))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f1004])).
% 31.73/4.40 thf(f1004,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => $true)))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f1003])).
% 31.73/4.40 thf(f1003,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => $true))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f1002])).
% 31.73/4.40 thf(f1002,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => $true)))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f1001])).
% 31.73/4.40 thf(f1001,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => $true))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f1000])).
% 31.73/4.40 thf(f1000,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => $true)))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f999])).
% 31.73/4.40 thf(f999,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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)),
% 31.73/4.40 inference(boolean_simplification,[],[f998])).
% 31.73/4.40 thf(f998,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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)))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f997])).
% 31.73/4.40 thf(f997,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f996])).
% 31.73/4.40 thf(f996,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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)))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f995])).
% 31.73/4.40 thf(f995,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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)),
% 31.73/4.40 inference(boolean_simplification,[],[f994])).
% 31.73/4.40 thf(f994,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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)))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f993])).
% 31.73/4.40 thf(f993,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f992])).
% 31.73/4.40 thf(f992,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => $true)))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f991])).
% 31.73/4.40 thf(f991,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => $true))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f990])).
% 31.73/4.40 thf(f990,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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))))))))))) => $true)))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f989])).
% 31.73/4.40 thf(f989,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f988])).
% 31.73/4.40 thf(f988,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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)))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f987])).
% 31.73/4.40 thf(f987,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f986])).
% 31.73/4.40 thf(f986,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => $true)))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f985])).
% 31.73/4.40 thf(f985,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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)),
% 31.73/4.40 inference(boolean_simplification,[],[f984])).
% 31.73/4.40 thf(f984,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => $true)))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f983])).
% 31.73/4.40 thf(f983,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => $true))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f982])).
% 31.73/4.40 thf(f982,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => $true)))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f981])).
% 31.73/4.40 thf(f981,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => $true))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f980])).
% 31.73/4.40 thf(f980,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => $true)))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f979])).
% 31.73/4.40 thf(f979,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => $true))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f978])).
% 31.73/4.40 thf(f978,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => $true)))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f977])).
% 31.73/4.40 thf(f977,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => Y2)))) => Y2)))))))) => $true))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f976])).
% 31.73/4.40 thf(f976,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => $true)))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f975])).
% 31.73/4.40 thf(f975,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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))))))))) => $true))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f974])).
% 31.73/4.40 thf(f974,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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))))))) => $true)))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f973])).
% 31.73/4.40 thf(f973,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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)))))) => $true))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f972])).
% 31.73/4.40 thf(f972,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f971])).
% 31.73/4.40 thf(f971,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f970])).
% 31.73/4.40 thf(f970,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f969])).
% 31.73/4.40 thf(f969,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f968])).
% 31.73/4.40 thf(f968,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f967])).
% 31.73/4.40 thf(f967,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f966])).
% 31.73/4.40 thf(f966,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f965])).
% 31.73/4.40 thf(f965,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ Y0)))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f964])).
% 31.73/4.40 thf(f964,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f963])).
% 31.73/4.40 thf(f963,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f962])).
% 31.73/4.40 thf(f962,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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)))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f961])).
% 31.73/4.40 thf(f961,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f960])).
% 31.73/4.40 thf(f960,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f959])).
% 31.73/4.40 thf(f959,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f958])).
% 31.73/4.40 thf(f958,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f957])).
% 31.73/4.40 thf(f957,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f956])).
% 31.73/4.40 thf(f956,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f955])).
% 31.73/4.40 thf(f955,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f954])).
% 31.73/4.40 thf(f954,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f953])).
% 31.73/4.40 thf(f953,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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)))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f952])).
% 31.73/4.40 thf(f952,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f951])).
% 31.73/4.40 thf(f951,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($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) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f950])).
% 31.73/4.40 thf(f950,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f949])).
% 31.73/4.40 thf(f949,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f948])).
% 31.73/4.40 thf(f948,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f947])).
% 31.73/4.40 thf(f947,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f946])).
% 31.73/4.40 thf(f946,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f945])).
% 31.73/4.40 thf(f945,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f944])).
% 31.73/4.40 thf(f944,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f943])).
% 31.73/4.40 thf(f943,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f942])).
% 31.73/4.40 thf(f942,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f941])).
% 31.73/4.40 thf(f941,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f940])).
% 31.73/4.40 thf(f940,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f939])).
% 31.73/4.40 thf(f939,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f938])).
% 31.73/4.40 thf(f938,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f937])).
% 31.73/4.40 thf(f937,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f936])).
% 31.73/4.40 thf(f936,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f935])).
% 31.73/4.40 thf(f935,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f934])).
% 31.73/4.40 thf(f934,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f933])).
% 31.73/4.40 thf(f933,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f932])).
% 31.73/4.40 thf(f932,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = Y0)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f931])).
% 31.73/4.40 thf(f931,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f930])).
% 31.73/4.40 thf(f930,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f929])).
% 31.73/4.40 thf(f929,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f928])).
% 31.73/4.40 thf(f928,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f927])).
% 31.73/4.40 thf(f927,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f926])).
% 31.73/4.40 thf(f926,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (Y1 = Y0))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f925])).
% 31.73/4.40 thf(f925,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f924])).
% 31.73/4.40 thf(f924,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f923])).
% 31.73/4.40 thf(f923,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f922])).
% 31.73/4.40 thf(f922,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f921])).
% 31.73/4.40 thf(f921,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f920])).
% 31.73/4.40 thf(f920,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f919])).
% 31.73/4.40 thf(f919,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ Y0) @ Y1))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f918])).
% 31.73/4.40 thf(f918,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f917])).
% 31.73/4.40 thf(f917,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f916])).
% 31.73/4.40 thf(f916,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f915])).
% 31.73/4.40 thf(f915,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f914])).
% 31.73/4.40 thf(f914,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f913])).
% 31.73/4.40 thf(f913,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0)))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f912])).
% 31.73/4.40 thf(f912,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f911])).
% 31.73/4.40 thf(f911,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? 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@ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ ($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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f910])).
% 31.73/4.40 thf(f910,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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)),
% 31.73/4.40 inference(boolean_simplification,[],[f909])).
% 31.73/4.40 thf(f909,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? 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@ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ ($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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f908])).
% 31.73/4.40 thf(f908,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f907])).
% 31.73/4.40 thf(f907,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f906])).
% 31.73/4.40 thf(f906,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! 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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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f905])).
% 31.73/4.40 thf(f905,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f904])).
% 31.73/4.40 thf(f904,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y0 @ Y1))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f903])).
% 31.73/4.40 thf(f903,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y1 @ Y0) @ Y0))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f902])).
% 31.73/4.40 thf(f902,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y1 @ Y0) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f901])).
% 31.73/4.40 thf(f901,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y1 @ Y0) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f900])).
% 31.73/4.40 thf(f900,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y1 @ Y0) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y1 @ Y0)) = (binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f899])).
% 31.73/4.40 thf(f899,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y1 @ Y0) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y1 @ Y0)) = (binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f898])).
% 31.73/4.40 thf(f898,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y1 @ Y0) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y1 @ Y0)) = (binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f897])).
% 31.73/4.40 thf(f897,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y1 @ Y0) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y1 @ Y0)) = (binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f896])).
% 31.73/4.40 thf(f896,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y1 @ Y0) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y1 @ Y0)) = (binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f895])).
% 31.73/4.40 thf(f895,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y1 @ Y0) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y1 @ Y0)) = (binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f894])).
% 31.73/4.40 thf(f894,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y1 @ Y0) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y1 @ Y0)) = (binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f893])).
% 31.73/4.40 thf(f893,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y1 @ Y0) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y1 @ Y0)) = (binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f892])).
% 31.73/4.40 thf(f892,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y1 @ Y0) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y1 @ Y0)) = (binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f891])).
% 31.73/4.40 thf(f891,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y1 @ Y0) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y1 @ Y0)) = (binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f890])).
% 31.73/4.40 thf(f890,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y1 @ Y0) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y1 @ Y0)) = (binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f889])).
% 31.73/4.40 thf(f889,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y1 @ Y0) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y1 @ Y0)) = (binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => Y3)) => Y3))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f888])).
% 31.73/4.40 thf(f888,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! 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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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! 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@ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f887])).
% 31.73/4.40 thf(f887,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y1 @ Y0) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y1 @ Y0)) = (binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => 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 @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f886])).
% 31.73/4.40 thf(f886,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! 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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 @ Y1 @ Y0) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y1 @ Y0)) = (binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => 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 @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f885])).
% 31.73/4.40 thf(f885,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y1 @ Y0) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y1 @ Y0)) = (binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => 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 @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f884])).
% 31.73/4.40 thf(f884,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y1 @ Y0) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y1 @ Y0)) = (binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => 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 @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f883])).
% 31.73/4.40 thf(f883,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y1 @ Y0) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y1 @ Y0)) = (binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => 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 @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f882])).
% 31.73/4.40 thf(f882,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y1 @ Y0) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y1 @ Y0)) = (binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => 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 @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f881])).
% 31.73/4.40 thf(f881,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! 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@ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => 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 @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f880])).
% 31.73/4.40 thf(f880,plain,(
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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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y1 @ Y0) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y1 @ Y0)) = (binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => 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 @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ 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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f879])).
% 31.73/4.40 thf(f879,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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y1 @ Y0) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y1 @ Y0)) = (binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => 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 @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ 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 @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f878])).
% 31.73/4.40 thf(f878,plain,(
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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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y1 @ Y0) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y1 @ Y0)) = (binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => 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 @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ 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 @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ Y0))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f877])).
% 31.73/4.40 thf(f877,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y1 @ Y0) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y1 @ Y0)) = (binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => 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 @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ 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 @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))) => ((!! @ $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 @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f876])).
% 31.73/4.40 thf(f876,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y1 @ Y0) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y1 @ Y0)) = (binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => 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 @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ 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 @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))) => ((!! @ $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 @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y0) | (Y2 = Y1))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f875])).
% 31.73/4.40 thf(f875,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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y1 @ Y0) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y1 @ Y0)) = (binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => 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 @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ 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 @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))) => ((!! @ $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 @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y2)))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f874])).
% 31.73/4.40 thf(f874,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y1 @ Y0) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y1 @ Y0)) = (binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => 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 @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ 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 @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))) => ((!! @ $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 @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y0))))))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f873])).
% 31.73/4.40 thf(f873,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y1 @ Y0) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y1 @ Y0)) = (binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => 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 @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ 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 @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))) => ((!! @ $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 @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y1 @ 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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f872])).
% 31.73/4.40 thf(f872,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => 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 @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ 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 @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))) => ((!! @ $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 @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y1 @ 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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f871])).
% 31.73/4.40 thf(f871,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y1 @ Y0) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y1 @ Y0)) = (binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => 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 @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ 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 @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))) => ((!! @ $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 @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y1 @ 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 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f870])).
% 31.73/4.40 thf(f870,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! 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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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! 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@ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => 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 @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ 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 @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))) => ((!! @ $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 @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y1 @ 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 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y2 @ Y1)))))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f869])).
% 31.73/4.40 thf(f869,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ 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 @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))) => ((!! @ $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 @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y1 @ 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 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y0) & (in @ Y4 @ Y2)))))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f868])).
% 31.73/4.40 thf(f868,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! 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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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y1 @ Y0) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y1 @ Y0)) = (binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => 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 @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ 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 @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))) => ((!! @ $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 @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y1 @ 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 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y0) & (in @ Y4 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (iskpair @ Y1)))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f867])).
% 31.73/4.40 thf(f867,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ 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 @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))) => ((!! @ $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 @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y1 @ 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 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y0) & (in @ Y4 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (iskpair @ Y1)))))))) => ((!! @ $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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f865])).
% 31.73/4.40 thf(f865,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! 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@ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! 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@ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => 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 @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ 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 @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))) => ((!! @ $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 @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y1 @ 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 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y0) & (in @ Y4 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (iskpair @ Y1)))))))) => ((!! @ $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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f864])).
% 31.73/4.40 thf(f864,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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y1 @ Y0) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y1 @ Y0)) = (binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => 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 @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ 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 @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))) => ((!! @ $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 @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y1 @ 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 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y0) & (in @ Y4 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (iskpair @ Y1)))))))) => ((!! @ $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))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f863])).
% 31.73/4.40 thf(f863,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ 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 @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))) => ((!! @ $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 @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y1 @ 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 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y0) & (in @ Y4 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (iskpair @ Y1)))))))) => ((!! @ $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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f862])).
% 31.73/4.40 thf(f862,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! 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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 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y0) & (in @ Y4 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (iskpair @ Y1)))))))) => ((!! @ $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]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f861])).
% 31.73/4.40 thf(f861,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y1 @ Y0) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y1 @ Y0)) = (binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => 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 @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ 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 @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))) => ((!! @ $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 @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y1 @ 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 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y0) & (in @ Y4 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (iskpair @ Y1)))))))) => ((!! @ $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]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y1 @ Y3) => (Y0 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y2 @ Y1)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y2 @ Y1)))))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f860])).
% 31.73/4.40 thf(f860,plain,(
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@ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! 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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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y1 @ Y0) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y1 @ Y0)) = (binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => 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 @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ 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 @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))) => ((!! @ $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 @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y1 @ 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 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y0) & (in @ Y4 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (iskpair @ Y1)))))))) => ((!! @ $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]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y1 @ Y3) => (Y0 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y2 @ Y1)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y2 @ Y1)))))))))))))) => ((!! @ $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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f859])).
% 31.73/4.40 thf(f859,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! 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@ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => 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 @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ 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 @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))) => ((!! @ $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 @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y1 @ 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 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y0) & (in @ Y4 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (iskpair @ Y1)))))))) => ((!! @ $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]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y1 @ Y3) => (Y0 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y2 @ Y1)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y2 @ Y1)))))))))))))) => ((!! @ $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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f858])).
% 31.73/4.40 thf(f858,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ 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 @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))) => ((!! @ $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 @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y1 @ 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 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y0) & (in @ Y4 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (iskpair @ Y1)))))))) => ((!! @ $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]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y1 @ Y3) => (Y0 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y2 @ Y1)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y2 @ Y1)))))))))))))) => ((!! @ $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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $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 @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = Y0)))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f857])).
% 31.73/4.40 thf(f857,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ 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 @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))) => ((!! @ $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 @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! 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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 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y0) & (in @ Y4 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (iskpair @ Y1)))))))) => ((!! @ $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]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y1 @ Y3) => (Y0 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y2 @ Y1)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y2 @ Y1)))))))))))))) => ((!! @ $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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $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 @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = 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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f856])).
% 31.73/4.40 thf(f856,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! 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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]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y1 @ Y3) => (Y0 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y2 @ Y1)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y2 @ Y1)))))))))))))) => ((!! @ $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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $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 @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = 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)))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f855])).
% 31.73/4.40 thf(f855,plain,(
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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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! 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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 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y0) & (in @ Y4 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (iskpair @ Y1)))))))) => ((!! @ $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]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y1 @ Y3) => (Y0 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y2 @ Y1)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y2 @ Y1)))))))))))))) => ((!! @ $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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $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 @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = 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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f854])).
% 31.73/4.40 thf(f854,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($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]: ((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]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y1 @ Y3) => (Y0 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y2 @ Y1)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y2 @ Y1)))))))))))))) => ((!! @ $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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $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 @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = 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 @ Y0 @ (cartprod @ Y2 @ Y1)) => (in @ (kfst @ Y0) @ Y2)))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f853])).
% 31.73/4.40 thf(f853,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y1 @ Y0) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y1 @ Y0)) = (binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => 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 @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ 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 @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))) => ((!! @ $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 @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y1 @ 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 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y0) & (in @ Y4 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (iskpair @ Y1)))))))) => ((!! @ $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]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y1 @ Y3) => (Y0 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y2 @ Y1)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y2 @ Y1)))))))))))))) => ((!! @ $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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $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 @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = 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 @ Y0 @ (cartprod @ Y2 @ Y1)) => (in @ (kfst @ Y0) @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f852])).
% 31.73/4.40 thf(f852,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0)))))) => ((!! 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@ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => 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 @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ 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 @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))) => ((!! @ $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 @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y1 @ 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 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y0) & (in @ Y4 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (iskpair @ Y1)))))))) => ((!! @ $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]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y1 @ Y3) => (Y0 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y2 @ Y1)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y2 @ Y1)))))))))))))) => ((!! @ $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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $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 @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = 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 @ Y0 @ (cartprod @ Y2 @ Y1)) => (in @ (kfst @ Y0) @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y1 = Y0)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f851])).
% 31.73/4.40 thf(f851,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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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 @ Y1 @ Y0) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y1 @ Y0)) = (binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => 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 @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ 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 @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))) => ((!! @ $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 @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y1 @ 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 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y0) & (in @ Y4 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (iskpair @ Y1)))))))) => ((!! @ $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]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y1 @ Y3) => (Y0 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y2 @ Y1)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y2 @ Y1)))))))))))))) => ((!! @ $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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $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 @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = 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 @ Y0 @ (cartprod @ Y2 @ Y1)) => (in @ (kfst @ Y0) @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) = (setadjoin @ Y1 @ emptyset))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f850])).
% 31.73/4.40 thf(f850,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! 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@ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => 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 @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ 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 @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))) => ((!! @ $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 @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! 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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 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y0) & (in @ Y4 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (iskpair @ Y1)))))))) => ((!! @ $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]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y1 @ Y3) => (Y0 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y2 @ Y1)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y2 @ Y1)))))))))))))) => ((!! @ $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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $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 @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = 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 @ Y0 @ (cartprod @ Y2 @ Y1)) => (in @ (kfst @ Y0) @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) = (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f849])).
% 31.73/4.40 thf(f849,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => 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 @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ 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 @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))) => ((!! @ $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 @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y1 @ 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 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y0) & (in @ Y4 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (iskpair @ Y1)))))))) => ((!! @ $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]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y1 @ Y3) => (Y0 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y2 @ Y1)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y2 @ Y1)))))))))))))) => ((!! @ $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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $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 @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = 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 @ Y0 @ (cartprod @ Y2 @ Y1)) => (in @ (kfst @ Y0) @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) = (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y2 = Y1))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f848])).
% 31.73/4.40 thf(f848,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => 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 @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ 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 @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))) => ((!! @ $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 @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y1 @ 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 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y0) & (in @ Y4 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (iskpair @ Y1)))))))) => ((!! @ $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]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y1 @ Y3) => (Y0 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y2 @ Y1)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y2 @ Y1)))))))))))))) => ((!! @ $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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $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 @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = 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 @ Y0 @ (cartprod @ Y2 @ Y1)) => (in @ (kfst @ Y0) @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) = (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y2 = Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))) => (Y1 = Y0)))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f847])).
% 31.73/4.40 thf(f847,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => 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 @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ 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 @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))) => ((!! @ $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 @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y1 @ 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 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y0) & (in @ Y4 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (iskpair @ Y1)))))))) => ((!! @ $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]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y1 @ Y3) => (Y0 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y2 @ Y1)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y2 @ Y1)))))))))))))) => ((!! @ $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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $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 @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = 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 @ Y0 @ (cartprod @ Y2 @ Y1)) => (in @ (kfst @ Y0) @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) = (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y2 = Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))) => (Y1 = Y0)))))))) => ((!! @ $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 @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f846])).
% 31.73/4.40 thf(f846,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => 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 @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ 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 @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))) => ((!! @ $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 @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y1 @ 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 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y0) & (in @ Y4 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (iskpair @ Y1)))))))) => ((!! @ $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]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y1 @ Y3) => (Y0 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y2 @ Y1)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y2 @ Y1)))))))))))))) => ((!! @ $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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $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 @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = 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 @ Y0 @ (cartprod @ Y2 @ Y1)) => (in @ (kfst @ Y0) @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) = (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y2 = Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))) => (Y1 = Y0)))))))) => ((!! @ $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 @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y3 @ Y0)) => (Y1 = Y0)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f845])).
% 31.73/4.40 thf(f845,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => 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 @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ 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 @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))) => ((!! @ $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 @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y1 @ 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 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y0) & (in @ Y4 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (iskpair @ Y1)))))))) => ((!! @ $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]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y1 @ Y3) => (Y0 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y2 @ Y1)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y2 @ Y1)))))))))))))) => ((!! @ $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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $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 @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = 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 @ Y0 @ (cartprod @ Y2 @ Y1)) => (in @ (kfst @ Y0) @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) = (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y2 = Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))) => (Y1 = Y0)))))))) => ((!! @ $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 @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y3 @ Y0)) => (Y1 = Y0)))))))))) => ((!! @ $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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.40 inference(boolean_simplification,[],[f844])).
% 31.73/4.40 thf(f844,plain,(
% 31.73/4.40 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! 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@ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => 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 @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ 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 @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))) => ((!! @ $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 @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y1 @ 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 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y0) & (in @ Y4 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (iskpair @ Y1)))))))) => ((!! @ $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]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y1 @ Y3) => (Y0 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y2 @ Y1)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y2 @ Y1)))))))))))))) => ((!! @ $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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $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 @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = 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 @ Y0 @ (cartprod @ Y2 @ Y1)) => (in @ (kfst @ Y0) @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) = (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y2 = Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))) => (Y1 = Y0)))))))) => ((!! @ $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 @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y3 @ Y0)) => (Y1 = Y0)))))))))) => ((!! @ $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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.40 inference(boolean_simplification,[],[f843])).
% 31.73/4.40 thf(f843,plain,(
% 31.73/4.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! 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@ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! 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@ $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 @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y3 @ Y0)) => (Y1 = Y0)))))))))) => ((!! @ $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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.41 inference(boolean_simplification,[],[f842])).
% 31.73/4.41 thf(f842,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 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y0) & (in @ Y4 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (iskpair @ Y1)))))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y1 @ Y3) => (Y0 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y2 @ Y1)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y2 @ Y1)))))))))))))) => ((!! @ $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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $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 @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = 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 @ Y0 @ (cartprod @ Y2 @ Y1)) => (in @ (kfst @ Y0) @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) = (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y2 = Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))) => (Y1 = Y0)))))))) => ((!! @ $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 @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y3 @ Y0)) => (Y1 = Y0)))))))))) => ((!! @ $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 @ Y1 @ (cartprod @ Y2 @ Y0)) => (in @ (ksnd @ Y1) @ Y0)))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.41 inference(boolean_simplification,[],[f841])).
% 31.73/4.41 thf(f841,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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y1 @ Y0) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y1 @ Y0)) = (binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => 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 @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ 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 @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))) => ((!! @ $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 @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y1 @ 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 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y0) & (in @ Y4 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (iskpair @ Y1)))))))) => ((!! @ $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]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y1 @ Y3) => (Y0 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y2 @ Y1)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y2 @ Y1)))))))))))))) => ((!! @ $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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $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 @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = 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 @ Y0 @ (cartprod @ Y2 @ Y1)) => (in @ (kfst @ Y0) @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) = (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y2 = Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))) => (Y1 = Y0)))))))) => ((!! @ $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 @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y3 @ Y0)) => (Y1 = Y0)))))))))) => ((!! @ $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 @ Y1 @ (cartprod @ Y2 @ Y0)) => (in @ (ksnd @ Y1) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y1) @ (cartprod @ Y0 @ Y2)) => (in @ Y3 @ Y0)))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.41 inference(boolean_simplification,[],[f840])).
% 31.73/4.41 thf(f840,plain,(
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@ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ 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 @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))) => ((!! @ $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 @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! 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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 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y0) & (in @ Y4 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (iskpair @ Y1)))))))) => ((!! @ $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]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y1 @ Y3) => (Y0 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y2 @ Y1)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y2 @ Y1)))))))))))))) => ((!! @ $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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $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 @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = 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 @ Y0 @ (cartprod @ Y2 @ Y1)) => (in @ (kfst @ Y0) @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) = (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y2 = Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))) => (Y1 = Y0)))))))) => ((!! @ $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 @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y3 @ Y0)) => (Y1 = Y0)))))))))) => ((!! @ $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 @ Y1 @ (cartprod @ Y2 @ Y0)) => (in @ (ksnd @ Y1) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y1) @ (cartprod @ Y0 @ Y2)) => (in @ Y3 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y1 @ Y2)) => (in @ Y3 @ Y2)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.41 inference(boolean_simplification,[],[f839])).
% 31.73/4.41 thf(f839,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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y1 @ Y0) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y1 @ Y0)) = (binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => 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 @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ 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 @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))) => ((!! @ $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 @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y1 @ 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 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y0) & (in @ Y4 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (iskpair @ Y1)))))))) => ((!! @ $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]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y1 @ Y3) => (Y0 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y2 @ Y1)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y2 @ Y1)))))))))))))) => ((!! @ $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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $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 @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = 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 @ Y0 @ (cartprod @ Y2 @ Y1)) => (in @ (kfst @ Y0) @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) = (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y2 = Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))) => (Y1 = Y0)))))))) => ((!! @ $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 @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y3 @ Y0)) => (Y1 = Y0)))))))))) => ((!! @ $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 @ Y1 @ (cartprod @ Y2 @ Y0)) => (in @ (ksnd @ Y1) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y1) @ (cartprod @ Y0 @ Y2)) => (in @ Y3 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y1 @ Y2)) => (in @ Y3 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kpair @ Y0 @ Y3) = (kpair @ Y0 @ Y3)))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.41 inference(boolean_simplification,[],[f838])).
% 31.73/4.41 thf(f838,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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! 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@ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => 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 @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ 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 @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))) => ((!! @ $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 @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y1 @ 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 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y0) & (in @ Y4 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (iskpair @ Y1)))))))) => ((!! @ $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]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y1 @ Y3) => (Y0 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y2 @ Y1)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y2 @ Y1)))))))))))))) => ((!! @ $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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $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 @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = 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 @ Y0 @ (cartprod @ Y2 @ Y1)) => (in @ (kfst @ Y0) @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) = (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y2 = Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))) => (Y1 = Y0)))))))) => ((!! @ $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 @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y3 @ Y0)) => (Y1 = Y0)))))))))) => ((!! @ $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 @ Y1 @ (cartprod @ Y2 @ Y0)) => (in @ (ksnd @ Y1) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y1) @ (cartprod @ Y0 @ Y2)) => (in @ Y3 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y1 @ Y2)) => (in @ Y3 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kpair @ Y0 @ Y3) = (kpair @ Y0 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((kfst @ (kpair @ Y1 @ Y3)) = Y1))))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.41 inference(boolean_simplification,[],[f837])).
% 31.73/4.41 thf(f837,plain,(
% 31.73/4.41 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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))))))) => ((!! 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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]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))))))) => ((!! 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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 @ Y0 @ (cartprod @ Y2 @ Y1)) => (in @ (kfst @ Y0) @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) = (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y2 = Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))) => (Y1 = Y0)))))))) => ((!! @ $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 @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y3 @ Y0)) => (Y1 = Y0)))))))))) => ((!! @ $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 @ Y1 @ (cartprod @ Y2 @ Y0)) => (in @ (ksnd @ Y1) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y1) @ (cartprod @ Y0 @ Y2)) => (in @ Y3 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y1 @ Y2)) => (in @ Y3 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kpair @ Y0 @ Y3) = (kpair @ Y0 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((kfst @ (kpair @ Y1 @ Y3)) = Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((ksnd @ (kpair @ Y1 @ Y3)) = Y3))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.41 inference(boolean_simplification,[],[f836])).
% 31.73/4.41 thf(f836,plain,(
% 31.73/4.41 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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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 @ Y0 @ (cartprod @ Y2 @ Y1)) => (in @ (kfst @ Y0) @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) = (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y2 = Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))) => (Y1 = Y0)))))))) => ((!! @ $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 @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y3 @ Y0)) => (Y1 = Y0)))))))))) => ((!! @ $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 @ Y1 @ (cartprod @ Y2 @ Y0)) => (in @ (ksnd @ Y1) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y1) @ (cartprod @ Y0 @ Y2)) => (in @ Y3 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y1 @ Y2)) => (in @ Y3 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kpair @ Y0 @ Y3) = (kpair @ Y0 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((kfst @ (kpair @ Y1 @ Y3)) = Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((ksnd @ (kpair @ Y1 @ Y3)) = Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => ((kpair @ (kfst @ Y1) @ (ksnd @ Y1)) = Y1)))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.41 inference(boolean_simplification,[],[f835])).
% 31.73/4.41 thf(f835,plain,(
% 31.73/4.41 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! 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@ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => 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 @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ 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 @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))) => ((!! @ $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 @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y1 @ 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 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y0) & (in @ Y4 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (iskpair @ Y1)))))))) => ((!! @ $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]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y1 @ Y3) => (Y0 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y2 @ Y1)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y2 @ Y1)))))))))))))) => ((!! @ $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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $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 @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = 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 @ Y0 @ (cartprod @ Y2 @ Y1)) => (in @ (kfst @ Y0) @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) = (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y2 = Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))) => (Y1 = Y0)))))))) => ((!! @ $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 @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y3 @ Y0)) => (Y1 = Y0)))))))))) => ((!! @ $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 @ Y1 @ (cartprod @ Y2 @ Y0)) => (in @ (ksnd @ Y1) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y1) @ (cartprod @ Y0 @ Y2)) => (in @ Y3 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y1 @ Y2)) => (in @ Y3 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kpair @ Y0 @ Y3) = (kpair @ Y0 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((kfst @ (kpair @ Y1 @ Y3)) = Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((ksnd @ (kpair @ Y1 @ Y3)) = Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => ((kpair @ (kfst @ Y1) @ (ksnd @ Y1)) = Y1)))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y0 @ Y3 @ Y4) => (in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y1 @ Y2 @ Y0))))))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.41 inference(boolean_simplification,[],[f834])).
% 31.73/4.41 thf(f834,plain,(
% 31.73/4.41 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = 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 @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (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 @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ ($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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y1 @ Y0) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y1 @ Y0)) = (binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => 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 @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ 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 @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))) => ((!! @ $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 @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y1 @ 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 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y0) & (in @ Y4 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (iskpair @ Y1)))))))) => ((!! @ $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]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y1 @ Y3) => (Y0 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y2 @ Y1)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y2 @ Y1)))))))))))))) => ((!! @ $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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $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 @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = 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 @ Y0 @ (cartprod @ Y2 @ Y1)) => (in @ (kfst @ Y0) @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) = (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y2 = Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))) => (Y1 = Y0)))))))) => ((!! @ $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 @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y3 @ Y0)) => (Y1 = Y0)))))))))) => ((!! @ $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 @ Y1 @ (cartprod @ Y2 @ Y0)) => (in @ (ksnd @ Y1) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y1) @ (cartprod @ Y0 @ Y2)) => (in @ Y3 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y1 @ Y2)) => (in @ Y3 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kpair @ Y0 @ Y3) = (kpair @ Y0 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((kfst @ (kpair @ Y1 @ Y3)) = Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((ksnd @ (kpair @ Y1 @ Y3)) = Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => ((kpair @ (kfst @ Y1) @ (ksnd @ Y1)) = Y1)))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y0 @ Y3 @ Y4) => (in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y1 @ Y2 @ Y0))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (subset @ (dpsetconstr @ Y2 @ Y0 @ Y1) @ (cartprod @ Y2 @ Y0)))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.41 inference(boolean_simplification,[],[f833])).
% 31.73/4.41 thf(f833,plain,(
% 31.73/4.41 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => ((kpair @ (kfst @ Y1) @ (ksnd @ Y1)) = Y1)))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y0 @ Y3 @ Y4) => (in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y1 @ Y2 @ Y0))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (subset @ (dpsetconstr @ Y2 @ Y0 @ Y1) @ (cartprod @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (subset @ (dpsetconstr @ Y0 @ Y2 @ Y1) @ (cartprod @ Y0 @ Y2)))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.41 inference(boolean_simplification,[],[f832])).
% 31.73/4.41 thf(f832,plain,(
% 31.73/4.41 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))))))) => ((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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ Y3) = (dsetconstr @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) = (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y2 = Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))) => (Y1 = Y0)))))))) => ((!! @ $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 @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y3 @ Y0)) => (Y1 = Y0)))))))))) => ((!! @ $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 @ Y1 @ (cartprod @ Y2 @ Y0)) => (in @ (ksnd @ Y1) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y1) @ (cartprod @ Y0 @ Y2)) => (in @ Y3 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y1 @ Y2)) => (in @ Y3 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kpair @ Y0 @ Y3) = (kpair @ Y0 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((kfst @ (kpair @ Y1 @ Y3)) = Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((ksnd @ (kpair @ Y1 @ Y3)) = Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => ((kpair @ (kfst @ Y1) @ (ksnd @ Y1)) = Y1)))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y0 @ Y3 @ Y4) => (in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y1 @ Y2 @ Y0))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (subset @ (dpsetconstr @ Y2 @ Y0 @ Y1) @ (cartprod @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (subset @ (dpsetconstr @ Y0 @ Y2 @ Y1) @ (cartprod @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y1 @ Y3 @ Y2)) => (Y2 @ Y0 @ Y4)))))))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.41 inference(boolean_simplification,[],[f831])).
% 31.73/4.41 thf(f831,plain,(
% 31.73/4.41 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! 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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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $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]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y1 @ Y3) => (Y0 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y2 @ Y1)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y2 @ Y1)))))))))))))) => ((!! @ $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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $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 @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = 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 @ Y0 @ (cartprod @ Y2 @ Y1)) => (in @ (kfst @ Y0) @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) = (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y2 = Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))) => (Y1 = Y0)))))))) => ((!! @ $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 @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y3 @ Y0)) => (Y1 = Y0)))))))))) => ((!! @ $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 @ Y1 @ (cartprod @ Y2 @ Y0)) => (in @ (ksnd @ Y1) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y1) @ (cartprod @ Y0 @ Y2)) => (in @ Y3 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y1 @ Y2)) => (in @ Y3 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kpair @ Y0 @ Y3) = (kpair @ Y0 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((kfst @ (kpair @ Y1 @ Y3)) = Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((ksnd @ (kpair @ Y1 @ Y3)) = Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => ((kpair @ (kfst @ Y1) @ (ksnd @ Y1)) = Y1)))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y0 @ Y3 @ Y4) => (in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y1 @ Y2 @ Y0))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (subset @ (dpsetconstr @ Y2 @ Y0 @ Y1) @ (cartprod @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (subset @ (dpsetconstr @ Y0 @ Y2 @ Y1) @ (cartprod @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y1 @ Y3 @ 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 @ Y3 @ Y4) @ (dpsetconstr @ Y2 @ Y0 @ Y1)) => (in @ Y3 @ Y2)))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.41 inference(boolean_simplification,[],[f830])).
% 31.73/4.41 thf(f830,plain,(
% 31.73/4.41 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ 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 @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))) => ((!! @ $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 @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))) => ((!! 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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 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y0) & (in @ Y4 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (iskpair @ Y1)))))))) => ((!! @ $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]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y1 @ Y3) => (Y0 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y2 @ Y1)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y2 @ Y1)))))))))))))) => ((!! @ $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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $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 @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = 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 @ Y0 @ (cartprod @ Y2 @ Y1)) => (in @ (kfst @ Y0) @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) = (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y2 = Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))) => (Y1 = Y0)))))))) => ((!! @ $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 @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y3 @ Y0)) => (Y1 = Y0)))))))))) => ((!! @ $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 @ Y1 @ (cartprod @ Y2 @ Y0)) => (in @ (ksnd @ Y1) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y1) @ (cartprod @ Y0 @ Y2)) => (in @ Y3 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y1 @ Y2)) => (in @ Y3 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kpair @ Y0 @ Y3) = (kpair @ Y0 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((kfst @ (kpair @ Y1 @ Y3)) = Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((ksnd @ (kpair @ Y1 @ Y3)) = Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => ((kpair @ (kfst @ Y1) @ (ksnd @ Y1)) = Y1)))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y0 @ Y3 @ Y4) => (in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y1 @ Y2 @ Y0))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (subset @ (dpsetconstr @ Y2 @ Y0 @ Y1) @ (cartprod @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (subset @ (dpsetconstr @ Y0 @ Y2 @ Y1) @ (cartprod @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y1 @ Y3 @ 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 @ Y3 @ Y4) @ (dpsetconstr @ Y2 @ Y0 @ Y1)) => (in @ Y3 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y2) @ (dpsetconstr @ Y0 @ Y1 @ Y3)) => (in @ Y2 @ Y1)))))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.41 inference(boolean_simplification,[],[f829])).
% 31.73/4.41 thf(f829,plain,(
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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => ((kpair @ (kfst @ Y1) @ (ksnd @ Y1)) = Y1)))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y0 @ Y3 @ Y4) => (in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y1 @ Y2 @ Y0))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (subset @ (dpsetconstr @ Y2 @ Y0 @ Y1) @ (cartprod @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (subset @ (dpsetconstr @ Y0 @ Y2 @ Y1) @ (cartprod @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y1 @ Y3 @ 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 @ Y3 @ Y4) @ (dpsetconstr @ Y2 @ Y0 @ Y1)) => (in @ Y3 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y2) @ (dpsetconstr @ Y0 @ Y1 @ Y3)) => (in @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: ((in @ (kpair @ Y2 @ Y1) @ (dpsetconstr @ Y0 @ Y3 @ Y4)) => (Y4 @ Y2 @ Y1)))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.41 inference(boolean_simplification,[],[f828])).
% 31.73/4.41 thf(f828,plain,(
% 31.73/4.41 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ 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 @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => 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 @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ Y1)) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ 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)))))))))) => ((!! @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ 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 > $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]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $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 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($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))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($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]: ((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]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))))))) => ((!! 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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 @ Y0 @ (cartprod @ Y2 @ Y1)) => (in @ (kfst @ Y0) @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) = (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y2 = Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))) => (Y1 = Y0)))))))) => ((!! @ $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 @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y3 @ Y0)) => (Y1 = Y0)))))))))) => ((!! @ $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 @ Y1 @ (cartprod @ Y2 @ Y0)) => (in @ (ksnd @ Y1) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y1) @ (cartprod @ Y0 @ Y2)) => (in @ Y3 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y1 @ Y2)) => (in @ Y3 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kpair @ Y0 @ Y3) = (kpair @ Y0 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((kfst @ (kpair @ Y1 @ Y3)) = Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((ksnd @ (kpair @ Y1 @ Y3)) = Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => ((kpair @ (kfst @ Y1) @ (ksnd @ Y1)) = Y1)))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y0 @ Y3 @ Y4) => (in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y1 @ Y2 @ Y0))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (subset @ (dpsetconstr @ Y2 @ Y0 @ Y1) @ (cartprod @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (subset @ (dpsetconstr @ Y0 @ Y2 @ Y1) @ (cartprod @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y1 @ Y3 @ 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 @ Y3 @ Y4) @ (dpsetconstr @ Y2 @ Y0 @ Y1)) => (in @ Y3 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y2) @ (dpsetconstr @ Y0 @ Y1 @ Y3)) => (in @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: ((in @ (kpair @ Y2 @ Y1) @ (dpsetconstr @ Y0 @ Y3 @ Y4)) => (Y4 @ Y2 @ Y1)))))))))))) => ((!! @ $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) => (?? @ $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))))))))))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.41 inference(boolean_simplification,[],[f827])).
% 31.73/4.41 thf(f827,plain,(
% 31.73/4.41 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))) => ((!! @ ($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 @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (Y0 @ Y1)))))))) => ((!! @ ($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) => (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) => ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) = (Y2 @ Y1))))))))) => ((!! @ $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 @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y1 @ 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 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y0) & (in @ Y4 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (iskpair @ Y1)))))))) => ((!! @ $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]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y1 @ Y3) => (Y0 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y2 @ Y1)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y2 @ Y1)))))))))))))) => ((!! @ $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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $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 @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = 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 @ Y0 @ (cartprod @ Y2 @ Y1)) => (in @ (kfst @ Y0) @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) = (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y2 = Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))) => (Y1 = Y0)))))))) => ((!! @ $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 @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y3 @ Y0)) => (Y1 = Y0)))))))))) => ((!! @ $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 @ Y1 @ (cartprod @ Y2 @ Y0)) => (in @ (ksnd @ Y1) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y1) @ (cartprod @ Y0 @ Y2)) => (in @ Y3 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y1 @ Y2)) => (in @ Y3 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kpair @ Y0 @ Y3) = (kpair @ Y0 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((kfst @ (kpair @ Y1 @ Y3)) = Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((ksnd @ (kpair @ Y1 @ Y3)) = Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => ((kpair @ (kfst @ Y1) @ (ksnd @ Y1)) = Y1)))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y0 @ Y3 @ Y4) => (in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y1 @ Y2 @ Y0))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (subset @ (dpsetconstr @ Y2 @ Y0 @ Y1) @ (cartprod @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (subset @ (dpsetconstr @ Y0 @ Y2 @ Y1) @ (cartprod @ Y0 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y1 @ Y3 @ 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 @ Y3 @ Y4) @ (dpsetconstr @ Y2 @ Y0 @ Y1)) => (in @ Y3 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y2) @ (dpsetconstr @ Y0 @ Y1 @ Y3)) => (in @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: ((in @ (kpair @ Y2 @ Y1) @ (dpsetconstr @ Y0 @ Y3 @ Y4)) => (Y4 @ Y2 @ Y1)))))))))))) => ((!! @ $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) => (?? @ $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 @ (^[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))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setunion @ (dsetconstr @ Y2 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y0)))) @ Y2))))))))))) => (!! @ $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))))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setunion @ (dsetconstr @ Y2 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y0)))) @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)),
% 31.73/4.41 inference(beta_eta_normalization,[],[f824])).
% 31.73/4.41 thf(f824,plain,(
% 31.73/4.41 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y3 @ Y0)) => (Y1 = Y0)))))))))) => ((!! @ $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))))))) => ((!! @ $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 @ Y1 @ (cartprod @ Y2 @ Y0)) => (in @ (ksnd @ Y1) @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y1) @ (cartprod @ Y0 @ Y2)) => (in @ Y3 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y1 @ Y2)) => (in @ Y3 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kpair @ Y0 @ Y3) = (kpair @ Y0 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((kfst @ (kpair @ Y1 @ Y3)) = Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((ksnd @ (kpair @ Y1 @ Y3)) = Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => ((kpair @ (kfst @ Y1) @ (ksnd @ Y1)) = Y1)))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y0 @ Y3 @ Y4) => (in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y1 @ Y2 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y0 @ Y5 @ Y6))))))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (subset @ (dpsetconstr @ Y2 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y1 @ Y3 @ Y4))))) @ (cartprod @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y0 @ Y2 @ (dpsetconstr @ Y0 @ Y2 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y1 @ Y3 @ Y4)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y1 @ Y3 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y2 @ Y5 @ Y6)))))) => (Y2 @ Y0 @ Y4)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y2 @ Y0 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y1 @ Y5 @ Y6)))))) => (in @ Y3 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y2) @ (dpsetconstr @ Y0 @ Y1 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y3 @ Y5 @ Y6)))))) => (in @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: ((in @ (kpair @ Y2 @ Y1) @ (dpsetconstr @ Y0 @ Y3 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y4 @ Y5 @ Y6)))))) => (Y4 @ Y2 @ Y1)))))))))))) => ((!! @ $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) => ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & ((setadjoin @ Y5 @ emptyset) = Y4))))) @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))))))))))) => ((!! @ $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 @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setunion @ (dsetconstr @ Y2 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y0)))) @ Y2))))))))))) => (!! @ $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 @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (setunion @ (dsetconstr @ Y5 @ (^[Y8 : $i]: (in @ (kpair @ Y7 @ Y8) @ Y6))))))))))) @ Y1 @ Y2 @ Y0 @ Y3) @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.41 inference(definition_unfolding,[],[f748,f612,f603,f665,f764,f606,f689,f641,f695,f795,f789,f776,f796,f615,f621,f766,f797,f600,f645,f653,f777,f798,f625,f634,f624,f726,f799,f800,f801,f638,f632,f751,f791,f734,f779,f660,f745,f656,f761,f758,f687,f719,f802,f803,f618,f671,f793,f685,f742,f785,f737,f644,f711,f771,f716,f666,f787,f720,f649,f596,f792,f804,f805,f806,f728,f759,f807,f808,f607,f749,f697,f767,f763,f809,f810,f677,f631,f626,f620,f642,f713,f688,f691,f672,f775,f765,f770,f746,f659,f681,f602,f675,f701,f628,f630,f664,f718,f670,f729,f712,f599,f773,f633,f727,f707,f629,f684,f640,f735,f786,f725,f738,f608,f680,f724,f619,f708,f627,f686,f610,f757,f730,f690,f769,f635,f722,f694,f605,f703,f693,f658,f715,f754,f604,f762,f788,f655,f663,f650,f651,f609,f772,f699,f790,f733,f710,f705,f794,f752,f706,f679,f736,f778,f780,f811,f813,f814,f815,f622,f682,f816,f817,f747,f613,f753,f731,f744,f702,f652,f709,f717,f643,f818,f662,f647,f657,f676,f750,f739,f714,f696,f646,f741,f669,f819,f774,f667,f700,f723,f822,f823,f820,f614])).
% 31.73/4.41 thf(f614,plain,(
% 31.73/4.41 (ap = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (setunion @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2))))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f434])).
% 31.73/4.41 thf(f434,plain,(
% 31.73/4.41 (ap = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (setunion @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2))))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f433])).
% 31.73/4.41 thf(f433,plain,(
% 31.73/4.41 (ap = (^[X0 : $i, X1 : $i, X2 : $i, X3 : $i] : (setunion @ (dsetconstr @ X1 @ (^[X4 : $i] : (in @ (kpair @ X3 @ X4) @ X2))))))),
% 31.73/4.41 inference(rectify,[],[f198])).
% 31.73/4.41 thf(f198,axiom,(
% 31.73/4.41 (ap = (^[X3 : $i, X4 : $i, X13 : $i, X1 : $i] : (setunion @ (dsetconstr @ X4 @ (^[X2 : $i] : (in @ (kpair @ X1 @ X2) @ X13))))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap)).
% 31.73/4.41 thf(f820,plain,(
% 31.73/4.41 (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)))))))))))))),
% 31.73/4.41 inference(definition_unfolding,[],[f698,f704,f812])).
% 31.73/4.41 thf(f812,plain,(
% 31.73/4.41 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) & ((setadjoin @ Y3 @ emptyset) = Y2))))) @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 31.73/4.41 inference(definition_unfolding,[],[f678,f755])).
% 31.73/4.41 thf(f755,plain,(
% 31.73/4.41 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f430])).
% 31.73/4.41 thf(f430,plain,(
% 31.73/4.41 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0))))))),
% 31.73/4.41 inference(fool_elimination,[],[f429])).
% 31.73/4.41 thf(f429,plain,(
% 31.73/4.41 (singleton = (^[X0 : $i] : (? [X1] : (((setadjoin @ X1 @ emptyset) = X0) & (in @ X1 @ X0)))))),
% 31.73/4.41 inference(rectify,[],[f156])).
% 31.73/4.41 thf(f156,axiom,(
% 31.73/4.41 (singleton = (^[X3 : $i] : (? [X1] : (((setadjoin @ X1 @ emptyset) = X3) & (in @ X1 @ X3)))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton)).
% 31.73/4.41 thf(f678,plain,(
% 31.73/4.41 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f494])).
% 31.73/4.41 thf(f494,plain,(
% 31.73/4.41 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f493])).
% 31.73/4.41 thf(f493,plain,(
% 31.73/4.41 (ex1 = (^[X0 : $i, X1 : $i > $o] : (singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))))))),
% 31.73/4.41 inference(rectify,[],[f158])).
% 31.73/4.41 thf(f158,axiom,(
% 31.73/4.41 (ex1 = (^[X3 : $i, X0 : $i > $o] : (singleton @ (dsetconstr @ X3 @ (^[X1 : $i] : (X0 @ X1))))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1)).
% 31.73/4.41 thf(f704,plain,(
% 31.73/4.41 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f402])).
% 31.73/4.41 thf(f402,plain,(
% 31.73/4.41 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f401])).
% 31.73/4.41 thf(f401,plain,(
% 31.73/4.41 (breln = (^[X0 : $i, X1 : $i, X2 : $i] : (subset @ X2 @ (cartprod @ X0 @ X1))))),
% 31.73/4.41 inference(rectify,[],[f186])).
% 31.73/4.41 thf(f186,axiom,(
% 31.73/4.41 (breln = (^[X3 : $i, X4 : $i, X5 : $i] : (subset @ X5 @ (cartprod @ X3 @ X4))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln)).
% 31.73/4.41 thf(f698,plain,(
% 31.73/4.41 (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)))))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f422])).
% 31.73/4.41 thf(f422,plain,(
% 31.73/4.41 (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)))))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f421])).
% 31.73/4.41 thf(f421,plain,(
% 31.73/4.41 ((^[X0 : $i, X1 : $i, X2 : $i] : (! [X3] : ((in @ X3 @ X0) => (ex1 @ X1 @ (^[X4 : $i] : (in @ (kpair @ X3 @ X4) @ X2)))) & (breln @ X0 @ X1 @ X2))) = func)),
% 31.73/4.41 inference(rectify,[],[f194])).
% 31.73/4.41 thf(f194,axiom,(
% 31.73/4.41 ((^[X3 : $i, X4 : $i, X12 : $i] : (! [X1] : ((in @ X1 @ X3) => (ex1 @ X4 @ (^[X2 : $i] : (in @ (kpair @ X1 @ X2) @ X12)))) & (breln @ X3 @ X4 @ X12))) = func)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',func)).
% 31.73/4.41 thf(f823,plain,(
% 31.73/4.41 (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 @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setunion @ (dsetconstr @ Y2 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y0)))) @ Y2))))))))))))),
% 31.73/4.41 inference(definition_unfolding,[],[f639,f820])).
% 31.73/4.41 thf(f639,plain,(
% 31.73/4.41 (apProp = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y1 @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setunion @ (dsetconstr @ Y2 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y0)))) @ Y2))))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f203])).
% 31.73/4.41 thf(f203,plain,(
% 31.73/4.41 (apProp = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y1 @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setunion @ (dsetconstr @ Y2 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y0)))) @ Y2))))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f202])).
% 31.73/4.41 thf(f202,plain,(
% 31.73/4.41 (! [X0,X1,X2] : ((func @ X1 @ X0 @ X2) => ! [X3] : ((in @ X3 @ X1) => (in @ (setunion @ (dsetconstr @ X0 @ (^[X4 : $i] : (in @ (kpair @ X3 @ X4) @ X2)))) @ X0))) = apProp)),
% 31.73/4.41 inference(rectify,[],[f197])).
% 31.73/4.41 thf(f197,axiom,(
% 31.73/4.41 (! [X4,X3,X13] : ((func @ X3 @ X4 @ X13) => ! [X1] : ((in @ X1 @ X3) => (in @ (setunion @ (dsetconstr @ X4 @ (^[X2 : $i] : (in @ (kpair @ X1 @ X2) @ X13)))) @ X4))) = apProp)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',apProp)).
% 31.73/4.41 thf(f822,plain,(
% 31.73/4.41 (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 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & ((setadjoin @ Y5 @ emptyset) = Y4))))) @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))))))))))))),
% 31.73/4.41 inference(definition_unfolding,[],[f740,f820,f755])).
% 31.73/4.41 thf(f740,plain,(
% 31.73/4.41 (funcImageSingleton = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (singleton @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f221])).
% 31.73/4.41 thf(f221,plain,(
% 31.73/4.41 (funcImageSingleton = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y0 @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (singleton @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f220])).
% 31.73/4.41 thf(f220,plain,(
% 31.73/4.41 (! [X0,X1,X2] : ((func @ X2 @ X1 @ X0) => ! [X3] : ((in @ X3 @ X2) => (singleton @ (dsetconstr @ X1 @ (^[X4 : $i] : (in @ (kpair @ X3 @ X4) @ X0)))))) = funcImageSingleton)),
% 31.73/4.41 inference(rectify,[],[f196])).
% 31.73/4.41 thf(f196,axiom,(
% 31.73/4.41 (! [X13,X4,X3] : ((func @ X3 @ X4 @ X13) => ! [X1] : ((in @ X1 @ X3) => (singleton @ (dsetconstr @ X4 @ (^[X2 : $i] : (in @ (kpair @ X1 @ X2) @ X13)))))) = funcImageSingleton)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcImageSingleton)).
% 31.73/4.41 thf(f723,plain,(
% 31.73/4.41 (dpsetconstrER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: ((in @ (kpair @ Y2 @ Y1) @ (dpsetconstr @ Y0 @ Y3 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y4 @ Y5 @ Y6)))))) => (Y4 @ Y2 @ Y1)))))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f522])).
% 31.73/4.41 thf(f522,plain,(
% 31.73/4.41 (dpsetconstrER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: ((in @ (kpair @ Y2 @ Y1) @ (dpsetconstr @ Y0 @ Y3 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y4 @ Y5 @ Y6)))))) => (Y4 @ Y2 @ Y1)))))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f521])).
% 31.73/4.41 thf(f521,plain,(
% 31.73/4.41 (! [X0 : $i > $i > $o,X1,X2,X3,X4] : ((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X1 @ (^[X5 : $i, X6 : $i] : (X0 @ X5 @ X6)))) => (X0 @ X2 @ X3)) = dpsetconstrER)),
% 31.73/4.41 inference(rectify,[],[f193])).
% 31.73/4.41 thf(f193,axiom,(
% 31.73/4.41 (! [X0 : $i > $i > $o,X4,X1,X2,X3] : ((in @ (kpair @ X1 @ X2) @ (dpsetconstr @ X3 @ X4 @ (^[X8 : $i, X10 : $i] : (X0 @ X8 @ X10)))) => (X0 @ X1 @ X2)) = dpsetconstrER)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrER)).
% 31.73/4.41 thf(f700,plain,(
% 31.73/4.41 (dpsetconstrEL2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y2) @ (dpsetconstr @ Y0 @ Y1 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y3 @ Y5 @ Y6)))))) => (in @ Y2 @ Y1)))))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f337])).
% 31.73/4.41 thf(f337,plain,(
% 31.73/4.41 (dpsetconstrEL2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y4 @ Y2) @ (dpsetconstr @ Y0 @ Y1 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y3 @ Y5 @ Y6)))))) => (in @ Y2 @ Y1)))))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f336])).
% 31.73/4.41 thf(f336,plain,(
% 31.73/4.41 (dpsetconstrEL2 = ! [X0,X1 : $i > $i > $o,X2,X3,X4] : ((in @ (kpair @ X0 @ X2) @ (dpsetconstr @ X4 @ X3 @ (^[X5 : $i, X6 : $i] : (X1 @ X5 @ X6)))) => (in @ X2 @ X3)))),
% 31.73/4.41 inference(rectify,[],[f192])).
% 31.73/4.41 thf(f192,axiom,(
% 31.73/4.41 (dpsetconstrEL2 = ! [X1,X0 : $i > $i > $o,X2,X4,X3] : ((in @ (kpair @ X1 @ X2) @ (dpsetconstr @ X3 @ X4 @ (^[X8 : $i, X10 : $i] : (X0 @ X8 @ X10)))) => (in @ X2 @ X4)))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL2)).
% 31.73/4.41 thf(f667,plain,(
% 31.73/4.41 (dpsetconstrEL1 = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y2 @ Y0 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y1 @ Y5 @ Y6)))))) => (in @ Y3 @ Y2)))))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f484])).
% 31.73/4.41 thf(f484,plain,(
% 31.73/4.41 (dpsetconstrEL1 = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y2 @ Y0 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y1 @ Y5 @ Y6)))))) => (in @ Y3 @ Y2)))))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f483])).
% 31.73/4.41 thf(f483,plain,(
% 31.73/4.41 (! [X0,X1,X2,X3 : $i > $i > $o,X4] : ((in @ (kpair @ X1 @ X0) @ (dpsetconstr @ X2 @ X4 @ (^[X5 : $i, X6 : $i] : (X3 @ X5 @ X6)))) => (in @ X1 @ X2)) = dpsetconstrEL1)),
% 31.73/4.41 inference(rectify,[],[f191])).
% 31.73/4.41 thf(f191,axiom,(
% 31.73/4.41 (! [X2,X1,X3,X0 : $i > $i > $o,X4] : ((in @ (kpair @ X1 @ X2) @ (dpsetconstr @ X3 @ X4 @ (^[X8 : $i, X10 : $i] : (X0 @ X8 @ X10)))) => (in @ X1 @ X3)) = dpsetconstrEL1)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL1)).
% 31.73/4.41 thf(f774,plain,(
% 31.73/4.41 (dpsetconstrERa = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y1 @ Y3 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y2 @ Y5 @ Y6)))))) => (Y2 @ Y0 @ Y4)))))))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f217])).
% 31.73/4.41 thf(f217,plain,(
% 31.73/4.41 (dpsetconstrERa = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y1 @ Y3 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y2 @ Y5 @ Y6)))))) => (Y2 @ Y0 @ Y4)))))))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f216])).
% 31.73/4.41 thf(f216,plain,(
% 31.73/4.41 (! [X0,X1 : $i > $i > $o,X2,X3] : ((in @ X3 @ X2) => ! [X4] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ (dpsetconstr @ X2 @ X0 @ (^[X5 : $i, X6 : $i] : (X1 @ X5 @ X6)))) => (X1 @ X3 @ X4)))) = dpsetconstrERa)),
% 31.73/4.41 inference(rectify,[],[f190])).
% 31.73/4.41 thf(f190,axiom,(
% 31.73/4.41 (! [X4,X0 : $i > $i > $o,X3,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)))) = dpsetconstrERa)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrERa)).
% 31.73/4.41 thf(f819,plain,(
% 31.73/4.41 (setOfPairsIsBReln = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y0 @ Y2 @ (dpsetconstr @ Y0 @ Y2 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y1 @ Y3 @ Y4)))))))))))))),
% 31.73/4.41 inference(definition_unfolding,[],[f616,f704])).
% 31.73/4.41 thf(f616,plain,(
% 31.73/4.41 (setOfPairsIsBReln = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (breln @ Y0 @ Y2 @ (dpsetconstr @ Y0 @ Y2 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y1 @ Y3 @ Y4)))))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f446])).
% 31.73/4.41 thf(f446,plain,(
% 31.73/4.41 (setOfPairsIsBReln = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (breln @ Y0 @ Y2 @ (dpsetconstr @ Y0 @ Y2 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y1 @ Y3 @ Y4)))))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f445])).
% 31.73/4.41 thf(f445,plain,(
% 31.73/4.41 (! [X0,X1 : $i > $i > $o,X2] : (breln @ X2 @ X0 @ (dpsetconstr @ X2 @ X0 @ (^[X3 : $i, X4 : $i] : (X1 @ X3 @ X4)))) = setOfPairsIsBReln)),
% 31.73/4.41 inference(rectify,[],[f189])).
% 31.73/4.41 thf(f189,axiom,(
% 31.73/4.41 (! [X4,X0 : $i > $i > $o,X3] : (breln @ X3 @ X4 @ (dpsetconstr @ X3 @ X4 @ (^[X1 : $i, X2 : $i] : (X0 @ X1 @ X2)))) = setOfPairsIsBReln)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setOfPairsIsBReln)).
% 31.73/4.41 thf(f669,plain,(
% 31.73/4.41 (dpsetconstrSub = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (subset @ (dpsetconstr @ Y2 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y1 @ Y3 @ Y4))))) @ (cartprod @ Y2 @ Y0)))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f424])).
% 31.73/4.41 thf(f424,plain,(
% 31.73/4.41 (dpsetconstrSub = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (subset @ (dpsetconstr @ Y2 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y1 @ Y3 @ Y4))))) @ (cartprod @ Y2 @ Y0)))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f423])).
% 31.73/4.41 thf(f423,plain,(
% 31.73/4.41 (! [X0,X1 : $i > $i > $o,X2] : (subset @ (dpsetconstr @ X0 @ X2 @ (^[X3 : $i, X4 : $i] : (X1 @ X3 @ X4))) @ (cartprod @ X0 @ X2)) = dpsetconstrSub)),
% 31.73/4.41 inference(rectify,[],[f188])).
% 31.73/4.41 thf(f188,axiom,(
% 31.73/4.41 (! [X3,X0 : $i > $i > $o,X4] : (subset @ (dpsetconstr @ X3 @ X4 @ (^[X1 : $i, X2 : $i] : (X0 @ X1 @ X2))) @ (cartprod @ X3 @ X4)) = dpsetconstrSub)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrSub)).
% 31.73/4.41 thf(f741,plain,(
% 31.73/4.41 (dpsetconstrI = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y0 @ Y3 @ Y4) => (in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y1 @ Y2 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y0 @ Y5 @ Y6))))))))))))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f474])).
% 31.73/4.41 thf(f474,plain,(
% 31.73/4.41 (dpsetconstrI = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y0 @ Y3 @ Y4) => (in @ (kpair @ Y3 @ Y4) @ (dpsetconstr @ Y1 @ Y2 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y0 @ Y5 @ Y6))))))))))))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f473])).
% 31.73/4.41 thf(f473,plain,(
% 31.73/4.41 (dpsetconstrI = ! [X0,X1,X2,X3 : $i > $i > $o] : ((in @ X0 @ X2) => ! [X4] : ((in @ X4 @ X1) => ((X3 @ X0 @ X4) => (in @ (kpair @ X0 @ X4) @ (dpsetconstr @ X2 @ X1 @ (^[X5 : $i, X6 : $i] : (X3 @ X5 @ X6))))))))),
% 31.73/4.41 inference(rectify,[],[f187])).
% 31.73/4.41 thf(f187,axiom,(
% 31.73/4.41 (dpsetconstrI = ! [X1,X4,X3,X0 : $i > $i > $o] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => ((X0 @ X1 @ X2) => (in @ (kpair @ X1 @ X2) @ (dpsetconstr @ X3 @ X4 @ (^[X8 : $i, X10 : $i] : (X0 @ X8 @ X10))))))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrI)).
% 31.73/4.41 thf(f646,plain,(
% 31.73/4.41 (cartprodpairsurjEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => ((kpair @ (kfst @ Y1) @ (ksnd @ Y1)) = Y1)))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f486])).
% 31.73/4.41 thf(f486,plain,(
% 31.73/4.41 (cartprodpairsurjEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => ((kpair @ (kfst @ Y1) @ (ksnd @ Y1)) = Y1)))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f485])).
% 31.73/4.41 thf(f485,plain,(
% 31.73/4.41 (cartprodpairsurjEq = ! [X0,X1,X2] : ((in @ X1 @ (cartprod @ X2 @ X0)) => ((kpair @ (kfst @ X1) @ (ksnd @ X1)) = X1)))),
% 31.73/4.41 inference(rectify,[],[f185])).
% 31.73/4.41 thf(f185,axiom,(
% 31.73/4.41 (cartprodpairsurjEq = ! [X4,X10,X3] : ((in @ X10 @ (cartprod @ X3 @ X4)) => ((kpair @ (kfst @ X10) @ (ksnd @ X10)) = X10)))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairsurjEq)).
% 31.73/4.41 thf(f696,plain,(
% 31.73/4.41 (cartprodsndpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((ksnd @ (kpair @ Y1 @ Y3)) = Y3))))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f566])).
% 31.73/4.41 thf(f566,plain,(
% 31.73/4.41 (cartprodsndpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((ksnd @ (kpair @ Y1 @ Y3)) = Y3))))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f565])).
% 31.73/4.41 thf(f565,plain,(
% 31.73/4.41 (cartprodsndpairEq = ! [X0,X1,X2] : ((in @ X1 @ X2) => ! [X3] : ((in @ X3 @ X0) => ((ksnd @ (kpair @ X1 @ X3)) = X3))))),
% 31.73/4.41 inference(rectify,[],[f184])).
% 31.73/4.41 thf(f184,axiom,(
% 31.73/4.41 (cartprodsndpairEq = ! [X4,X1,X3] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => ((ksnd @ (kpair @ X1 @ X2)) = X2))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndpairEq)).
% 31.73/4.41 thf(f714,plain,(
% 31.73/4.41 (cartprodfstpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((kfst @ (kpair @ Y1 @ Y3)) = Y1))))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f398])).
% 31.73/4.41 thf(f398,plain,(
% 31.73/4.41 (cartprodfstpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((kfst @ (kpair @ Y1 @ Y3)) = Y1))))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f397])).
% 31.73/4.41 thf(f397,plain,(
% 31.73/4.41 (! [X0,X1,X2] : ((in @ X1 @ X2) => ! [X3] : ((in @ X3 @ X0) => ((kfst @ (kpair @ X1 @ X3)) = X1))) = cartprodfstpairEq)),
% 31.73/4.41 inference(rectify,[],[f183])).
% 31.73/4.41 thf(f183,axiom,(
% 31.73/4.41 (! [X4,X1,X3] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => ((kfst @ (kpair @ X1 @ X2)) = X1))) = cartprodfstpairEq)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstpairEq)).
% 31.73/4.41 thf(f739,plain,(
% 31.73/4.41 (cartprodmempaircEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kpair @ Y0 @ Y3) = (kpair @ Y0 @ Y3)))))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f492])).
% 31.73/4.41 thf(f492,plain,(
% 31.73/4.41 (cartprodmempaircEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kpair @ Y0 @ Y3) = (kpair @ Y0 @ Y3)))))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f491])).
% 31.73/4.41 thf(f491,plain,(
% 31.73/4.41 (! [X0,X1,X2] : ((in @ X2 @ X0) => ! [X3] : ((in @ X3 @ X1) => ((kpair @ X2 @ X3) = (kpair @ X2 @ X3)))) = cartprodmempaircEq)),
% 31.73/4.41 inference(rectify,[],[f182])).
% 31.73/4.41 thf(f182,axiom,(
% 31.73/4.41 (! [X3,X4,X1] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => ((kpair @ X1 @ X2) = (kpair @ X1 @ X2)))) = cartprodmempaircEq)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempaircEq)).
% 31.73/4.41 thf(f750,plain,(
% 31.73/4.41 (cartprodpairmemER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y1 @ Y2)) => (in @ Y3 @ Y2)))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f382])).
% 31.73/4.41 thf(f382,plain,(
% 31.73/4.41 (cartprodpairmemER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y1 @ Y2)) => (in @ Y3 @ Y2)))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f381])).
% 31.73/4.41 thf(f381,plain,(
% 31.73/4.41 (! [X0,X1,X2,X3] : ((in @ (kpair @ X3 @ X0) @ (cartprod @ X2 @ X1)) => (in @ X0 @ X1)) = cartprodpairmemER)),
% 31.73/4.41 inference(rectify,[],[f181])).
% 31.73/4.41 thf(f181,axiom,(
% 31.73/4.41 (! [X2,X4,X3,X1] : ((in @ (kpair @ X1 @ X2) @ (cartprod @ X3 @ X4)) => (in @ X2 @ X4)) = cartprodpairmemER)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemER)).
% 31.73/4.41 thf(f676,plain,(
% 31.73/4.41 (cartprodpairmemEL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y1) @ (cartprod @ Y0 @ Y2)) => (in @ Y3 @ Y0)))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f299])).
% 31.73/4.41 thf(f299,plain,(
% 31.73/4.41 (cartprodpairmemEL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y1) @ (cartprod @ Y0 @ Y2)) => (in @ Y3 @ Y0)))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f298])).
% 31.73/4.41 thf(f298,plain,(
% 31.73/4.41 (cartprodpairmemEL = ! [X0,X1,X2,X3] : ((in @ (kpair @ X0 @ X2) @ (cartprod @ X3 @ X1)) => (in @ X0 @ X3)))),
% 31.73/4.41 inference(rectify,[],[f180])).
% 31.73/4.41 thf(f180,axiom,(
% 31.73/4.41 (cartprodpairmemEL = ! [X1,X4,X2,X3] : ((in @ (kpair @ X1 @ X2) @ (cartprod @ X3 @ X4)) => (in @ X1 @ X3)))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemEL)).
% 31.73/4.41 thf(f657,plain,(
% 31.73/4.41 (cartprodsndin = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (in @ (ksnd @ Y1) @ Y0)))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f225])).
% 31.73/4.41 thf(f225,plain,(
% 31.73/4.41 (cartprodsndin = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (in @ (ksnd @ Y1) @ Y0)))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f224])).
% 31.73/4.41 thf(f224,plain,(
% 31.73/4.41 (cartprodsndin = ! [X0,X1,X2] : ((in @ X1 @ (cartprod @ X0 @ X2)) => (in @ (ksnd @ X1) @ X2)))),
% 31.73/4.41 inference(rectify,[],[f179])).
% 31.73/4.41 thf(f179,axiom,(
% 31.73/4.41 (cartprodsndin = ! [X3,X10,X4] : ((in @ X10 @ (cartprod @ X3 @ X4)) => (in @ (ksnd @ X10) @ X4)))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndin)).
% 31.73/4.41 thf(f647,plain,(
% 31.73/4.41 (kpairsurjEq = (!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => ((kpair @ (kfst @ Y0) @ (ksnd @ Y0)) = Y0)))))),
% 31.73/4.41 inference(cnf_transformation,[],[f490])).
% 31.73/4.41 thf(f490,plain,(
% 31.73/4.41 (kpairsurjEq = (!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => ((kpair @ (kfst @ Y0) @ (ksnd @ Y0)) = Y0)))))),
% 31.73/4.41 inference(fool_elimination,[],[f489])).
% 31.73/4.41 thf(f489,plain,(
% 31.73/4.41 (! [X0] : ((iskpair @ X0) => ((kpair @ (kfst @ X0) @ (ksnd @ X0)) = X0)) = kpairsurjEq)),
% 31.73/4.41 inference(rectify,[],[f178])).
% 31.73/4.41 thf(f178,axiom,(
% 31.73/4.41 (! [X10] : ((iskpair @ X10) => ((kpair @ (kfst @ X10) @ (ksnd @ X10)) = X10)) = kpairsurjEq)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairsurjEq)).
% 31.73/4.41 thf(f662,plain,(
% 31.73/4.41 (ksndpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y1 @ Y0)) = Y0))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f320])).
% 31.73/4.41 thf(f320,plain,(
% 31.73/4.41 (ksndpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y1 @ Y0)) = Y0))))))),
% 31.73/4.41 inference(fool_elimination,[],[f319])).
% 31.73/4.41 thf(f319,plain,(
% 31.73/4.41 (! [X0,X1] : ((ksnd @ (kpair @ X0 @ X1)) = X1) = ksndpairEq)),
% 31.73/4.41 inference(rectify,[],[f177])).
% 31.73/4.41 thf(f177,axiom,(
% 31.73/4.41 (! [X1,X2] : ((ksnd @ (kpair @ X1 @ X2)) = X2) = ksndpairEq)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndpairEq)).
% 31.73/4.41 thf(f818,plain,(
% 31.73/4.41 (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))))))))),
% 31.73/4.41 inference(definition_unfolding,[],[f756,f755])).
% 31.73/4.41 thf(f756,plain,(
% 31.73/4.41 (ksndsingleton = (!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (singleton @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: ((kpair @ (kfst @ Y0) @ Y1) = Y0))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f279])).
% 31.73/4.41 thf(f279,plain,(
% 31.73/4.41 (ksndsingleton = (!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (singleton @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: ((kpair @ (kfst @ Y0) @ Y1) = Y0))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f278])).
% 31.73/4.41 thf(f278,plain,(
% 31.73/4.41 (ksndsingleton = ! [X0] : ((iskpair @ X0) => (singleton @ (dsetconstr @ (setunion @ X0) @ (^[X1 : $i] : (((kpair @ (kfst @ X0) @ X1) = X0)))))))),
% 31.73/4.41 inference(rectify,[],[f176])).
% 31.73/4.41 thf(f176,axiom,(
% 31.73/4.41 (ksndsingleton = ! [X10] : ((iskpair @ X10) => (singleton @ (dsetconstr @ (setunion @ X10) @ (^[X1 : $i] : (((kpair @ (kfst @ X10) @ X1) = X10)))))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndsingleton)).
% 31.73/4.41 thf(f643,plain,(
% 31.73/4.41 (setukpairinjR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y3 @ Y0)) => (Y1 = Y0)))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f328])).
% 31.73/4.41 thf(f328,plain,(
% 31.73/4.41 (setukpairinjR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y3 @ Y0)) => (Y1 = Y0)))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f327])).
% 31.73/4.41 thf(f327,plain,(
% 31.73/4.41 (! [X0,X1,X2,X3] : (((kpair @ X1 @ X2) = (kpair @ X0 @ X3)) => (X2 = X3)) = setukpairinjR)),
% 31.73/4.41 inference(rectify,[],[f175])).
% 31.73/4.41 thf(f175,axiom,(
% 31.73/4.41 (! [X1,X8,X10,X2] : (((kpair @ X1 @ X2) = (kpair @ X8 @ X10)) => (X2 = X10)) = setukpairinjR)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR)).
% 31.73/4.41 thf(f717,plain,(
% 31.73/4.41 (setukpairinjR2 = (!! @ $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 @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f360])).
% 31.73/4.41 thf(f360,plain,(
% 31.73/4.41 (setukpairinjR2 = (!! @ $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 @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f359])).
% 31.73/4.41 thf(f359,plain,(
% 31.73/4.41 (setukpairinjR2 = ! [X0,X1,X2,X3] : (((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) => (X1 = X3)))),
% 31.73/4.41 inference(rectify,[],[f174])).
% 31.73/4.41 thf(f174,axiom,(
% 31.73/4.41 (setukpairinjR2 = ! [X8,X10,X1,X2] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X8 @ emptyset) @ (setadjoin @ (setadjoin @ X8 @ (setadjoin @ X10 @ emptyset)) @ emptyset))) => (X2 = X10)))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR2)).
% 31.73/4.41 thf(f709,plain,(
% 31.73/4.41 (upairequniteq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))) => (Y1 = Y0)))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f530])).
% 31.73/4.41 thf(f530,plain,(
% 31.73/4.41 (upairequniteq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y2 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))) => (Y1 = Y0)))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f529])).
% 31.73/4.41 thf(f529,plain,(
% 31.73/4.41 (! [X0,X1,X2] : (((setadjoin @ X0 @ emptyset) = (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset))) => (X1 = X2)) = upairequniteq)),
% 31.73/4.41 inference(rectify,[],[f173])).
% 31.73/4.41 thf(f173,axiom,(
% 31.73/4.41 (! [X8,X2,X1] : (((setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) = (setadjoin @ X8 @ emptyset)) => (X1 = X2)) = upairequniteq)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairequniteq)).
% 31.73/4.41 thf(f652,plain,(
% 31.73/4.41 (setukpairinjR1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y2 = Y1))))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f368])).
% 31.73/4.41 thf(f368,plain,(
% 31.73/4.41 (setukpairinjR1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y2 = Y1))))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f367])).
% 31.73/4.41 thf(f367,plain,(
% 31.73/4.41 (! [X0,X1,X2,X3] : (((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset)) @ emptyset))) => ((X0 = X1) => (X1 = X2))) = setukpairinjR1)),
% 31.73/4.41 inference(rectify,[],[f172])).
% 31.73/4.41 thf(f172,axiom,(
% 31.73/4.41 (! [X8,X10,X2,X1] : (((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))) = setukpairinjR1)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR1)).
% 31.73/4.41 thf(f702,plain,(
% 31.73/4.41 (setukpairinjR12 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f432])).
% 31.73/4.41 thf(f432,plain,(
% 31.73/4.41 (setukpairinjR12 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f431])).
% 31.73/4.41 thf(f431,plain,(
% 31.73/4.41 (setukpairinjR12 = ! [X0,X1] : ((X0 = X1) => ((setadjoin @ (setadjoin @ X1 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset)))))),
% 31.73/4.41 inference(rectify,[],[f171])).
% 31.73/4.41 thf(f171,axiom,(
% 31.73/4.41 (setukpairinjR12 = ! [X2,X1] : ((X1 = X2) => ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X1 @ emptyset) @ emptyset))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR12)).
% 31.73/4.41 thf(f744,plain,(
% 31.73/4.41 (setukpairinjR11 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) = (setadjoin @ Y1 @ emptyset))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f239])).
% 31.73/4.41 thf(f239,plain,(
% 31.73/4.41 (setukpairinjR11 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) = (setadjoin @ Y1 @ emptyset))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f238])).
% 31.73/4.41 thf(f238,plain,(
% 31.73/4.41 (! [X0,X1] : ((X0 = X1) => ((setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) = (setadjoin @ X0 @ emptyset))) = setukpairinjR11)),
% 31.73/4.41 inference(rectify,[],[f170])).
% 31.73/4.41 thf(f170,axiom,(
% 31.73/4.41 (! [X1,X2] : ((X1 = X2) => ((setadjoin @ X1 @ emptyset) = (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)))) = setukpairinjR11)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR11)).
% 31.73/4.41 thf(f731,plain,(
% 31.73/4.41 (setukpairinjL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y1 = Y0)))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f227])).
% 31.73/4.41 thf(f227,plain,(
% 31.73/4.41 (setukpairinjL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y1 @ Y3) = (kpair @ Y0 @ Y2)) => (Y1 = Y0)))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f226])).
% 31.73/4.41 thf(f226,plain,(
% 31.73/4.41 (! [X0,X1,X2,X3] : (((kpair @ X2 @ X0) = (kpair @ X3 @ X1)) => (X2 = X3)) = setukpairinjL)),
% 31.73/4.41 inference(rectify,[],[f169])).
% 31.73/4.41 thf(f169,axiom,(
% 31.73/4.41 (! [X10,X2,X8,X1] : (((kpair @ X1 @ X2) = (kpair @ X8 @ X10)) => (X1 = X8)) = setukpairinjL)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL)).
% 31.73/4.41 thf(f753,plain,(
% 31.73/4.41 (setukpairinjL2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f418])).
% 31.73/4.41 thf(f418,plain,(
% 31.73/4.41 (setukpairinjL2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f417])).
% 31.73/4.41 thf(f417,plain,(
% 31.73/4.41 (setukpairinjL2 = ! [X0,X1,X2,X3] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X0 @ emptyset)) @ emptyset))) => (X1 = X3)))),
% 31.73/4.41 inference(rectify,[],[f168])).
% 31.73/4.41 thf(f168,axiom,(
% 31.73/4.41 (setukpairinjL2 = ! [X2,X8,X10,X1] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X8 @ emptyset) @ (setadjoin @ (setadjoin @ X8 @ (setadjoin @ X10 @ emptyset)) @ emptyset))) => (X1 = X8)))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL2)).
% 31.73/4.41 thf(f613,plain,(
% 31.73/4.41 (cartprodfstin = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y2 @ Y1)) => (in @ (kfst @ Y0) @ Y2)))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f334])).
% 31.73/4.41 thf(f334,plain,(
% 31.73/4.41 (cartprodfstin = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y2 @ Y1)) => (in @ (kfst @ Y0) @ Y2)))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f333])).
% 31.73/4.41 thf(f333,plain,(
% 31.73/4.41 (! [X0,X1,X2] : ((in @ X2 @ (cartprod @ X0 @ X1)) => (in @ (kfst @ X2) @ X0)) = cartprodfstin)),
% 31.73/4.41 inference(rectify,[],[f167])).
% 31.73/4.41 thf(f167,axiom,(
% 31.73/4.41 (! [X3,X4,X10] : ((in @ X10 @ (cartprod @ X3 @ X4)) => (in @ (kfst @ X10) @ X3)) = cartprodfstin)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstin)).
% 31.73/4.41 thf(f747,plain,(
% 31.73/4.41 (kfstpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y0 @ Y1)) = Y0))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f273])).
% 31.73/4.41 thf(f273,plain,(
% 31.73/4.41 (kfstpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y0 @ Y1)) = Y0))))))),
% 31.73/4.41 inference(fool_elimination,[],[f272])).
% 31.73/4.41 thf(f272,plain,(
% 31.73/4.41 (! [X0,X1] : ((kfst @ (kpair @ X1 @ X0)) = X1) = kfstpairEq)),
% 31.73/4.41 inference(rectify,[],[f166])).
% 31.73/4.41 thf(f166,axiom,(
% 31.73/4.41 (! [X2,X1] : ((kfst @ (kpair @ X1 @ X2)) = X1) = kfstpairEq)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstpairEq)).
% 31.73/4.41 thf(f817,plain,(
% 31.73/4.41 (theprop = (!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & ((setadjoin @ Y2 @ emptyset) = Y1))))) @ Y0) => (in @ (setunion @ Y0) @ Y0)))))),
% 31.73/4.41 inference(definition_unfolding,[],[f721,f755])).
% 31.73/4.41 thf(f721,plain,(
% 31.73/4.41 (theprop = (!! @ $i @ (^[Y0 : $i]: ((singleton @ Y0) => (in @ (setunion @ Y0) @ Y0)))))),
% 31.73/4.41 inference(cnf_transformation,[],[f291])).
% 31.73/4.41 thf(f291,plain,(
% 31.73/4.41 (theprop = (!! @ $i @ (^[Y0 : $i]: ((singleton @ Y0) => (in @ (setunion @ Y0) @ Y0)))))),
% 31.73/4.41 inference(fool_elimination,[],[f290])).
% 31.73/4.41 thf(f290,plain,(
% 31.73/4.41 (! [X0] : ((singleton @ X0) => (in @ (setunion @ X0) @ X0)) = theprop)),
% 31.73/4.41 inference(rectify,[],[f165])).
% 31.73/4.41 thf(f165,axiom,(
% 31.73/4.41 (! [X11] : ((singleton @ X11) => (in @ (setunion @ X11) @ X11)) = theprop)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',theprop)).
% 31.73/4.41 thf(f816,plain,(
% 31.73/4.41 (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))))))))),
% 31.73/4.41 inference(definition_unfolding,[],[f782,f755])).
% 31.73/4.41 thf(f782,plain,(
% 31.73/4.41 (kfstsingleton = (!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (singleton @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: (in @ (setadjoin @ Y1 @ emptyset) @ Y0))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f316])).
% 31.73/4.41 thf(f316,plain,(
% 31.73/4.41 (kfstsingleton = (!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (singleton @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: (in @ (setadjoin @ Y1 @ emptyset) @ Y0))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f315])).
% 31.73/4.41 thf(f315,plain,(
% 31.73/4.41 (! [X0] : ((iskpair @ X0) => (singleton @ (dsetconstr @ (setunion @ X0) @ (^[X1 : $i] : (in @ (setadjoin @ X1 @ emptyset) @ X0))))) = kfstsingleton)),
% 31.73/4.41 inference(rectify,[],[f164])).
% 31.73/4.41 thf(f164,axiom,(
% 31.73/4.41 (! [X10] : ((iskpair @ X10) => (singleton @ (dsetconstr @ (setunion @ X10) @ (^[X1 : $i] : (in @ (setadjoin @ X1 @ emptyset) @ X10))))) = kfstsingleton)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstsingleton)).
% 31.73/4.41 thf(f682,plain,(
% 31.73/4.41 (setukpairinjL1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = Y0)))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f376])).
% 31.73/4.41 thf(f376,plain,(
% 31.73/4.41 (setukpairinjL1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = Y0)))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f375])).
% 31.73/4.41 thf(f375,plain,(
% 31.73/4.41 (setukpairinjL1 = ! [X0,X1,X2] : ((in @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset)) @ emptyset))) => (X1 = X2)))),
% 31.73/4.41 inference(rectify,[],[f163])).
% 31.73/4.41 thf(f163,axiom,(
% 31.73/4.41 (setukpairinjL1 = ! [X2,X8,X1] : ((in @ (setadjoin @ X8 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset))) => (X1 = X8)))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL1)).
% 31.73/4.41 thf(f622,plain,(
% 31.73/4.41 (singletonsuniq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f520])).
% 31.73/4.41 thf(f520,plain,(
% 31.73/4.41 (singletonsuniq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))))),
% 31.73/4.41 inference(fool_elimination,[],[f519])).
% 31.73/4.41 thf(f519,plain,(
% 31.73/4.41 (! [X0,X1] : (((setadjoin @ X1 @ emptyset) = (setadjoin @ X0 @ emptyset)) => (X0 = X1)) = singletonsuniq)),
% 31.73/4.41 inference(rectify,[],[f162])).
% 31.73/4.41 thf(f162,axiom,(
% 31.73/4.41 (! [X2,X1] : (((setadjoin @ X2 @ emptyset) = (setadjoin @ X1 @ emptyset)) => (X1 = X2)) = singletonsuniq)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsuniq)).
% 31.73/4.41 thf(f815,plain,(
% 31.73/4.41 (ex1I2 = (!! @ $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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((^[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))))))))))),
% 31.73/4.41 inference(definition_unfolding,[],[f597,f812])).
% 31.73/4.41 thf(f597,plain,(
% 31.73/4.41 (ex1I2 = (!! @ $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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (ex1 @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f582])).
% 31.73/4.41 thf(f582,plain,(
% 31.73/4.41 (ex1I2 = (!! @ $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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (ex1 @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f581])).
% 31.73/4.41 thf(f581,plain,(
% 31.73/4.41 (! [X0 : $i > $o,X1] : (! [X2] : ((in @ X2 @ X1) => ! [X3] : ((in @ X3 @ X1) => ((X0 @ X2) => ((X0 @ X3) => (X2 = X3))))) => (? [X4] : ((in @ X4 @ X1) & (X0 @ X4)) => (ex1 @ X1 @ (^[X5 : $i] : (X0 @ X5))))) = ex1I2)),
% 31.73/4.41 inference(rectify,[],[f161])).
% 31.73/4.41 thf(f161,axiom,(
% 31.73/4.41 (! [X0 : $i > $o,X3] : (! [X1] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X3) => ((X0 @ X1) => ((X0 @ X2) => (X1 = X2))))) => (? [X1] : ((in @ X1 @ X3) & (X0 @ X1)) => (ex1 @ X3 @ (^[X1 : $i] : (X0 @ X1))))) = ex1I2)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I2)).
% 31.73/4.41 thf(f814,plain,(
% 31.73/4.41 (ex1I = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y1 @ Y3) => (Y0 = Y3))))) => ((^[Y3 : $i]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) & ((setadjoin @ Y6 @ emptyset) = Y5))))) @ (dsetconstr @ Y3 @ (^[Y5 : $i]: (Y4 @ Y5))))))) @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3)))))))))))))),
% 31.73/4.41 inference(definition_unfolding,[],[f637,f812])).
% 31.73/4.41 thf(f637,plain,(
% 31.73/4.41 (ex1I = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y1 @ Y3) => (Y0 = Y3))))) => (ex1 @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3)))))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f440])).
% 31.73/4.41 thf(f440,plain,(
% 31.73/4.41 (ex1I = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((Y1 @ Y3) => (Y0 = Y3))))) => (ex1 @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3)))))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f439])).
% 31.73/4.41 thf(f439,plain,(
% 31.73/4.41 (ex1I = ! [X0,X1 : $i > $o,X2] : ((in @ X2 @ X0) => ((X1 @ X2) => (! [X3] : ((in @ X3 @ X0) => ((X1 @ X3) => (X2 = X3))) => (ex1 @ X0 @ (^[X4 : $i] : (X1 @ X4)))))))),
% 31.73/4.41 inference(rectify,[],[f160])).
% 31.73/4.41 thf(f160,axiom,(
% 31.73/4.41 (ex1I = ! [X3,X0 : $i > $o,X1] : ((in @ X1 @ X3) => ((X0 @ X1) => (! [X2] : ((in @ X2 @ X3) => ((X0 @ X2) => (X1 = X2))) => (ex1 @ X3 @ (^[X2 : $i] : (X0 @ X2)))))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I)).
% 31.73/4.41 thf(f813,plain,(
% 31.73/4.41 (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]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))))))))),
% 31.73/4.41 inference(definition_unfolding,[],[f760,f812])).
% 31.73/4.41 thf(f760,plain,(
% 31.73/4.41 (ex1E1 = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((ex1 @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f330])).
% 31.73/4.41 thf(f330,plain,(
% 31.73/4.41 (ex1E1 = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((ex1 @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f329])).
% 31.73/4.41 thf(f329,plain,(
% 31.73/4.41 (! [X0 : $i > $o,X1] : ((ex1 @ X1 @ (^[X2 : $i] : (X0 @ X2))) => ? [X3] : ((X0 @ X3) & (in @ X3 @ X1))) = ex1E1)),
% 31.73/4.41 inference(rectify,[],[f159])).
% 31.73/4.41 thf(f159,axiom,(
% 31.73/4.41 (! [X0 : $i > $o,X3] : ((ex1 @ X3 @ (^[X1 : $i] : (X0 @ X1))) => ? [X1] : ((X0 @ X1) & (in @ X1 @ X3))) = ex1E1)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E1)).
% 31.73/4.41 thf(f811,plain,(
% 31.73/4.41 (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)))))))))))),
% 31.73/4.41 inference(definition_unfolding,[],[f781,f755])).
% 31.73/4.41 thf(f781,plain,(
% 31.73/4.41 (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)))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f550])).
% 31.73/4.41 thf(f550,plain,(
% 31.73/4.41 (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)))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f549])).
% 31.73/4.41 thf(f549,plain,(
% 31.73/4.41 (singletonprop = ! [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)))))))),
% 31.73/4.41 inference(rectify,[],[f157])).
% 31.73/4.41 thf(f157,axiom,(
% 31.73/4.41 (singletonprop = ! [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)))))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonprop)).
% 31.73/4.41 thf(f780,plain,(
% 31.73/4.41 (setunionsingleton = (!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))))),
% 31.73/4.41 inference(cnf_transformation,[],[f247])).
% 31.73/4.41 thf(f247,plain,(
% 31.73/4.41 (setunionsingleton = (!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))))),
% 31.73/4.41 inference(fool_elimination,[],[f246])).
% 31.73/4.41 thf(f246,plain,(
% 31.73/4.41 (! [X0] : ((setunion @ (setadjoin @ X0 @ emptyset)) = X0) = setunionsingleton)),
% 31.73/4.41 inference(rectify,[],[f155])).
% 31.73/4.41 thf(f155,axiom,(
% 31.73/4.41 (! [X1] : ((setunion @ (setadjoin @ X1 @ emptyset)) = X1) = setunionsingleton)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton)).
% 31.73/4.41 thf(f778,plain,(
% 31.73/4.41 (setunionsingleton2 = (!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f326])).
% 31.73/4.41 thf(f326,plain,(
% 31.73/4.41 (setunionsingleton2 = (!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))))),
% 31.73/4.41 inference(fool_elimination,[],[f325])).
% 31.73/4.41 thf(f325,plain,(
% 31.73/4.41 (setunionsingleton2 = ! [X0] : (subset @ X0 @ (setunion @ (setadjoin @ X0 @ emptyset))))),
% 31.73/4.41 inference(rectify,[],[f154])).
% 31.73/4.41 thf(f154,axiom,(
% 31.73/4.41 (setunionsingleton2 = ! [X3] : (subset @ X3 @ (setunion @ (setadjoin @ X3 @ emptyset))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton2)).
% 31.73/4.41 thf(f736,plain,(
% 31.73/4.41 (setunionsingleton1 = (!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))))),
% 31.73/4.41 inference(cnf_transformation,[],[f249])).
% 31.73/4.41 thf(f249,plain,(
% 31.73/4.41 (setunionsingleton1 = (!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))))),
% 31.73/4.41 inference(fool_elimination,[],[f248])).
% 31.73/4.41 thf(f248,plain,(
% 31.73/4.41 (setunionsingleton1 = ! [X0] : (subset @ (setunion @ (setadjoin @ X0 @ emptyset)) @ X0))),
% 31.73/4.41 inference(rectify,[],[f153])).
% 31.73/4.41 thf(f153,axiom,(
% 31.73/4.41 (setunionsingleton1 = ! [X3] : (subset @ (setunion @ (setadjoin @ X3 @ emptyset)) @ X3))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton1)).
% 31.73/4.41 thf(f679,plain,(
% 31.73/4.41 (setunionE2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f332])).
% 31.73/4.41 thf(f332,plain,(
% 31.73/4.41 (setunionE2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f331])).
% 31.73/4.41 thf(f331,plain,(
% 31.73/4.41 (! [X0,X1] : ((in @ X0 @ (setunion @ X1)) => ? [X2] : ((in @ X0 @ X2) & (in @ X2 @ X1))) = setunionE2)),
% 31.73/4.41 inference(rectify,[],[f152])).
% 31.73/4.41 thf(f152,axiom,(
% 31.73/4.41 (! [X1,X3] : ((in @ X1 @ (setunion @ X3)) => ? [X11] : ((in @ X1 @ X11) & (in @ X11 @ X3))) = setunionE2)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE2)).
% 31.73/4.41 thf(f706,plain,(
% 31.73/4.41 (cartprodmempair = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (iskpair @ Y1)))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f532])).
% 31.73/4.41 thf(f532,plain,(
% 31.73/4.41 (cartprodmempair = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (iskpair @ Y1)))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f531])).
% 31.73/4.41 thf(f531,plain,(
% 31.73/4.41 (! [X0,X1,X2] : ((in @ X1 @ (cartprod @ X2 @ X0)) => (iskpair @ X1)) = cartprodmempair)),
% 31.73/4.41 inference(rectify,[],[f151])).
% 31.73/4.41 thf(f151,axiom,(
% 31.73/4.41 (! [X4,X10,X3] : ((in @ X10 @ (cartprod @ X3 @ X4)) => (iskpair @ X10)) = cartprodmempair)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair)).
% 31.73/4.41 thf(f752,plain,(
% 31.73/4.41 (cartprodmempair1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y0) & (in @ Y4 @ Y2)))))))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f526])).
% 31.73/4.41 thf(f526,plain,(
% 31.73/4.41 (cartprodmempair1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y0) & (in @ Y4 @ Y2)))))))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f525])).
% 31.73/4.41 thf(f525,plain,(
% 31.73/4.41 (cartprodmempair1 = ! [X0,X1,X2] : ((in @ X2 @ (cartprod @ X1 @ X0)) => ? [X3] : (? [X4] : ((in @ X4 @ X0) & ((kpair @ X3 @ X4) = X2)) & (in @ X3 @ X1))))),
% 31.73/4.41 inference(rectify,[],[f150])).
% 31.73/4.41 thf(f150,axiom,(
% 31.73/4.41 (cartprodmempair1 = ! [X4,X3,X10] : ((in @ X10 @ (cartprod @ X3 @ X4)) => ? [X1] : (? [X2] : ((in @ X2 @ X4) & ((kpair @ X1 @ X2) = X10)) & (in @ X1 @ X3))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair1)).
% 31.73/4.41 thf(f794,plain,(
% 31.73/4.41 (cartprodpairin = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y2 @ Y1)))))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f346])).
% 31.73/4.41 thf(f346,plain,(
% 31.73/4.41 (cartprodpairin = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y2 @ Y1)))))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f345])).
% 31.73/4.41 thf(f345,plain,(
% 31.73/4.41 (! [X0,X1,X2] : ((in @ X2 @ X0) => ! [X3] : ((in @ X3 @ X1) => (in @ (kpair @ X2 @ X3) @ (cartprod @ X0 @ X1)))) = cartprodpairin)),
% 31.73/4.41 inference(rectify,[],[f149])).
% 31.73/4.41 thf(f149,axiom,(
% 31.73/4.41 (! [X3,X4,X1] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => (in @ (kpair @ X1 @ X2) @ (cartprod @ X3 @ X4)))) = cartprodpairin)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairin)).
% 31.73/4.41 thf(f705,plain,(
% 31.73/4.41 (ubforcartprodlem3 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f231])).
% 31.73/4.41 thf(f231,plain,(
% 31.73/4.41 (ubforcartprodlem3 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y1)))))))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f230])).
% 31.73/4.41 thf(f230,plain,(
% 31.73/4.41 (! [X0,X1,X2] : ((in @ X2 @ X0) => ! [X3] : ((in @ X3 @ X1) => (in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X0 @ X1)))))) = ubforcartprodlem3)),
% 31.73/4.41 inference(rectify,[],[f148])).
% 31.73/4.41 thf(f148,axiom,(
% 31.73/4.41 (! [X3,X4,X1] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => (in @ (kpair @ X1 @ X2) @ (powerset @ (powerset @ (binunion @ X3 @ X4)))))) = ubforcartprodlem3)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem3)).
% 31.73/4.41 thf(f710,plain,(
% 31.73/4.41 (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)))))))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f548])).
% 31.73/4.41 thf(f548,plain,(
% 31.73/4.41 (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)))))))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f547])).
% 31.73/4.41 thf(f547,plain,(
% 31.73/4.41 (ubforcartprodlem2 = ! [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)))))))),
% 31.73/4.41 inference(rectify,[],[f147])).
% 31.73/4.41 thf(f147,axiom,(
% 31.73/4.41 (ubforcartprodlem2 = ! [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)))))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem2)).
% 31.73/4.41 thf(f733,plain,(
% 31.73/4.41 (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))))))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f462])).
% 31.73/4.41 thf(f462,plain,(
% 31.73/4.41 (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))))))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f461])).
% 31.73/4.41 thf(f461,plain,(
% 31.73/4.41 (ubforcartprodlem1 = ! [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))))))),
% 31.73/4.41 inference(rectify,[],[f146])).
% 31.73/4.41 thf(f146,axiom,(
% 31.73/4.41 (ubforcartprodlem1 = ! [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))))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem1)).
% 31.73/4.41 thf(f790,plain,(
% 31.73/4.41 (upairinpowunion = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y0))))))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f538])).
% 31.73/4.41 thf(f538,plain,(
% 31.73/4.41 (upairinpowunion = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y0))))))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f537])).
% 31.73/4.41 thf(f537,plain,(
% 31.73/4.41 (upairinpowunion = ! [X0,X1,X2] : ((in @ X0 @ X1) => ! [X3] : ((in @ X3 @ X2) => (in @ (setadjoin @ X0 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X1 @ X2))))))),
% 31.73/4.41 inference(rectify,[],[f145])).
% 31.73/4.41 thf(f145,axiom,(
% 31.73/4.41 (upairinpowunion = ! [X1,X3,X4] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => (in @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ (powerset @ (binunion @ X3 @ X4))))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairinpowunion)).
% 31.73/4.41 thf(f699,plain,(
% 31.73/4.41 (upairsubunion = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y2)))))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f392])).
% 31.73/4.41 thf(f392,plain,(
% 31.73/4.41 (upairsubunion = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y0 @ Y2)))))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f391])).
% 31.73/4.41 thf(f391,plain,(
% 31.73/4.41 (upairsubunion = ! [X0,X1,X2] : ((in @ X1 @ X2) => ! [X3] : ((in @ X3 @ X0) => (subset @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X2 @ X0)))))),
% 31.73/4.41 inference(rectify,[],[f144])).
% 31.73/4.41 thf(f144,axiom,(
% 31.73/4.41 (upairsubunion = ! [X4,X1,X3] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => (subset @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ (binunion @ X3 @ X4)))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsubunion)).
% 31.73/4.41 thf(f772,plain,(
% 31.73/4.41 (upairset2E = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y0) | (Y2 = Y1))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f404])).
% 31.73/4.41 thf(f404,plain,(
% 31.73/4.41 (upairset2E = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))) => ((Y2 = Y0) | (Y2 = Y1))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f403])).
% 31.73/4.41 thf(f403,plain,(
% 31.73/4.41 (upairset2E = ! [X0,X1,X2] : ((in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset))) => ((X0 = X1) | (X0 = X2))))),
% 31.73/4.41 inference(rectify,[],[f143])).
% 31.73/4.41 thf(f143,axiom,(
% 31.73/4.41 (upairset2E = ! [X8,X1,X2] : ((in @ X8 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset))) => ((X1 = X8) | (X2 = X8))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2E)).
% 31.73/4.41 thf(f609,plain,(
% 31.73/4.41 (singletoninpowunion = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f572])).
% 31.73/4.41 thf(f572,plain,(
% 31.73/4.41 (singletoninpowunion = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y0 @ Y2)))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f571])).
% 31.73/4.41 thf(f571,plain,(
% 31.73/4.41 (! [X0,X1,X2] : ((in @ X1 @ X2) => (in @ (setadjoin @ X1 @ emptyset) @ (powerset @ (binunion @ X2 @ X0)))) = singletoninpowunion)),
% 31.73/4.41 inference(rectify,[],[f142])).
% 31.73/4.41 thf(f142,axiom,(
% 31.73/4.41 (! [X4,X1,X3] : ((in @ X1 @ X3) => (in @ (setadjoin @ X1 @ emptyset) @ (powerset @ (binunion @ X3 @ X4)))) = singletoninpowunion)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowunion)).
% 31.73/4.41 thf(f651,plain,(
% 31.73/4.41 (singletoninpowerset = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ Y0))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f289])).
% 31.73/4.41 thf(f289,plain,(
% 31.73/4.41 (singletoninpowerset = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ Y0))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f288])).
% 31.73/4.41 thf(f288,plain,(
% 31.73/4.41 (singletoninpowerset = ! [X0,X1] : ((in @ X0 @ X1) => (in @ (setadjoin @ X0 @ emptyset) @ (powerset @ X1))))),
% 31.73/4.41 inference(rectify,[],[f141])).
% 31.73/4.41 thf(f141,axiom,(
% 31.73/4.41 (singletoninpowerset = ! [X1,X3] : ((in @ X1 @ X3) => (in @ (setadjoin @ X1 @ emptyset) @ (powerset @ X3))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowerset)).
% 31.73/4.41 thf(f650,plain,(
% 31.73/4.41 (singletonsubset = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f504])).
% 31.73/4.41 thf(f504,plain,(
% 31.73/4.41 (singletonsubset = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (subset @ (setadjoin @ Y0 @ emptyset) @ Y1)))))))),
% 31.73/4.41 inference(fool_elimination,[],[f503])).
% 31.73/4.41 thf(f503,plain,(
% 31.73/4.41 (singletonsubset = ! [X0,X1] : ((in @ X1 @ X0) => (subset @ (setadjoin @ X1 @ emptyset) @ X0)))),
% 31.73/4.41 inference(rectify,[],[f140])).
% 31.73/4.41 thf(f140,axiom,(
% 31.73/4.41 (singletonsubset = ! [X3,X1] : ((in @ X1 @ X3) => (subset @ (setadjoin @ X1 @ emptyset) @ X3)))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsubset)).
% 31.73/4.41 thf(f663,plain,(
% 31.73/4.41 (kpairp = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y0 @ Y1)))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f586])).
% 31.73/4.41 thf(f586,plain,(
% 31.73/4.41 (kpairp = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y0 @ Y1)))))))),
% 31.73/4.41 inference(fool_elimination,[],[f585])).
% 31.73/4.41 thf(f585,plain,(
% 31.73/4.41 (kpairp = ! [X0,X1] : (iskpair @ (kpair @ X1 @ X0)))),
% 31.73/4.41 inference(rectify,[],[f139])).
% 31.73/4.41 thf(f139,axiom,(
% 31.73/4.41 (kpairp = ! [X2,X1] : (iskpair @ (kpair @ X1 @ X2)))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairp)).
% 31.73/4.41 thf(f655,plain,(
% 31.73/4.41 (kpairiskpair = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f241])).
% 31.73/4.41 thf(f241,plain,(
% 31.73/4.41 (kpairiskpair = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f240])).
% 31.73/4.41 thf(f240,plain,(
% 31.73/4.41 (! [X0,X1] : (iskpair @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) = kpairiskpair)),
% 31.73/4.41 inference(rectify,[],[f138])).
% 31.73/4.41 thf(f138,axiom,(
% 31.73/4.41 (! [X1,X2] : (iskpair @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset))) = kpairiskpair)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairiskpair)).
% 31.73/4.41 thf(f788,plain,(
% 31.73/4.41 (setukpairIR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f466])).
% 31.73/4.41 thf(f466,plain,(
% 31.73/4.41 (setukpairIR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f465])).
% 31.73/4.41 thf(f465,plain,(
% 31.73/4.41 (! [X0,X1] : (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))) = setukpairIR)),
% 31.73/4.41 inference(rectify,[],[f137])).
% 31.73/4.41 thf(f137,axiom,(
% 31.73/4.41 (! [X1,X2] : (in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)))) = setukpairIR)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIR)).
% 31.73/4.41 thf(f762,plain,(
% 31.73/4.41 (setukpairIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f245])).
% 31.73/4.41 thf(f245,plain,(
% 31.73/4.41 (setukpairIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f244])).
% 31.73/4.41 thf(f244,plain,(
% 31.73/4.41 (! [X0,X1] : (in @ X0 @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))) = setukpairIL)),
% 31.73/4.41 inference(rectify,[],[f136])).
% 31.73/4.41 thf(f136,axiom,(
% 31.73/4.41 (! [X1,X2] : (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)))) = setukpairIL)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIL)).
% 31.73/4.41 thf(f604,plain,(
% 31.73/4.41 (secondinupair = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f542])).
% 31.73/4.41 thf(f542,plain,(
% 31.73/4.41 (secondinupair = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f541])).
% 31.73/4.41 thf(f541,plain,(
% 31.73/4.41 (! [X0,X1] : (in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = secondinupair)),
% 31.73/4.41 inference(rectify,[],[f135])).
% 31.73/4.41 thf(f135,axiom,(
% 31.73/4.41 (! [X1,X2] : (in @ X2 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset))) = secondinupair)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',secondinupair)).
% 31.73/4.41 thf(f754,plain,(
% 31.73/4.41 (symdiffIneg2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f219])).
% 31.73/4.41 thf(f219,plain,(
% 31.73/4.41 (symdiffIneg2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f218])).
% 31.73/4.41 thf(f218,plain,(
% 31.73/4.41 (! [X0,X1,X2] : (~(in @ X2 @ X1) => (~(in @ X2 @ X0) => ~(in @ X2 @ (symdiff @ X1 @ X0)))) = symdiffIneg2)),
% 31.73/4.41 inference(rectify,[],[f134])).
% 31.73/4.41 thf(f134,axiom,(
% 31.73/4.41 (! [X4,X3,X1] : (~(in @ X1 @ X3) => (~(in @ X1 @ X4) => ~(in @ X1 @ (symdiff @ X3 @ X4)))) = symdiffIneg2)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg2)).
% 31.73/4.41 thf(f715,plain,(
% 31.73/4.41 (symdiffIneg1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f394])).
% 31.73/4.41 thf(f394,plain,(
% 31.73/4.41 (symdiffIneg1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (~ (in @ Y0 @ (symdiff @ Y1 @ Y2))))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f393])).
% 31.73/4.41 thf(f393,plain,(
% 31.73/4.41 (! [X0,X1,X2] : ((in @ X2 @ X1) => ((in @ X2 @ X0) => ~(in @ X2 @ (symdiff @ X1 @ X0)))) = symdiffIneg1)),
% 31.73/4.41 inference(rectify,[],[f133])).
% 31.73/4.41 thf(f133,axiom,(
% 31.73/4.41 (! [X4,X3,X1] : ((in @ X1 @ X3) => ((in @ X1 @ X4) => ~(in @ X1 @ (symdiff @ X3 @ X4)))) = symdiffIneg1)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg1)).
% 31.73/4.41 thf(f658,plain,(
% 31.73/4.41 (symdiffI2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f233])).
% 31.73/4.41 thf(f233,plain,(
% 31.73/4.41 (symdiffI2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f232])).
% 31.73/4.41 thf(f232,plain,(
% 31.73/4.41 (symdiffI2 = ! [X0,X1,X2] : (~(in @ X0 @ X1) => ((in @ X0 @ X2) => (in @ X0 @ (symdiff @ X1 @ X2)))))),
% 31.73/4.41 inference(rectify,[],[f132])).
% 31.73/4.41 thf(f132,axiom,(
% 31.73/4.41 (symdiffI2 = ! [X1,X3,X4] : (~(in @ X1 @ X3) => ((in @ X1 @ X4) => (in @ X1 @ (symdiff @ X3 @ X4)))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI2)).
% 31.73/4.41 thf(f693,plain,(
% 31.73/4.41 (symdiffI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f388])).
% 31.73/4.41 thf(f388,plain,(
% 31.73/4.41 (symdiffI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f387])).
% 31.73/4.41 thf(f387,plain,(
% 31.73/4.41 (! [X0,X1,X2] : ((in @ X2 @ X0) => (~(in @ X2 @ X1) => (in @ X2 @ (symdiff @ X0 @ X1)))) = symdiffI1)),
% 31.73/4.41 inference(rectify,[],[f131])).
% 31.73/4.41 thf(f131,axiom,(
% 31.73/4.41 (! [X3,X4,X1] : ((in @ X1 @ X3) => (~(in @ X1 @ X4) => (in @ X1 @ (symdiff @ X3 @ X4)))) = symdiffI1)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI1)).
% 31.73/4.41 thf(f703,plain,(
% 31.73/4.41 (symdiffE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => Y3)) => Y3))))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f310])).
% 31.73/4.41 thf(f310,plain,(
% 31.73/4.41 (symdiffE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => Y3)) => Y3))))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f309])).
% 31.73/4.41 thf(f309,plain,(
% 31.73/4.41 (! [X0,X1,X2] : ((in @ X0 @ (symdiff @ X2 @ X1)) => ! [X3 : $o] : (((in @ X0 @ X2) => (~(in @ X0 @ X1) => X3)) => ((~(in @ X0 @ X2) => ((in @ X0 @ X1) => X3)) => X3))) = symdiffE)),
% 31.73/4.41 inference(rectify,[],[f130])).
% 31.73/4.41 thf(f130,axiom,(
% 31.73/4.41 (! [X1,X4,X3] : ((in @ X1 @ (symdiff @ X3 @ X4)) => ! [X0 : $o] : (((in @ X1 @ X3) => (~(in @ X1 @ X4) => X0)) => ((~(in @ X1 @ X3) => ((in @ X1 @ X4) => X0)) => X0))) = symdiffE)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffE)).
% 31.73/4.41 thf(f605,plain,(
% 31.73/4.41 (setminusSubset1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f536])).
% 31.73/4.41 thf(f536,plain,(
% 31.73/4.41 (setminusSubset1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))))),
% 31.73/4.41 inference(fool_elimination,[],[f535])).
% 31.73/4.41 thf(f535,plain,(
% 31.73/4.41 (setminusSubset1 = ! [X0,X1] : ((emptyset = (setminus @ X0 @ X1)) => (subset @ X0 @ X1)))),
% 31.73/4.41 inference(rectify,[],[f129])).
% 31.73/4.41 thf(f129,axiom,(
% 31.73/4.41 (setminusSubset1 = ! [X3,X4] : ((emptyset = (setminus @ X3 @ X4)) => (subset @ X3 @ X4)))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset1)).
% 31.73/4.41 thf(f694,plain,(
% 31.73/4.41 (setminusLsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f205])).
% 31.73/4.41 thf(f205,plain,(
% 31.73/4.41 (setminusLsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))))),
% 31.73/4.41 inference(fool_elimination,[],[f204])).
% 31.73/4.41 thf(f204,plain,(
% 31.73/4.41 (! [X0,X1] : (subset @ (setminus @ X0 @ X1) @ X0) = setminusLsub)),
% 31.73/4.41 inference(rectify,[],[f128])).
% 31.73/4.41 thf(f128,axiom,(
% 31.73/4.41 (! [X3,X4] : (subset @ (setminus @ X3 @ X4) @ X3) = setminusLsub)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusLsub)).
% 31.73/4.41 thf(f722,plain,(
% 31.73/4.41 (setminusIRneg = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f500])).
% 31.73/4.41 thf(f500,plain,(
% 31.73/4.41 (setminusIRneg = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f499])).
% 31.73/4.41 thf(f499,plain,(
% 31.73/4.41 (setminusIRneg = ! [X0,X1,X2] : ((in @ X2 @ X1) => ~(in @ X2 @ (setminus @ X0 @ X1))))),
% 31.73/4.41 inference(rectify,[],[f127])).
% 31.73/4.41 thf(f127,axiom,(
% 31.73/4.41 (setminusIRneg = ! [X3,X4,X1] : ((in @ X1 @ X4) => ~(in @ X1 @ (setminus @ X3 @ X4))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusIRneg)).
% 31.73/4.41 thf(f635,plain,(
% 31.73/4.41 (setminusILneg = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f275])).
% 31.73/4.41 thf(f275,plain,(
% 31.73/4.41 (setminusILneg = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f274])).
% 31.73/4.41 thf(f274,plain,(
% 31.73/4.41 (! [X0,X1,X2] : (~(in @ X2 @ X0) => ~(in @ X2 @ (setminus @ X0 @ X1))) = setminusILneg)),
% 31.73/4.41 inference(rectify,[],[f126])).
% 31.73/4.41 thf(f126,axiom,(
% 31.73/4.41 (! [X3,X4,X1] : (~(in @ X1 @ X3) => ~(in @ X1 @ (setminus @ X3 @ X4))) = setminusILneg)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusILneg)).
% 31.73/4.41 thf(f769,plain,(
% 31.73/4.41 (setminusELneg = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f396])).
% 31.73/4.41 thf(f396,plain,(
% 31.73/4.41 (setminusELneg = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y1 @ Y2))) => ((~ (in @ Y0 @ Y2)) => (~ (in @ Y0 @ Y1)))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f395])).
% 31.73/4.41 thf(f395,plain,(
% 31.73/4.41 (! [X0,X1,X2] : (~(in @ X2 @ (setminus @ X1 @ X0)) => (~(in @ X2 @ X0) => ~(in @ X2 @ X1))) = setminusELneg)),
% 31.73/4.41 inference(rectify,[],[f125])).
% 31.73/4.41 thf(f125,axiom,(
% 31.73/4.41 (! [X4,X3,X1] : (~(in @ X1 @ (setminus @ X3 @ X4)) => (~(in @ X1 @ X4) => ~(in @ X1 @ X3))) = setminusELneg)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusELneg)).
% 31.73/4.41 thf(f690,plain,(
% 31.73/4.41 (setminusERneg = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f318])).
% 31.73/4.41 thf(f318,plain,(
% 31.73/4.41 (setminusERneg = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f317])).
% 31.73/4.41 thf(f317,plain,(
% 31.73/4.41 (setminusERneg = ! [X0,X1,X2] : (~(in @ X0 @ (setminus @ X1 @ X2)) => ((in @ X0 @ X1) => (in @ X0 @ X2))))),
% 31.73/4.41 inference(rectify,[],[f124])).
% 31.73/4.41 thf(f124,axiom,(
% 31.73/4.41 (setminusERneg = ! [X1,X3,X4] : (~(in @ X1 @ (setminus @ X3 @ X4)) => ((in @ X1 @ X3) => (in @ X1 @ X4))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusERneg)).
% 31.73/4.41 thf(f730,plain,(
% 31.73/4.41 (setminusSubset2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f546])).
% 31.73/4.41 thf(f546,plain,(
% 31.73/4.41 (setminusSubset2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (emptyset = (setminus @ Y0 @ Y1))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f545])).
% 31.73/4.41 thf(f545,plain,(
% 31.73/4.41 (setminusSubset2 = ! [X0,X1] : ((subset @ X1 @ X0) => (emptyset = (setminus @ X1 @ X0))))),
% 31.73/4.41 inference(rectify,[],[f123])).
% 31.73/4.41 thf(f123,axiom,(
% 31.73/4.41 (setminusSubset2 = ! [X4,X3] : ((subset @ X3 @ X4) => (emptyset = (setminus @ X3 @ X4))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset2)).
% 31.73/4.41 thf(f757,plain,(
% 31.73/4.41 (setminusER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f420])).
% 31.73/4.41 thf(f420,plain,(
% 31.73/4.41 (setminusER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f419])).
% 31.73/4.41 thf(f419,plain,(
% 31.73/4.41 (! [X0,X1,X2] : ((in @ X2 @ (setminus @ X1 @ X0)) => ~(in @ X2 @ X0)) = setminusER)),
% 31.73/4.41 inference(rectify,[],[f122])).
% 31.73/4.41 thf(f122,axiom,(
% 31.73/4.41 (! [X4,X3,X1] : ((in @ X1 @ (setminus @ X3 @ X4)) => ~(in @ X1 @ X4)) = setminusER)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusER)).
% 31.73/4.41 thf(f610,plain,(
% 31.73/4.41 (setminusEL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f380])).
% 31.73/4.41 thf(f380,plain,(
% 31.73/4.41 (setminusEL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f379])).
% 31.73/4.41 thf(f379,plain,(
% 31.73/4.41 (! [X0,X1,X2] : ((in @ X2 @ (setminus @ X1 @ X0)) => (in @ X2 @ X1)) = setminusEL)),
% 31.73/4.41 inference(rectify,[],[f121])).
% 31.73/4.41 thf(f121,axiom,(
% 31.73/4.41 (! [X4,X3,X1] : ((in @ X1 @ (setminus @ X3 @ X4)) => (in @ X1 @ X3)) = setminusEL)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusEL)).
% 31.73/4.41 thf(f686,plain,(
% 31.73/4.41 (setminusI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f283])).
% 31.73/4.41 thf(f283,plain,(
% 31.73/4.41 (setminusI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((~ (in @ Y0 @ Y2)) => (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f282])).
% 31.73/4.41 thf(f282,plain,(
% 31.73/4.41 (! [X0,X1,X2] : ((in @ X2 @ X1) => (~(in @ X2 @ X0) => (in @ X2 @ (setminus @ X1 @ X0)))) = setminusI)),
% 31.73/4.41 inference(rectify,[],[f120])).
% 31.73/4.41 thf(f120,axiom,(
% 31.73/4.41 (! [X4,X3,X1] : ((in @ X1 @ X3) => (~(in @ X1 @ X4) => (in @ X1 @ (setminus @ X3 @ X4)))) = setminusI)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusI)).
% 31.73/4.41 thf(f627,plain,(
% 31.73/4.41 (bs114d = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y1 @ Y0)) = (binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f400])).
% 31.73/4.41 thf(f400,plain,(
% 31.73/4.41 (bs114d = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binintersect @ Y2 @ (binunion @ Y1 @ Y0)) = (binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f399])).
% 31.73/4.41 thf(f399,plain,(
% 31.73/4.41 (! [X0,X1,X2] : ((binintersect @ X0 @ (binunion @ X1 @ X2)) = (binunion @ (binintersect @ X0 @ X1) @ (binintersect @ X0 @ X2))) = bs114d)),
% 31.73/4.41 inference(rectify,[],[f119])).
% 31.73/4.41 thf(f119,axiom,(
% 31.73/4.41 (! [X3,X4,X5] : ((binintersect @ X3 @ (binunion @ X4 @ X5)) = (binunion @ (binintersect @ X3 @ X4) @ (binintersect @ X3 @ X5))) = bs114d)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',bs114d)).
% 31.73/4.41 thf(f708,plain,(
% 31.73/4.41 (binintersectSubset1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f384])).
% 31.73/4.41 thf(f384,plain,(
% 31.73/4.41 (binintersectSubset1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))))),
% 31.73/4.41 inference(fool_elimination,[],[f383])).
% 31.73/4.41 thf(f383,plain,(
% 31.73/4.41 (binintersectSubset1 = ! [X0,X1] : (((binintersect @ X0 @ X1) = X0) => (subset @ X0 @ X1)))),
% 31.73/4.41 inference(rectify,[],[f118])).
% 31.73/4.41 thf(f118,axiom,(
% 31.73/4.41 (binintersectSubset1 = ! [X3,X4] : (((binintersect @ X3 @ X4) = X3) => (subset @ X3 @ X4)))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset1)).
% 31.73/4.41 thf(f619,plain,(
% 31.73/4.41 (binintersectSubset4 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f237])).
% 31.73/4.41 thf(f237,plain,(
% 31.73/4.41 (binintersectSubset4 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))))),
% 31.73/4.41 inference(fool_elimination,[],[f236])).
% 31.73/4.41 thf(f236,plain,(
% 31.73/4.41 (! [X0,X1] : ((subset @ X1 @ X0) => ((binintersect @ X0 @ X1) = X1)) = binintersectSubset4)),
% 31.73/4.41 inference(rectify,[],[f117])).
% 31.73/4.41 thf(f117,axiom,(
% 31.73/4.41 (! [X3,X4] : ((subset @ X4 @ X3) => ((binintersect @ X3 @ X4) = X4)) = binintersectSubset4)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset4)).
% 31.73/4.41 thf(f724,plain,(
% 31.73/4.41 (binintersectRsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y0))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f544])).
% 31.73/4.41 thf(f544,plain,(
% 31.73/4.41 (binintersectRsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y0))))))),
% 31.73/4.41 inference(fool_elimination,[],[f543])).
% 31.73/4.41 thf(f543,plain,(
% 31.73/4.41 (binintersectRsub = ! [X0,X1] : (subset @ (binintersect @ X0 @ X1) @ X1))),
% 31.73/4.41 inference(rectify,[],[f116])).
% 31.73/4.41 thf(f116,axiom,(
% 31.73/4.41 (binintersectRsub = ! [X3,X4] : (subset @ (binintersect @ X3 @ X4) @ X4))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectRsub)).
% 31.73/4.41 thf(f680,plain,(
% 31.73/4.41 (disjointsetsI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y0 @ Y1))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f251])).
% 31.73/4.41 thf(f251,plain,(
% 31.73/4.41 (disjointsetsI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y0 @ Y1))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f250])).
% 31.73/4.41 thf(f250,plain,(
% 31.73/4.41 (disjointsetsI1 = ! [X0,X1] : (~? [X2] : ((in @ X2 @ X0) & (in @ X2 @ X1)) => (emptyset = (binintersect @ X1 @ X0))))),
% 31.73/4.41 inference(rectify,[],[f115])).
% 31.73/4.41 thf(f115,axiom,(
% 31.73/4.41 (disjointsetsI1 = ! [X4,X3] : (~? [X1] : ((in @ X1 @ X4) & (in @ X1 @ X3)) => (emptyset = (binintersect @ X3 @ X4))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjointsetsI1)).
% 31.73/4.41 thf(f608,plain,(
% 31.73/4.41 (binintersectER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f554])).
% 31.73/4.41 thf(f554,plain,(
% 31.73/4.41 (binintersectER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y0)))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f553])).
% 31.73/4.41 thf(f553,plain,(
% 31.73/4.41 (! [X0,X1,X2] : ((in @ X1 @ (binintersect @ X0 @ X2)) => (in @ X1 @ X2)) = binintersectER)),
% 31.73/4.41 inference(rectify,[],[f114])).
% 31.73/4.41 thf(f114,axiom,(
% 31.73/4.41 (! [X3,X1,X4] : ((in @ X1 @ (binintersect @ X3 @ X4)) => (in @ X1 @ X4)) = binintersectER)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectER)).
% 31.73/4.41 thf(f738,plain,(
% 31.73/4.41 (binintersectSubset3 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f480])).
% 31.73/4.41 thf(f480,plain,(
% 31.73/4.41 (binintersectSubset3 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y0) => (subset @ Y0 @ Y1)))))))),
% 31.73/4.41 inference(fool_elimination,[],[f479])).
% 31.73/4.41 thf(f479,plain,(
% 31.73/4.41 (binintersectSubset3 = ! [X0,X1] : (((binintersect @ X0 @ X1) = X1) => (subset @ X1 @ X0)))),
% 31.73/4.41 inference(rectify,[],[f113])).
% 31.73/4.41 thf(f113,axiom,(
% 31.73/4.41 (binintersectSubset3 = ! [X3,X4] : (((binintersect @ X3 @ X4) = X4) => (subset @ X4 @ X3)))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset3)).
% 31.73/4.41 thf(f725,plain,(
% 31.73/4.41 (binintersectSubset2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f528])).
% 31.73/4.41 thf(f528,plain,(
% 31.73/4.41 (binintersectSubset2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))))),
% 31.73/4.41 inference(fool_elimination,[],[f527])).
% 31.73/4.41 thf(f527,plain,(
% 31.73/4.41 (! [X0,X1] : ((subset @ X0 @ X1) => ((binintersect @ X0 @ X1) = X0)) = binintersectSubset2)),
% 31.73/4.41 inference(rectify,[],[f112])).
% 31.73/4.41 thf(f112,axiom,(
% 31.73/4.41 (! [X3,X4] : ((subset @ X3 @ X4) => ((binintersect @ X3 @ X4) = X3)) = binintersectSubset2)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset2)).
% 31.73/4.41 thf(f786,plain,(
% 31.73/4.41 (binintersectLsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f464])).
% 31.73/4.41 thf(f464,plain,(
% 31.73/4.41 (binintersectLsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y0))))))),
% 31.73/4.41 inference(fool_elimination,[],[f463])).
% 31.73/4.41 thf(f463,plain,(
% 31.73/4.41 (binintersectLsub = ! [X0,X1] : (subset @ (binintersect @ X1 @ X0) @ X1))),
% 31.73/4.41 inference(rectify,[],[f111])).
% 31.73/4.41 thf(f111,axiom,(
% 31.73/4.41 (binintersectLsub = ! [X4,X3] : (subset @ (binintersect @ X3 @ X4) @ X3))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectLsub)).
% 31.73/4.41 thf(f735,plain,(
% 31.73/4.41 (binintersectEL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f366])).
% 31.73/4.41 thf(f366,plain,(
% 31.73/4.41 (binintersectEL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f365])).
% 31.73/4.41 thf(f365,plain,(
% 31.73/4.41 (! [X0,X1,X2] : ((in @ X1 @ (binintersect @ X0 @ X2)) => (in @ X1 @ X0)) = binintersectEL)),
% 31.73/4.41 inference(rectify,[],[f110])).
% 31.73/4.41 thf(f110,axiom,(
% 31.73/4.41 (! [X3,X1,X4] : ((in @ X1 @ (binintersect @ X3 @ X4)) => (in @ X1 @ X3)) = binintersectEL)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectEL)).
% 31.73/4.41 thf(f640,plain,(
% 31.73/4.41 (binintersectSubset5 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y0 @ Y2) => (subset @ Y0 @ (binintersect @ Y1 @ Y2)))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f207])).
% 31.73/4.41 thf(f207,plain,(
% 31.73/4.41 (binintersectSubset5 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y0 @ Y2) => (subset @ Y0 @ (binintersect @ Y1 @ Y2)))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f206])).
% 31.73/4.41 thf(f206,plain,(
% 31.73/4.41 (! [X0,X1,X2] : ((subset @ X2 @ X1) => ((subset @ X2 @ X0) => (subset @ X2 @ (binintersect @ X1 @ X0)))) = binintersectSubset5)),
% 31.73/4.41 inference(rectify,[],[f109])).
% 31.73/4.41 thf(f109,axiom,(
% 31.73/4.41 (! [X4,X3,X5] : ((subset @ X5 @ X3) => ((subset @ X5 @ X4) => (subset @ X5 @ (binintersect @ X3 @ X4)))) = binintersectSubset5)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset5)).
% 31.73/4.41 thf(f684,plain,(
% 31.73/4.41 (binintersectI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f211])).
% 31.73/4.41 thf(f211,plain,(
% 31.73/4.41 (binintersectI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f210])).
% 31.73/4.41 thf(f210,plain,(
% 31.73/4.41 (! [X0,X1,X2] : ((in @ X0 @ X2) => ((in @ X0 @ X1) => (in @ X0 @ (binintersect @ X2 @ X1)))) = binintersectI)),
% 31.73/4.41 inference(rectify,[],[f108])).
% 31.73/4.41 thf(f108,axiom,(
% 31.73/4.41 (! [X1,X4,X3] : ((in @ X1 @ X3) => ((in @ X1 @ X4) => (in @ X1 @ (binintersect @ X3 @ X4)))) = binintersectI)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectI)).
% 31.73/4.41 thf(f629,plain,(
% 31.73/4.41 (binunionRsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f452])).
% 31.73/4.41 thf(f452,plain,(
% 31.73/4.41 (binunionRsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))))),
% 31.73/4.41 inference(fool_elimination,[],[f451])).
% 31.73/4.41 thf(f451,plain,(
% 31.73/4.41 (! [X0,X1] : (subset @ X1 @ (binunion @ X0 @ X1)) = binunionRsub)),
% 31.73/4.41 inference(rectify,[],[f107])).
% 31.73/4.41 thf(f107,axiom,(
% 31.73/4.41 (! [X3,X4] : (subset @ X4 @ (binunion @ X3 @ X4)) = binunionRsub)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionRsub)).
% 31.73/4.41 thf(f707,plain,(
% 31.73/4.41 (binunionLsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0)))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f312])).
% 31.73/4.41 thf(f312,plain,(
% 31.73/4.41 (binunionLsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y1 @ Y0)))))))),
% 31.73/4.41 inference(fool_elimination,[],[f311])).
% 31.73/4.41 thf(f311,plain,(
% 31.73/4.41 (binunionLsub = ! [X0,X1] : (subset @ X0 @ (binunion @ X0 @ X1)))),
% 31.73/4.41 inference(rectify,[],[f106])).
% 31.73/4.41 thf(f106,axiom,(
% 31.73/4.41 (binunionLsub = ! [X3,X4] : (subset @ X3 @ (binunion @ X3 @ X4)))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionLsub)).
% 31.73/4.41 thf(f727,plain,(
% 31.73/4.41 (binunionE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f512])).
% 31.73/4.41 thf(f512,plain,(
% 31.73/4.41 (binunionE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y0) | (in @ Y1 @ Y2))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f511])).
% 31.73/4.41 thf(f511,plain,(
% 31.73/4.41 (! [X0,X1,X2] : ((in @ X1 @ (binunion @ X0 @ X2)) => ((in @ X1 @ X0) | (in @ X1 @ X2))) = binunionE)),
% 31.73/4.41 inference(rectify,[],[f105])).
% 31.73/4.41 thf(f105,axiom,(
% 31.73/4.41 (! [X3,X1,X4] : ((in @ X1 @ (binunion @ X3 @ X4)) => ((in @ X1 @ X3) | (in @ X1 @ X4))) = binunionE)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionE)).
% 31.73/4.41 thf(f633,plain,(
% 31.73/4.41 (binunionEcases = (!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f524])).
% 31.73/4.41 thf(f524,plain,(
% 31.73/4.41 (binunionEcases = (!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (binunion @ Y2 @ Y1)) => (((in @ Y3 @ Y2) => Y0) => (((in @ Y3 @ Y1) => Y0) => Y0))))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f523])).
% 31.73/4.41 thf(f523,plain,(
% 31.73/4.41 (binunionEcases = ! [X0,X1,X2,X3 : $o] : ((in @ X0 @ (binunion @ X1 @ X2)) => (((in @ X0 @ X1) => X3) => (((in @ X0 @ X2) => X3) => X3))))),
% 31.73/4.41 inference(rectify,[],[f104])).
% 31.73/4.41 thf(f104,axiom,(
% 31.73/4.41 (binunionEcases = ! [X1,X3,X4,X0 : $o] : ((in @ X1 @ (binunion @ X3 @ X4)) => (((in @ X1 @ X3) => X0) => (((in @ X1 @ X4) => X0) => X0))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionEcases)).
% 31.73/4.41 thf(f773,plain,(
% 31.73/4.41 (binunionIR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f229])).
% 31.73/4.41 thf(f229,plain,(
% 31.73/4.41 (binunionIR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f228])).
% 31.73/4.41 thf(f228,plain,(
% 31.73/4.41 (! [X0,X1,X2] : ((in @ X2 @ X1) => (in @ X2 @ (binunion @ X0 @ X1))) = binunionIR)),
% 31.73/4.41 inference(rectify,[],[f103])).
% 31.73/4.41 thf(f103,axiom,(
% 31.73/4.41 (! [X3,X4,X1] : ((in @ X1 @ X4) => (in @ X1 @ (binunion @ X3 @ X4))) = binunionIR)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIR)).
% 31.73/4.41 thf(f599,plain,(
% 31.73/4.41 (upairset2IR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f213])).
% 31.73/4.41 thf(f213,plain,(
% 31.73/4.41 (upairset2IR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f212])).
% 31.73/4.41 thf(f212,plain,(
% 31.73/4.41 (upairset2IR = ! [X0,X1] : (in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))))),
% 31.73/4.41 inference(rectify,[],[f102])).
% 31.73/4.41 thf(f102,axiom,(
% 31.73/4.41 (upairset2IR = ! [X2,X1] : (in @ X2 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2IR)).
% 31.73/4.41 thf(f712,plain,(
% 31.73/4.41 (binunionIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f253])).
% 31.73/4.41 thf(f253,plain,(
% 31.73/4.41 (binunionIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ (binunion @ Y1 @ Y0))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f252])).
% 31.73/4.41 thf(f252,plain,(
% 31.73/4.41 (binunionIL = ! [X0,X1,X2] : ((in @ X0 @ X1) => (in @ X0 @ (binunion @ X1 @ X2))))),
% 31.73/4.41 inference(rectify,[],[f101])).
% 31.73/4.41 thf(f101,axiom,(
% 31.73/4.41 (binunionIL = ! [X1,X3,X4] : ((in @ X1 @ X3) => (in @ X1 @ (binunion @ X3 @ X4))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIL)).
% 31.73/4.41 thf(f729,plain,(
% 31.73/4.41 (sepSubset = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ (^[Y2 : $i]: (Y0 @ Y2))) @ Y1))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f277])).
% 31.73/4.41 thf(f277,plain,(
% 31.73/4.41 (sepSubset = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ (^[Y2 : $i]: (Y0 @ Y2))) @ Y1))))))),
% 31.73/4.41 inference(fool_elimination,[],[f276])).
% 31.73/4.41 thf(f276,plain,(
% 31.73/4.41 (sepSubset = ! [X0,X1 : $i > $o] : (subset @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))) @ X0))),
% 31.73/4.41 inference(rectify,[],[f100])).
% 31.73/4.41 thf(f100,axiom,(
% 31.73/4.41 (sepSubset = ! [X3,X0 : $i > $o] : (subset @ (dsetconstr @ X3 @ (^[X1 : $i] : (X0 @ X1))) @ X3))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepSubset)).
% 31.73/4.41 thf(f670,plain,(
% 31.73/4.41 (sepInPowerset = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) @ (powerset @ Y0)))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f267])).
% 31.73/4.41 thf(f267,plain,(
% 31.73/4.41 (sepInPowerset = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) @ (powerset @ Y0)))))))),
% 31.73/4.41 inference(fool_elimination,[],[f266])).
% 31.73/4.41 thf(f266,plain,(
% 31.73/4.41 (sepInPowerset = ! [X0 : $i > $o,X1] : (in @ (dsetconstr @ X1 @ (^[X2 : $i] : (X0 @ X2))) @ (powerset @ X1)))),
% 31.73/4.41 inference(rectify,[],[f99])).
% 31.73/4.41 thf(f99,axiom,(
% 31.73/4.41 (sepInPowerset = ! [X0 : $i > $o,X3] : (in @ (dsetconstr @ X3 @ (^[X1 : $i] : (X0 @ X1))) @ (powerset @ X3)))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepInPowerset)).
% 31.73/4.41 thf(f718,plain,(
% 31.73/4.41 (powersetsubset = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (subset @ (powerset @ Y1) @ (powerset @ Y0))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f356])).
% 31.73/4.41 thf(f356,plain,(
% 31.73/4.41 (powersetsubset = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (subset @ (powerset @ Y1) @ (powerset @ Y0))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f355])).
% 31.73/4.41 thf(f355,plain,(
% 31.73/4.41 (powersetsubset = ! [X0,X1] : ((subset @ X0 @ X1) => (subset @ (powerset @ X0) @ (powerset @ X1))))),
% 31.73/4.41 inference(rectify,[],[f98])).
% 31.73/4.41 thf(f98,axiom,(
% 31.73/4.41 (powersetsubset = ! [X3,X4] : ((subset @ X3 @ X4) => (subset @ (powerset @ X3) @ (powerset @ X4))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetsubset)).
% 31.73/4.41 thf(f664,plain,(
% 31.73/4.41 (inPowerset = (!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))))),
% 31.73/4.41 inference(cnf_transformation,[],[f255])).
% 31.73/4.41 thf(f255,plain,(
% 31.73/4.41 (inPowerset = (!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))))),
% 31.73/4.41 inference(fool_elimination,[],[f254])).
% 31.73/4.41 thf(f254,plain,(
% 31.73/4.41 (inPowerset = ! [X0] : (in @ X0 @ (powerset @ X0)))),
% 31.73/4.41 inference(rectify,[],[f97])).
% 31.73/4.41 thf(f97,axiom,(
% 31.73/4.41 (inPowerset = ! [X3] : (in @ X3 @ (powerset @ X3)))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',inPowerset)).
% 31.73/4.41 thf(f630,plain,(
% 31.73/4.41 (powersetE1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f496])).
% 31.73/4.41 thf(f496,plain,(
% 31.73/4.41 (powersetE1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))))),
% 31.73/4.41 inference(fool_elimination,[],[f495])).
% 31.73/4.41 thf(f495,plain,(
% 31.73/4.41 (powersetE1 = ! [X0,X1] : ((in @ X0 @ (powerset @ X1)) => (subset @ X0 @ X1)))),
% 31.73/4.41 inference(rectify,[],[f96])).
% 31.73/4.41 thf(f96,axiom,(
% 31.73/4.41 (powersetE1 = ! [X4,X3] : ((in @ X4 @ (powerset @ X3)) => (subset @ X4 @ X3)))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1)).
% 31.73/4.41 thf(f628,plain,(
% 31.73/4.41 (powersetI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f414])).
% 31.73/4.41 thf(f414,plain,(
% 31.73/4.41 (powersetI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f413])).
% 31.73/4.41 thf(f413,plain,(
% 31.73/4.41 (powersetI1 = ! [X0,X1] : ((subset @ X0 @ X1) => (in @ X0 @ (powerset @ X1))))),
% 31.73/4.41 inference(rectify,[],[f95])).
% 31.73/4.41 thf(f95,axiom,(
% 31.73/4.41 (powersetI1 = ! [X4,X3] : ((subset @ X4 @ X3) => (in @ X4 @ (powerset @ X3))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI1)).
% 31.73/4.41 thf(f701,plain,(
% 31.73/4.41 (subsetemptysetimpeq = (!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))))),
% 31.73/4.41 inference(cnf_transformation,[],[f223])).
% 31.73/4.41 thf(f223,plain,(
% 31.73/4.41 (subsetemptysetimpeq = (!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))))),
% 31.73/4.41 inference(fool_elimination,[],[f222])).
% 31.73/4.41 thf(f222,plain,(
% 31.73/4.41 (subsetemptysetimpeq = ! [X0] : ((subset @ X0 @ emptyset) => (emptyset = X0)))),
% 31.73/4.41 inference(rectify,[],[f94])).
% 31.73/4.41 thf(f94,axiom,(
% 31.73/4.41 (subsetemptysetimpeq = ! [X3] : ((subset @ X3 @ emptyset) => (emptyset = X3)))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetemptysetimpeq)).
% 31.73/4.41 thf(f675,plain,(
% 31.73/4.41 (setextsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (Y1 = Y0))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f297])).
% 31.73/4.41 thf(f297,plain,(
% 31.73/4.41 (setextsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (Y1 = Y0))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f296])).
% 31.73/4.41 thf(f296,plain,(
% 31.73/4.41 (setextsub = ! [X0,X1] : ((subset @ X1 @ X0) => ((subset @ X0 @ X1) => (X0 = X1))))),
% 31.73/4.41 inference(rectify,[],[f93])).
% 31.73/4.41 thf(f93,axiom,(
% 31.73/4.41 (setextsub = ! [X4,X3] : ((subset @ X3 @ X4) => ((subset @ X4 @ X3) => (X3 = X4))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextsub)).
% 31.73/4.41 thf(f602,plain,(
% 31.73/4.41 (subset2powerset = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f285])).
% 31.73/4.41 thf(f285,plain,(
% 31.73/4.41 (subset2powerset = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (in @ Y1 @ (powerset @ Y0))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f284])).
% 31.73/4.41 thf(f284,plain,(
% 31.73/4.41 (! [X0,X1] : ((subset @ X0 @ X1) => (in @ X0 @ (powerset @ X1))) = subset2powerset)),
% 31.73/4.41 inference(rectify,[],[f92])).
% 31.73/4.41 thf(f92,axiom,(
% 31.73/4.41 (! [X3,X4] : ((subset @ X3 @ X4) => (in @ X3 @ (powerset @ X4))) = subset2powerset)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2powerset)).
% 31.73/4.41 thf(f681,plain,(
% 31.73/4.41 (setadjoinSub2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f374])).
% 31.73/4.41 thf(f374,plain,(
% 31.73/4.41 (setadjoinSub2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f373])).
% 31.73/4.41 thf(f373,plain,(
% 31.73/4.41 (! [X0,X1,X2] : ((subset @ X1 @ X0) => (subset @ X1 @ (setadjoin @ X2 @ X0))) = setadjoinSub2)),
% 31.73/4.41 inference(rectify,[],[f91])).
% 31.73/4.41 thf(f91,axiom,(
% 31.73/4.41 (! [X4,X3,X1] : ((subset @ X3 @ X4) => (subset @ X3 @ (setadjoin @ X1 @ X4))) = setadjoinSub2)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub2)).
% 31.73/4.41 thf(f659,plain,(
% 31.73/4.41 (setadjoinSub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (setadjoin @ Y1 @ Y0)))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f468])).
% 31.73/4.41 thf(f468,plain,(
% 31.73/4.41 (setadjoinSub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (setadjoin @ Y1 @ Y0)))))))),
% 31.73/4.41 inference(fool_elimination,[],[f467])).
% 31.73/4.41 thf(f467,plain,(
% 31.73/4.41 (! [X0,X1] : (subset @ X1 @ (setadjoin @ X0 @ X1)) = setadjoinSub)),
% 31.73/4.41 inference(rectify,[],[f90])).
% 31.73/4.41 thf(f90,axiom,(
% 31.73/4.41 (! [X1,X3] : (subset @ X3 @ (setadjoin @ X1 @ X3)) = setadjoinSub)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub)).
% 31.73/4.41 thf(f746,plain,(
% 31.73/4.41 (subsetTrans = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f594])).
% 31.73/4.41 thf(f594,plain,(
% 31.73/4.41 (subsetTrans = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f593])).
% 31.73/4.41 thf(f593,plain,(
% 31.73/4.41 (! [X0,X1,X2] : ((subset @ X2 @ X0) => ((subset @ X0 @ X1) => (subset @ X2 @ X1))) = subsetTrans)),
% 31.73/4.41 inference(rectify,[],[f89])).
% 31.73/4.41 thf(f89,axiom,(
% 31.73/4.41 (! [X4,X5,X3] : ((subset @ X3 @ X4) => ((subset @ X4 @ X5) => (subset @ X3 @ X5))) = subsetTrans)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTrans)).
% 31.73/4.41 thf(f770,plain,(
% 31.73/4.41 (subsetRefl = (!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))))),
% 31.73/4.41 inference(cnf_transformation,[],[f482])).
% 31.73/4.41 thf(f482,plain,(
% 31.73/4.41 (subsetRefl = (!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))))),
% 31.73/4.41 inference(fool_elimination,[],[f481])).
% 31.73/4.41 thf(f481,plain,(
% 31.73/4.41 (! [X0] : (subset @ X0 @ X0) = subsetRefl)),
% 31.73/4.41 inference(rectify,[],[f88])).
% 31.73/4.41 thf(f88,axiom,(
% 31.73/4.41 (! [X3] : (subset @ X3 @ X3) = subsetRefl)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetRefl)).
% 31.73/4.41 thf(f765,plain,(
% 31.73/4.41 (notequalI2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = Y0)))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f358])).
% 31.73/4.41 thf(f358,plain,(
% 31.73/4.41 (notequalI2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = Y0)))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f357])).
% 31.73/4.41 thf(f357,plain,(
% 31.73/4.41 (! [X0,X1,X2] : ((in @ X1 @ X0) => (~(in @ X1 @ X2) => (X0 != X2))) = notequalI2)),
% 31.73/4.41 inference(rectify,[],[f87])).
% 31.73/4.41 thf(f87,axiom,(
% 31.73/4.41 (! [X3,X1,X4] : ((in @ X1 @ X3) => (~(in @ X1 @ X4) => (X3 != X4))) = notequalI2)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI2)).
% 31.73/4.41 thf(f775,plain,(
% 31.73/4.41 (notequalI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f348])).
% 31.73/4.41 thf(f348,plain,(
% 31.73/4.41 (notequalI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f347])).
% 31.73/4.41 thf(f347,plain,(
% 31.73/4.41 (notequalI1 = ! [X0,X1] : (~(subset @ X1 @ X0) => (X0 != X1)))),
% 31.73/4.41 inference(rectify,[],[f86])).
% 31.73/4.41 thf(f86,axiom,(
% 31.73/4.41 (notequalI1 = ! [X4,X3] : (~(subset @ X3 @ X4) => (X3 != X4)))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI1)).
% 31.73/4.41 thf(f672,plain,(
% 31.73/4.41 (notsubsetI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f564])).
% 31.73/4.41 thf(f564,plain,(
% 31.73/4.41 (notsubsetI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (~ (subset @ Y2 @ Y1)))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f563])).
% 31.73/4.41 thf(f563,plain,(
% 31.73/4.41 (notsubsetI = ! [X0,X1,X2] : ((in @ X2 @ X0) => (~(in @ X2 @ X1) => ~(subset @ X0 @ X1))))),
% 31.73/4.41 inference(rectify,[],[f85])).
% 31.73/4.41 thf(f85,axiom,(
% 31.73/4.41 (notsubsetI = ! [X3,X4,X1] : ((in @ X1 @ X3) => (~(in @ X1 @ X4) => ~(subset @ X3 @ X4))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',notsubsetI)).
% 31.73/4.41 thf(f691,plain,(
% 31.73/4.41 (subsetE2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f588])).
% 31.73/4.41 thf(f588,plain,(
% 31.73/4.41 (subsetE2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f587])).
% 31.73/4.41 thf(f587,plain,(
% 31.73/4.41 (subsetE2 = ! [X0,X1,X2] : ((subset @ X0 @ X1) => (~(in @ X2 @ X1) => ~(in @ X2 @ X0))))),
% 31.73/4.41 inference(rectify,[],[f84])).
% 31.73/4.41 thf(f84,axiom,(
% 31.73/4.41 (subsetE2 = ! [X3,X4,X1] : ((subset @ X3 @ X4) => (~(in @ X1 @ X4) => ~(in @ X1 @ X3))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE2)).
% 31.73/4.41 thf(f688,plain,(
% 31.73/4.41 (subsetE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f592])).
% 31.73/4.41 thf(f592,plain,(
% 31.73/4.41 (subsetE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f591])).
% 31.73/4.41 thf(f591,plain,(
% 31.73/4.41 (! [X0,X1,X2] : ((subset @ X1 @ X2) => ((in @ X0 @ X1) => (in @ X0 @ X2))) = subsetE)),
% 31.73/4.41 inference(rectify,[],[f83])).
% 31.73/4.41 thf(f83,axiom,(
% 31.73/4.41 (! [X1,X3,X4] : ((subset @ X3 @ X4) => ((in @ X1 @ X3) => (in @ X1 @ X4))) = subsetE)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE)).
% 31.73/4.41 thf(f713,plain,(
% 31.73/4.41 (emptysetsubset = (!! @ $i @ (^[Y0 : $i]: (subset @ emptyset @ Y0))))),
% 31.73/4.41 inference(cnf_transformation,[],[f406])).
% 31.73/4.41 thf(f406,plain,(
% 31.73/4.41 (emptysetsubset = (!! @ $i @ (^[Y0 : $i]: (subset @ emptyset @ Y0))))),
% 31.73/4.41 inference(fool_elimination,[],[f405])).
% 31.73/4.41 thf(f405,plain,(
% 31.73/4.41 (! [X0] : (subset @ emptyset @ X0) = emptysetsubset)),
% 31.73/4.41 inference(rectify,[],[f82])).
% 31.73/4.41 thf(f82,axiom,(
% 31.73/4.41 (! [X3] : (subset @ emptyset @ X3) = emptysetsubset)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetsubset)).
% 31.73/4.41 thf(f642,plain,(
% 31.73/4.41 (subsetI2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f261])).
% 31.73/4.41 thf(f261,plain,(
% 31.73/4.41 (subsetI2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))))),
% 31.73/4.41 inference(fool_elimination,[],[f260])).
% 31.73/4.41 thf(f260,plain,(
% 31.73/4.41 (subsetI2 = ! [X0,X1] : (! [X2] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)))),
% 31.73/4.41 inference(rectify,[],[f81])).
% 31.73/4.41 thf(f81,axiom,(
% 31.73/4.41 (subsetI2 = ! [X4,X3] : (! [X1] : ((in @ X1 @ X3) => (in @ X1 @ X4)) => (subset @ X3 @ X4)))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2)).
% 31.73/4.41 thf(f620,plain,(
% 31.73/4.41 (eqimpsubset1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f322])).
% 31.73/4.41 thf(f322,plain,(
% 31.73/4.41 (eqimpsubset1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))))),
% 31.73/4.41 inference(fool_elimination,[],[f321])).
% 31.73/4.41 thf(f321,plain,(
% 31.73/4.41 (eqimpsubset1 = ! [X0,X1] : ((X0 = X1) => (subset @ X1 @ X0)))),
% 31.73/4.41 inference(rectify,[],[f80])).
% 31.73/4.41 thf(f80,axiom,(
% 31.73/4.41 (eqimpsubset1 = ! [X4,X3] : ((X3 = X4) => (subset @ X3 @ X4)))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset1)).
% 31.73/4.41 thf(f626,plain,(
% 31.73/4.41 (eqimpsubset2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f352])).
% 31.73/4.41 thf(f352,plain,(
% 31.73/4.41 (eqimpsubset2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))))),
% 31.73/4.41 inference(fool_elimination,[],[f351])).
% 31.73/4.41 thf(f351,plain,(
% 31.73/4.41 (eqimpsubset2 = ! [X0,X1] : ((X0 = X1) => (subset @ X1 @ X0)))),
% 31.73/4.41 inference(rectify,[],[f79])).
% 31.73/4.41 thf(f79,axiom,(
% 31.73/4.41 (eqimpsubset2 = ! [X3,X4] : ((X3 = X4) => (subset @ X4 @ X3)))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset2)).
% 31.73/4.41 thf(f631,plain,(
% 31.73/4.41 (subsetI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f209])).
% 31.73/4.41 thf(f209,plain,(
% 31.73/4.41 (subsetI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))))),
% 31.73/4.41 inference(fool_elimination,[],[f208])).
% 31.73/4.41 thf(f208,plain,(
% 31.73/4.41 (! [X0,X1] : (! [X2] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI1)),
% 31.73/4.41 inference(rectify,[],[f78])).
% 31.73/4.41 thf(f78,axiom,(
% 31.73/4.41 (! [X3,X4] : (! [X1] : ((in @ X1 @ X3) => (in @ X1 @ X4)) => (subset @ X3 @ X4)) = subsetI1)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI1)).
% 31.73/4.41 thf(f677,plain,(
% 31.73/4.41 (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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ (^[Y4 : $i]: (Y3 @ Y4))) = (dsetconstr @ Y1 @ (^[Y4 : $i]: (Y2 @ Y4)))))))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f370])).
% 31.73/4.41 thf(f370,plain,(
% 31.73/4.41 (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 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((Y4 = Y5) => ((Y2 @ Y5) = (Y3 @ Y4))))))))) => ((dsetconstr @ Y0 @ (^[Y4 : $i]: (Y3 @ Y4))) = (dsetconstr @ Y1 @ (^[Y4 : $i]: (Y2 @ Y4)))))))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f369])).
% 31.73/4.41 thf(f369,plain,(
% 31.73/4.41 (! [X0,X1] : ((X0 = X1) => ! [X2 : $i > $o,X3 : $i > $o] : (! [X4] : ((in @ X4 @ X1) => ! [X5] : ((in @ X5 @ X0) => ((X4 = X5) => ((X3 @ X5) <=> (X2 @ X4))))) => ((dsetconstr @ X1 @ (^[X6 : $i] : (X2 @ X6))) = (dsetconstr @ X0 @ (^[X7 : $i] : (X3 @ X7)))))) = dsetconstr__Cong)),
% 31.73/4.41 inference(rectify,[],[f77])).
% 31.73/4.41 thf(f77,axiom,(
% 31.73/4.41 (! [X4,X3] : ((X3 = X4) => ! [X0 : $i > $o,X9 : $i > $o] : (! [X1] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => ((X1 = X2) => ((X9 @ X2) <=> (X0 @ X1))))) => ((dsetconstr @ X3 @ (^[X1 : $i] : (X0 @ X1))) = (dsetconstr @ X4 @ (^[X1 : $i] : (X9 @ X1)))))) = dsetconstr__Cong)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstr__Cong)).
% 31.73/4.41 thf(f810,plain,(
% 31.73/4.41 (descr__Cong = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ 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))) => ((descr @ (^[Y2 : $i]: (Y0 @ Y2))) = (descr @ (^[Y2 : $i]: (Y1 @ Y2))))))))))))),
% 31.73/4.41 inference(definition_unfolding,[],[f783,f598,f598])).
% 31.73/4.41 thf(f598,plain,(
% 31.73/4.41 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f514])).
% 31.73/4.41 thf(f514,plain,(
% 31.73/4.41 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f513])).
% 31.73/4.41 thf(f513,plain,(
% 31.73/4.41 ((^[X0 : $i > $o] : (? [X1] : (! [X2] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))) = exu)),
% 31.73/4.41 inference(rectify,[],[f1])).
% 31.73/4.41 thf(f1,axiom,(
% 31.73/4.41 ((^[X0 : $i > $o] : (? [X1] : (! [X2] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))) = exu)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu)).
% 31.73/4.41 thf(f783,plain,(
% 31.73/4.41 (descr__Cong = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ Y3))))))) => ((exu @ (^[Y2 : $i]: (Y0 @ Y2))) => ((exu @ (^[Y2 : $i]: (Y1 @ Y2))) => ((descr @ (^[Y2 : $i]: (Y0 @ Y2))) = (descr @ (^[Y2 : $i]: (Y1 @ Y2))))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f478])).
% 31.73/4.41 thf(f478,plain,(
% 31.73/4.41 (descr__Cong = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ Y3))))))) => ((exu @ (^[Y2 : $i]: (Y0 @ Y2))) => ((exu @ (^[Y2 : $i]: (Y1 @ Y2))) => ((descr @ (^[Y2 : $i]: (Y0 @ Y2))) = (descr @ (^[Y2 : $i]: (Y1 @ Y2))))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f477])).
% 31.73/4.41 thf(f477,plain,(
% 31.73/4.41 (descr__Cong = ! [X0 : $i > $o,X1 : $i > $o] : (! [X2,X3] : ((X2 = X3) => ((X1 @ X3) <=> (X0 @ X2))) => ((exu @ (^[X4 : $i] : (X1 @ X4))) => ((exu @ (^[X5 : $i] : (X0 @ X5))) => ((descr @ (^[X6 : $i] : (X1 @ X6))) = (descr @ (^[X7 : $i] : (X0 @ X7))))))))),
% 31.73/4.41 inference(rectify,[],[f76])).
% 31.73/4.41 thf(f76,axiom,(
% 31.73/4.41 (descr__Cong = ! [X9 : $i > $o,X0 : $i > $o] : (! [X2,X1] : ((X1 = X2) => ((X0 @ X1) <=> (X9 @ X2))) => ((exu @ (^[X1 : $i] : (X0 @ X1))) => ((exu @ (^[X1 : $i] : (X9 @ X1))) => ((descr @ (^[X1 : $i] : (X0 @ X1))) = (descr @ (^[X1 : $i] : (X9 @ X1))))))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',descr__Cong)).
% 31.73/4.41 thf(f809,plain,(
% 31.73/4.41 (exuEu = (!! @ ($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 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))))),
% 31.73/4.41 inference(definition_unfolding,[],[f636,f598])).
% 31.73/4.41 thf(f636,plain,(
% 31.73/4.41 (exuEu = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f428])).
% 31.73/4.41 thf(f428,plain,(
% 31.73/4.41 (exuEu = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1)))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f427])).
% 31.73/4.41 thf(f427,plain,(
% 31.73/4.41 (! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ! [X2,X3] : ((X0 @ X3) => ((X0 @ X2) => (X2 = X3)))) = exuEu)),
% 31.73/4.41 inference(rectify,[],[f75])).
% 31.73/4.41 thf(f75,axiom,(
% 31.73/4.41 (! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ! [X2,X1] : ((X0 @ X1) => ((X0 @ X2) => (X1 = X2)))) = exuEu)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuEu)).
% 31.73/4.41 thf(f763,plain,(
% 31.73/4.41 (omega__Cong = (omega = omega))),
% 31.73/4.41 inference(cnf_transformation,[],[f342])).
% 31.73/4.41 thf(f342,plain,(
% 31.73/4.41 (omega__Cong = (omega = omega))),
% 31.73/4.41 inference(fool_elimination,[],[f74])).
% 31.73/4.41 thf(f74,axiom,(
% 31.73/4.41 (omega__Cong = (omega = omega))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega__Cong)).
% 31.73/4.41 thf(f767,plain,(
% 31.73/4.41 (setunion__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f578])).
% 31.73/4.41 thf(f578,plain,(
% 31.73/4.41 (setunion__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f577])).
% 31.73/4.41 thf(f577,plain,(
% 31.73/4.41 (setunion__Cong = ! [X0,X1] : ((X0 = X1) => ((setunion @ X0) = (setunion @ X1))))),
% 31.73/4.41 inference(rectify,[],[f73])).
% 31.73/4.41 thf(f73,axiom,(
% 31.73/4.41 (setunion__Cong = ! [X3,X4] : ((X3 = X4) => ((setunion @ X3) = (setunion @ X4))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunion__Cong)).
% 31.73/4.41 thf(f697,plain,(
% 31.73/4.41 (powerset__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f450])).
% 31.73/4.41 thf(f450,plain,(
% 31.73/4.41 (powerset__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y1) = (powerset @ Y0))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f449])).
% 31.73/4.41 thf(f449,plain,(
% 31.73/4.41 (powerset__Cong = ! [X0,X1] : ((X0 = X1) => ((powerset @ X0) = (powerset @ X1))))),
% 31.73/4.41 inference(rectify,[],[f72])).
% 31.73/4.41 thf(f72,axiom,(
% 31.73/4.41 (powerset__Cong = ! [X4,X3] : ((X3 = X4) => ((powerset @ X3) = (powerset @ X4))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset__Cong)).
% 31.73/4.41 thf(f749,plain,(
% 31.73/4.41 (setadjoin__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f259])).
% 31.73/4.41 thf(f259,plain,(
% 31.73/4.41 (setadjoin__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y2) = (setadjoin @ Y1 @ Y3)))))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f258])).
% 31.73/4.41 thf(f258,plain,(
% 31.73/4.41 (! [X0,X1] : ((X0 = X1) => ! [X2,X3] : ((X2 = X3) => ((setadjoin @ X1 @ X3) = (setadjoin @ X0 @ X2)))) = setadjoin__Cong)),
% 31.73/4.41 inference(rectify,[],[f71])).
% 31.73/4.41 thf(f71,axiom,(
% 31.73/4.41 (! [X1,X2] : ((X1 = X2) => ! [X8,X10] : ((X8 = X10) => ((setadjoin @ X1 @ X8) = (setadjoin @ X2 @ X10)))) = setadjoin__Cong)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoin__Cong)).
% 31.73/4.41 thf(f607,plain,(
% 31.73/4.41 (emptyset__Cong = (emptyset = emptyset))),
% 31.73/4.41 inference(cnf_transformation,[],[f302])).
% 31.73/4.41 thf(f302,plain,(
% 31.73/4.41 (emptyset__Cong = (emptyset = emptyset))),
% 31.73/4.41 inference(fool_elimination,[],[f70])).
% 31.73/4.41 thf(f70,axiom,(
% 31.73/4.41 (emptyset__Cong = (emptyset = emptyset))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyset__Cong)).
% 31.73/4.41 thf(f808,plain,(
% 31.73/4.41 (exu__Cong = (!! @ ($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 : $i]: (Y1 @ Y2))))))))))),
% 31.73/4.41 inference(definition_unfolding,[],[f654,f598,f598])).
% 31.73/4.41 thf(f654,plain,(
% 31.73/4.41 (exu__Cong = (!! @ ($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 : $i]: (Y1 @ Y2))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f476])).
% 31.73/4.41 thf(f476,plain,(
% 31.73/4.41 (exu__Cong = (!! @ ($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))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f475])).
% 31.73/4.41 thf(f475,plain,(
% 31.73/4.41 (! [X0 : $i > $o,X1 : $i > $o] : (! [X2,X3] : ((X2 = X3) => ((X1 @ X2) <=> (X0 @ X3))) => ((exu @ (^[X4 : $i] : (X1 @ X4))) <=> (exu @ (^[X5 : $i] : (X0 @ X5))))) = exu__Cong)),
% 31.73/4.41 inference(rectify,[],[f69])).
% 31.73/4.41 thf(f69,axiom,(
% 31.73/4.41 (! [X0 : $i > $o,X9 : $i > $o] : (! [X2,X1] : ((X1 = X2) => ((X9 @ X2) <=> (X0 @ X1))) => ((exu @ (^[X1 : $i] : (X9 @ X1))) <=> (exu @ (^[X1 : $i] : (X0 @ X1))))) = exu__Cong)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu__Cong)).
% 31.73/4.41 thf(f807,plain,(
% 31.73/4.41 (exuE3u = (!! @ ($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 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))))),
% 31.73/4.41 inference(definition_unfolding,[],[f683,f598])).
% 31.73/4.41 thf(f683,plain,(
% 31.73/4.41 (exuE3u = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f257])).
% 31.73/4.41 thf(f257,plain,(
% 31.73/4.41 (exuE3u = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f256])).
% 31.73/4.41 thf(f256,plain,(
% 31.73/4.41 (! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ! [X2,X3] : ((X0 @ X2) => ((X0 @ X3) => (X2 = X3)))) = exuE3u)),
% 31.73/4.41 inference(rectify,[],[f68])).
% 31.73/4.41 thf(f68,axiom,(
% 31.73/4.41 (! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ! [X1,X2] : ((X0 @ X1) => ((X0 @ X2) => (X1 = X2)))) = exuE3u)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3u)).
% 31.73/4.41 thf(f759,plain,(
% 31.73/4.41 (in__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f458])).
% 31.73/4.41 thf(f458,plain,(
% 31.73/4.41 (in__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) = (in @ Y2 @ Y0)))))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f457])).
% 31.73/4.41 thf(f457,plain,(
% 31.73/4.41 (in__Cong = ! [X0,X1] : ((X0 = X1) => ! [X2,X3] : ((X2 = X3) => ((in @ X2 @ X0) <=> (in @ X3 @ X1)))))),
% 31.73/4.41 inference(rectify,[],[f67])).
% 31.73/4.41 thf(f67,axiom,(
% 31.73/4.41 (in__Cong = ! [X4,X3] : ((X3 = X4) => ! [X2,X1] : ((X1 = X2) => ((in @ X2 @ X4) <=> (in @ X1 @ X3)))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',in__Cong)).
% 31.73/4.41 thf(f728,plain,(
% 31.73/4.41 (inCongP = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f510])).
% 31.73/4.41 thf(f510,plain,(
% 31.73/4.41 (inCongP = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f509])).
% 31.73/4.41 thf(f509,plain,(
% 31.73/4.41 (! [X0,X1] : ((X0 = X1) => ! [X2,X3] : ((X2 = X3) => ((in @ X2 @ X0) => (in @ X3 @ X1)))) = inCongP)),
% 31.73/4.41 inference(rectify,[],[f66])).
% 31.73/4.41 thf(f66,axiom,(
% 31.73/4.41 (! [X3,X4] : ((X3 = X4) => ! [X1,X2] : ((X1 = X2) => ((in @ X1 @ X3) => (in @ X2 @ X4)))) = inCongP)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',inCongP)).
% 31.73/4.41 thf(f806,plain,(
% 31.73/4.41 (exuI2 = (!! @ ($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 : $i]: (Y0 @ Y1)))))))),
% 31.73/4.41 inference(definition_unfolding,[],[f674,f598])).
% 31.73/4.41 thf(f674,plain,(
% 31.73/4.41 (exuI2 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f362])).
% 31.73/4.41 thf(f362,plain,(
% 31.73/4.41 (exuI2 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 31.73/4.41 inference(fool_elimination,[],[f361])).
% 31.73/4.41 thf(f361,plain,(
% 31.73/4.41 (! [X0 : $i > $o] : (? [X1] : ! [X2] : ((X0 @ X2) <=> (X1 = X2)) => (exu @ (^[X3 : $i] : (X0 @ X3)))) = exuI2)),
% 31.73/4.41 inference(rectify,[],[f65])).
% 31.73/4.41 thf(f65,axiom,(
% 31.73/4.41 (! [X0 : $i > $o] : (? [X1] : ! [X2] : ((X0 @ X2) <=> (X1 = X2)) => (exu @ (^[X1 : $i] : (X0 @ X1)))) = exuI2)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI2)).
% 31.73/4.41 thf(f805,plain,(
% 31.73/4.41 (exuI3 = (!! @ ($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 : $i]: (Y0 @ Y1))))))))),
% 31.73/4.41 inference(definition_unfolding,[],[f673,f598])).
% 31.73/4.41 thf(f673,plain,(
% 31.73/4.41 (exuI3 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f560])).
% 31.73/4.41 thf(f560,plain,(
% 31.73/4.41 (exuI3 = (!! @ ($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))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f559])).
% 31.73/4.41 thf(f559,plain,(
% 31.73/4.41 (exuI3 = ! [X0 : $i > $o] : (? [X1] : (X0 @ X1) => (! [X2,X3] : ((X0 @ X3) => ((X0 @ X2) => (X2 = X3))) => (exu @ (^[X4 : $i] : (X0 @ X4))))))),
% 31.73/4.41 inference(rectify,[],[f64])).
% 31.73/4.41 thf(f64,axiom,(
% 31.73/4.41 (exuI3 = ! [X0 : $i > $o] : (? [X1] : (X0 @ X1) => (! [X2,X1] : ((X0 @ X1) => ((X0 @ X2) => (X1 = X2))) => (exu @ (^[X1 : $i] : (X0 @ X1))))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI3)).
% 31.73/4.41 thf(f804,plain,(
% 31.73/4.41 (exuI1 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))))))) @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 31.73/4.41 inference(definition_unfolding,[],[f668,f598])).
% 31.73/4.41 thf(f668,plain,(
% 31.73/4.41 (exuI1 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f304])).
% 31.73/4.41 thf(f304,plain,(
% 31.73/4.41 (exuI1 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 31.73/4.41 inference(fool_elimination,[],[f303])).
% 31.73/4.41 thf(f303,plain,(
% 31.73/4.41 (exuI1 = ! [X0 : $i > $o] : (? [X1] : ((X0 @ X1) & ! [X2] : ((X0 @ X2) => (X1 = X2))) => (exu @ (^[X3 : $i] : (X0 @ X3)))))),
% 31.73/4.41 inference(rectify,[],[f63])).
% 31.73/4.41 thf(f63,axiom,(
% 31.73/4.41 (exuI1 = ! [X0 : $i > $o] : (? [X1] : ((X0 @ X1) & ! [X2] : ((X0 @ X2) => (X1 = X2))) => (exu @ (^[X1 : $i] : (X0 @ X1)))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI1)).
% 31.73/4.41 thf(f792,plain,(
% 31.73/4.41 (notdallE = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f558])).
% 31.73/4.41 thf(f558,plain,(
% 31.73/4.41 (notdallE = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f557])).
% 31.73/4.41 thf(f557,plain,(
% 31.73/4.41 (notdallE = ! [X0,X1 : $i > $o] : (~! [X2] : ((in @ X2 @ X0) => (X1 @ X2)) => ? [X3] : ((in @ X3 @ X0) & ~(X1 @ X3))))),
% 31.73/4.41 inference(rectify,[],[f62])).
% 31.73/4.41 thf(f62,axiom,(
% 31.73/4.41 (notdallE = ! [X3,X0 : $i > $o] : (~! [X1] : ((in @ X1 @ X3) => (X0 @ X1)) => ? [X1] : ((in @ X1 @ X3) & ~(X0 @ X1))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdallE)).
% 31.73/4.41 thf(f596,plain,(
% 31.73/4.41 (notdexE = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f386])).
% 31.73/4.41 thf(f386,plain,(
% 31.73/4.41 (notdexE = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f385])).
% 31.73/4.41 thf(f385,plain,(
% 31.73/4.41 (notdexE = ! [X0 : $i > $o,X1] : (~? [X2] : ((X0 @ X2) & (in @ X2 @ X1)) => ! [X3] : ((in @ X3 @ X1) => ~(X0 @ X3))))),
% 31.73/4.41 inference(rectify,[],[f61])).
% 31.73/4.41 thf(f61,axiom,(
% 31.73/4.41 (notdexE = ! [X0 : $i > $o,X3] : (~? [X1] : ((X0 @ X1) & (in @ X1 @ X3)) => ! [X1] : ((in @ X1 @ X3) => ~(X0 @ X1))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdexE)).
% 31.73/4.41 thf(f649,plain,(
% 31.73/4.41 (prop2set2propI = (!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f516])).
% 31.73/4.41 thf(f516,plain,(
% 31.73/4.41 (prop2set2propI = (!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))))),
% 31.73/4.41 inference(fool_elimination,[],[f515])).
% 31.73/4.41 thf(f515,plain,(
% 31.73/4.41 (! [X0 : $o] : (X0 => (set2prop @ (prop2set @ X0))) = prop2set2propI)),
% 31.73/4.41 inference(rectify,[],[f60])).
% 31.73/4.41 thf(f60,axiom,(
% 31.73/4.41 (! [X0 : $o] : (X0 => (set2prop @ (prop2set @ X0))) = prop2set2propI)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2set2propI)).
% 31.73/4.41 thf(f720,plain,(
% 31.73/4.41 (prop2setI = (!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f341])).
% 31.73/4.41 thf(f341,plain,(
% 31.73/4.41 (prop2setI = (!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))))),
% 31.73/4.41 inference(fool_elimination,[],[f340])).
% 31.73/4.41 thf(f340,plain,(
% 31.73/4.41 (prop2setI = ! [X0 : $o] : (X0 => (in @ emptyset @ (prop2set @ X0))))),
% 31.73/4.41 inference(rectify,[],[f59])).
% 31.73/4.41 thf(f59,axiom,(
% 31.73/4.41 (prop2setI = ! [X0 : $o] : (X0 => (in @ emptyset @ (prop2set @ X0))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setI)).
% 31.73/4.41 thf(f787,plain,(
% 31.73/4.41 (quantDeMorgan4 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f568])).
% 31.73/4.41 thf(f568,plain,(
% 31.73/4.41 (quantDeMorgan4 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f567])).
% 31.73/4.41 thf(f567,plain,(
% 31.73/4.41 (! [X0,X1 : $i > $o] : (? [X2] : (~(X1 @ X2) & (in @ X2 @ X0)) => ~! [X3] : ((in @ X3 @ X0) => (X1 @ X3))) = quantDeMorgan4)),
% 31.73/4.41 inference(rectify,[],[f58])).
% 31.73/4.41 thf(f58,axiom,(
% 31.73/4.41 (! [X3,X0 : $i > $o] : (? [X1] : (~(X0 @ X1) & (in @ X1 @ X3)) => ~! [X1] : ((in @ X1 @ X3) => (X0 @ X1))) = quantDeMorgan4)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan4)).
% 31.73/4.41 thf(f666,plain,(
% 31.73/4.41 (quantDeMorgan3 = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f552])).
% 31.73/4.41 thf(f552,plain,(
% 31.73/4.41 (quantDeMorgan3 = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f551])).
% 31.73/4.41 thf(f551,plain,(
% 31.73/4.41 (! [X0 : $i > $o,X1] : (~? [X2] : ((X0 @ X2) & (in @ X2 @ X1)) => ! [X3] : ((in @ X3 @ X1) => ~(X0 @ X3))) = quantDeMorgan3)),
% 31.73/4.41 inference(rectify,[],[f57])).
% 31.73/4.41 thf(f57,axiom,(
% 31.73/4.41 (! [X0 : $i > $o,X3] : (~? [X1] : ((X0 @ X1) & (in @ X1 @ X3)) => ! [X1] : ((in @ X1 @ X3) => ~(X0 @ X1))) = quantDeMorgan3)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan3)).
% 31.73/4.41 thf(f716,plain,(
% 31.73/4.41 (quantDeMorgan2 = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f378])).
% 31.73/4.41 thf(f378,plain,(
% 31.73/4.41 (quantDeMorgan2 = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f377])).
% 31.73/4.41 thf(f377,plain,(
% 31.73/4.41 (quantDeMorgan2 = ! [X0 : $i > $o,X1] : (! [X2] : ((in @ X2 @ X1) => ~(X0 @ X2)) => ~? [X3] : ((X0 @ X3) & (in @ X3 @ X1))))),
% 31.73/4.41 inference(rectify,[],[f56])).
% 31.73/4.41 thf(f56,axiom,(
% 31.73/4.41 (quantDeMorgan2 = ! [X0 : $i > $o,X3] : (! [X1] : ((in @ X1 @ X3) => ~(X0 @ X1)) => ~? [X1] : ((X0 @ X1) & (in @ X1 @ X3))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan2)).
% 31.73/4.41 thf(f771,plain,(
% 31.73/4.41 (quantDeMorgan1 = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2)))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f580])).
% 31.73/4.41 thf(f580,plain,(
% 31.73/4.41 (quantDeMorgan1 = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2)))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f579])).
% 31.73/4.41 thf(f579,plain,(
% 31.73/4.41 (quantDeMorgan1 = ! [X0 : $i > $o,X1] : (~! [X2] : ((in @ X2 @ X1) => (X0 @ X2)) => ? [X3] : (~(X0 @ X3) & (in @ X3 @ X1))))),
% 31.73/4.41 inference(rectify,[],[f55])).
% 31.73/4.41 thf(f55,axiom,(
% 31.73/4.41 (quantDeMorgan1 = ! [X0 : $i > $o,X3] : (~! [X1] : ((in @ X1 @ X3) => (X0 @ X1)) => ? [X1] : (~(X0 @ X1) & (in @ X1 @ X3))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan1)).
% 31.73/4.41 thf(f711,plain,(
% 31.73/4.41 (vacuousDall = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ Y0)))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f339])).
% 31.73/4.41 thf(f339,plain,(
% 31.73/4.41 (vacuousDall = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ Y0)))))))),
% 31.73/4.41 inference(fool_elimination,[],[f338])).
% 31.73/4.41 thf(f338,plain,(
% 31.73/4.41 (! [X0 : $i > $o,X1] : ((in @ X1 @ emptyset) => (X0 @ X1)) = vacuousDall)),
% 31.73/4.41 inference(rectify,[],[f54])).
% 31.73/4.41 thf(f54,axiom,(
% 31.73/4.41 (! [X0 : $i > $o,X1] : ((in @ X1 @ emptyset) => (X0 @ X1)) = vacuousDall)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall)).
% 31.73/4.41 thf(f644,plain,(
% 31.73/4.41 (emptyE1 = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2)))) => $false)))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f263])).
% 31.73/4.41 thf(f263,plain,(
% 31.73/4.41 (emptyE1 = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((emptyset = (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2)))) => $false)))))))),
% 31.73/4.41 inference(fool_elimination,[],[f262])).
% 31.73/4.41 thf(f262,plain,(
% 31.73/4.41 (! [X0 : $i > $o,X1] : (? [X2] : ((in @ X2 @ X1) & (X0 @ X2)) => ((emptyset = (dsetconstr @ X1 @ (^[X3 : $i] : (X0 @ X3)))) => $false)) = emptyE1)),
% 31.73/4.41 inference(rectify,[],[f53])).
% 31.73/4.41 thf(f53,axiom,(
% 31.73/4.41 (! [X0 : $i > $o,X3] : (? [X1] : ((in @ X1 @ X3) & (X0 @ X1)) => ((emptyset = (dsetconstr @ X3 @ (^[X1 : $i] : (X0 @ X1)))) => $false)) = emptyE1)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyE1)).
% 31.73/4.41 thf(f737,plain,(
% 31.73/4.41 (upairsetIR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f372])).
% 31.73/4.41 thf(f372,plain,(
% 31.73/4.41 (upairsetIR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f371])).
% 31.73/4.41 thf(f371,plain,(
% 31.73/4.41 (! [X0,X1] : (in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))) = upairsetIR)),
% 31.73/4.41 inference(rectify,[],[f52])).
% 31.73/4.41 thf(f52,axiom,(
% 31.73/4.41 (! [X2,X1] : (in @ X2 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset))) = upairsetIR)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIR)).
% 31.73/4.41 thf(f785,plain,(
% 31.73/4.41 (upairsetIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f215])).
% 31.73/4.41 thf(f215,plain,(
% 31.73/4.41 (upairsetIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f214])).
% 31.73/4.41 thf(f214,plain,(
% 31.73/4.41 (upairsetIL = ! [X0,X1] : (in @ X0 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))))),
% 31.73/4.41 inference(rectify,[],[f51])).
% 31.73/4.41 thf(f51,axiom,(
% 31.73/4.41 (upairsetIL = ! [X1,X2] : (in @ X1 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIL)).
% 31.73/4.41 thf(f742,plain,(
% 31.73/4.41 (upairsetE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f410])).
% 31.73/4.41 thf(f410,plain,(
% 31.73/4.41 (upairsetE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f409])).
% 31.73/4.41 thf(f409,plain,(
% 31.73/4.41 (upairsetE = ! [X0,X1,X2] : ((in @ X2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) => ((X1 = X2) | (X0 = X2))))),
% 31.73/4.41 inference(rectify,[],[f50])).
% 31.73/4.41 thf(f50,axiom,(
% 31.73/4.41 (upairsetE = ! [X1,X2,X8] : ((in @ X8 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset))) => ((X2 = X8) | (X1 = X8))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetE)).
% 31.73/4.41 thf(f685,plain,(
% 31.73/4.41 (singletonsswitch = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f444])).
% 31.73/4.41 thf(f444,plain,(
% 31.73/4.41 (singletonsswitch = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f443])).
% 31.73/4.41 thf(f443,plain,(
% 31.73/4.41 (! [X0,X1] : ((in @ X1 @ (setadjoin @ X0 @ emptyset)) => (in @ X0 @ (setadjoin @ X1 @ emptyset))) = singletonsswitch)),
% 31.73/4.41 inference(rectify,[],[f49])).
% 31.73/4.41 thf(f49,axiom,(
% 31.73/4.41 (! [X2,X1] : ((in @ X1 @ (setadjoin @ X2 @ emptyset)) => (in @ X2 @ (setadjoin @ X1 @ emptyset))) = singletonsswitch)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsswitch)).
% 31.73/4.41 thf(f793,plain,(
% 31.73/4.41 (eqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f488])).
% 31.73/4.41 thf(f488,plain,(
% 31.73/4.41 (eqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y0 @ (setadjoin @ Y1 @ emptyset))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f487])).
% 31.73/4.41 thf(f487,plain,(
% 31.73/4.41 (! [X0,X1] : ((X0 = X1) => (in @ X1 @ (setadjoin @ X0 @ emptyset))) = eqinunit)),
% 31.73/4.41 inference(rectify,[],[f48])).
% 31.73/4.41 thf(f48,axiom,(
% 31.73/4.41 (! [X2,X1] : ((X1 = X2) => (in @ X1 @ (setadjoin @ X2 @ emptyset))) = eqinunit)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit)).
% 31.73/4.41 thf(f671,plain,(
% 31.73/4.41 (notinsingleton = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f438])).
% 31.73/4.41 thf(f438,plain,(
% 31.73/4.41 (notinsingleton = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f437])).
% 31.73/4.41 thf(f437,plain,(
% 31.73/4.41 (! [X0,X1] : ((X0 != X1) => ~(in @ X1 @ (setadjoin @ X0 @ emptyset))) = notinsingleton)),
% 31.73/4.41 inference(rectify,[],[f47])).
% 31.73/4.41 thf(f47,axiom,(
% 31.73/4.41 (! [X1,X2] : ((X1 != X2) => ~(in @ X2 @ (setadjoin @ X1 @ emptyset))) = notinsingleton)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinsingleton)).
% 31.73/4.41 thf(f618,plain,(
% 31.73/4.41 (uniqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f235])).
% 31.73/4.41 thf(f235,plain,(
% 31.73/4.41 (uniqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))))),
% 31.73/4.41 inference(fool_elimination,[],[f234])).
% 31.73/4.41 thf(f234,plain,(
% 31.73/4.41 (! [X0,X1] : ((in @ X1 @ (setadjoin @ X0 @ emptyset)) => (X0 = X1)) = uniqinunit)),
% 31.73/4.41 inference(rectify,[],[f46])).
% 31.73/4.41 thf(f46,axiom,(
% 31.73/4.41 (! [X2,X1] : ((in @ X1 @ (setadjoin @ X2 @ emptyset)) => (X1 = X2)) = uniqinunit)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit)).
% 31.73/4.41 thf(f803,plain,(
% 31.73/4.41 (nonemptyImpWitness = (!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (~ (emptyset = Y1))) @ Y0) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))))),
% 31.73/4.41 inference(definition_unfolding,[],[f784,f648])).
% 31.73/4.41 thf(f648,plain,(
% 31.73/4.41 (nonempty = (^[Y0 : $i]: (~ (emptyset = Y0))))),
% 31.73/4.41 inference(cnf_transformation,[],[f448])).
% 31.73/4.41 thf(f448,plain,(
% 31.73/4.41 (nonempty = (^[Y0 : $i]: (~ (emptyset = Y0))))),
% 31.73/4.41 inference(fool_elimination,[],[f447])).
% 31.73/4.41 thf(f447,plain,(
% 31.73/4.41 ((^[X0 : $i] : ((emptyset != X0))) = nonempty)),
% 31.73/4.41 inference(rectify,[],[f27])).
% 31.73/4.41 thf(f27,axiom,(
% 31.73/4.41 ((^[X1 : $i] : ((emptyset != X1))) = nonempty)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty)).
% 31.73/4.41 thf(f784,plain,(
% 31.73/4.41 (nonemptyImpWitness = (!! @ $i @ (^[Y0 : $i]: ((nonempty @ Y0) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f350])).
% 31.73/4.41 thf(f350,plain,(
% 31.73/4.41 (nonemptyImpWitness = (!! @ $i @ (^[Y0 : $i]: ((nonempty @ Y0) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f349])).
% 31.73/4.41 thf(f349,plain,(
% 31.73/4.41 (! [X0] : ((nonempty @ X0) => ? [X1] : ((in @ X1 @ X0) & $true)) = nonemptyImpWitness)),
% 31.73/4.41 inference(rectify,[],[f45])).
% 31.73/4.41 thf(f45,axiom,(
% 31.73/4.41 (! [X3] : ((nonempty @ X3) => ? [X1] : ((in @ X1 @ X3) & $true)) = nonemptyImpWitness)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyImpWitness)).
% 31.73/4.41 thf(f802,plain,(
% 31.73/4.41 (exuE2 = (!! @ ($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 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))))),
% 31.73/4.41 inference(definition_unfolding,[],[f617,f598])).
% 31.73/4.41 thf(f617,plain,(
% 31.73/4.41 (exuE2 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f498])).
% 31.73/4.41 thf(f498,plain,(
% 31.73/4.41 (exuE2 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f497])).
% 31.73/4.41 thf(f497,plain,(
% 31.73/4.41 (exuE2 = ! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ? [X2] : ! [X3] : ((X2 = X3) <=> (X0 @ X3))))),
% 31.73/4.41 inference(rectify,[],[f44])).
% 31.73/4.41 thf(f44,axiom,(
% 31.73/4.41 (exuE2 = ! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ? [X1] : ! [X2] : ((X1 = X2) <=> (X0 @ X2))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE2)).
% 31.73/4.41 thf(f719,plain,(
% 31.73/4.41 (subPowSU = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f570])).
% 31.73/4.41 thf(f570,plain,(
% 31.73/4.41 (subPowSU = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f569])).
% 31.73/4.41 thf(f569,plain,(
% 31.73/4.41 (! [X0,X1] : ((in @ X1 @ X0) => (in @ X1 @ (powerset @ (setunion @ X0)))) = subPowSU)),
% 31.73/4.41 inference(rectify,[],[f43])).
% 31.73/4.41 thf(f43,axiom,(
% 31.73/4.41 (! [X3,X1] : ((in @ X1 @ X3) => (in @ X1 @ (powerset @ (setunion @ X3)))) = subPowSU)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subPowSU)).
% 31.73/4.41 thf(f687,plain,(
% 31.73/4.41 (setunionE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => Y2)))) => Y2)))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f293])).
% 31.73/4.41 thf(f293,plain,(
% 31.73/4.41 (setunionE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => ((in @ Y3 @ Y0) => Y2)))) => Y2)))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f292])).
% 31.73/4.41 thf(f292,plain,(
% 31.73/4.41 (setunionE = ! [X0,X1] : ((in @ X0 @ (setunion @ X1)) => ! [X2 : $o] : (! [X3] : ((in @ X0 @ X3) => ((in @ X3 @ X1) => X2)) => X2)))),
% 31.73/4.41 inference(rectify,[],[f42])).
% 31.73/4.41 thf(f42,axiom,(
% 31.73/4.41 (setunionE = ! [X1,X3] : ((in @ X1 @ (setunion @ X3)) => ! [X0 : $o] : (! [X4] : ((in @ X1 @ X4) => ((in @ X4 @ X3) => X0)) => X0)))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE)).
% 31.73/4.41 thf(f758,plain,(
% 31.73/4.41 (setunionI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f344])).
% 31.73/4.41 thf(f344,plain,(
% 31.73/4.41 (setunionI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y2 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f343])).
% 31.73/4.41 thf(f343,plain,(
% 31.73/4.41 (setunionI = ! [X0,X1,X2] : ((in @ X2 @ X0) => ((in @ X0 @ X1) => (in @ X2 @ (setunion @ X1)))))),
% 31.73/4.41 inference(rectify,[],[f41])).
% 31.73/4.41 thf(f41,axiom,(
% 31.73/4.41 (setunionI = ! [X4,X3,X1] : ((in @ X1 @ X4) => ((in @ X4 @ X3) => (in @ X1 @ (setunion @ X3)))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionI)).
% 31.73/4.41 thf(f761,plain,(
% 31.73/4.41 (powersetE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f502])).
% 31.73/4.41 thf(f502,plain,(
% 31.73/4.41 (powersetE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (powerset @ Y2)) => ((in @ Y1 @ Y0) => (in @ Y1 @ Y2))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f501])).
% 31.73/4.41 thf(f501,plain,(
% 31.73/4.41 (! [X0,X1,X2] : ((in @ X2 @ (powerset @ X0)) => ((in @ X1 @ X2) => (in @ X1 @ X0))) = powersetE)),
% 31.73/4.41 inference(rectify,[],[f40])).
% 31.73/4.41 thf(f40,axiom,(
% 31.73/4.41 (! [X3,X1,X4] : ((in @ X4 @ (powerset @ X3)) => ((in @ X1 @ X4) => (in @ X1 @ X3))) = powersetE)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE)).
% 31.73/4.41 thf(f656,plain,(
% 31.73/4.41 (emptyInPowerset = (!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))))),
% 31.73/4.41 inference(cnf_transformation,[],[f454])).
% 31.73/4.41 thf(f454,plain,(
% 31.73/4.41 (emptyInPowerset = (!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))))),
% 31.73/4.41 inference(fool_elimination,[],[f453])).
% 31.73/4.41 thf(f453,plain,(
% 31.73/4.41 (! [X0] : (in @ emptyset @ (powerset @ X0)) = emptyInPowerset)),
% 31.73/4.41 inference(rectify,[],[f39])).
% 31.73/4.41 thf(f39,axiom,(
% 31.73/4.41 (! [X3] : (in @ emptyset @ (powerset @ X3)) = emptyInPowerset)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyInPowerset)).
% 31.73/4.41 thf(f745,plain,(
% 31.73/4.41 (emptyinPowerset = (!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))))),
% 31.73/4.41 inference(cnf_transformation,[],[f308])).
% 31.73/4.41 thf(f308,plain,(
% 31.73/4.41 (emptyinPowerset = (!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))))),
% 31.73/4.41 inference(fool_elimination,[],[f307])).
% 31.73/4.41 thf(f307,plain,(
% 31.73/4.41 (emptyinPowerset = ! [X0] : (in @ emptyset @ (powerset @ X0)))),
% 31.73/4.41 inference(rectify,[],[f38])).
% 31.73/4.41 thf(f38,axiom,(
% 31.73/4.41 (emptyinPowerset = ! [X3] : (in @ emptyset @ (powerset @ X3)))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinPowerset)).
% 31.73/4.41 thf(f660,plain,(
% 31.73/4.41 (powersetI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f281])).
% 31.73/4.41 thf(f281,plain,(
% 31.73/4.41 (powersetI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f280])).
% 31.73/4.41 thf(f280,plain,(
% 31.73/4.41 (powersetI = ! [X0,X1] : (! [X2] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0))))),
% 31.73/4.41 inference(rectify,[],[f37])).
% 31.73/4.41 thf(f37,axiom,(
% 31.73/4.41 (powersetI = ! [X3,X4] : (! [X1] : ((in @ X1 @ X4) => (in @ X1 @ X3)) => (in @ X4 @ (powerset @ X3))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI)).
% 31.73/4.41 thf(f779,plain,(
% 31.73/4.41 (setoftrueEq = (!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f508])).
% 31.73/4.41 thf(f508,plain,(
% 31.73/4.41 (setoftrueEq = (!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))))),
% 31.73/4.41 inference(fool_elimination,[],[f507])).
% 31.73/4.41 thf(f507,plain,(
% 31.73/4.41 (setoftrueEq = ! [X0] : (X0 = (dsetconstr @ X0 @ (^[X1 : $i] : ($true)))))),
% 31.73/4.41 inference(rectify,[],[f36])).
% 31.73/4.41 thf(f36,axiom,(
% 31.73/4.41 (setoftrueEq = ! [X3] : (X3 = (dsetconstr @ X3 @ (^[X1 : $i] : ($true)))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setoftrueEq)).
% 31.73/4.41 thf(f734,plain,(
% 31.73/4.41 (setadjoinOr = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f472])).
% 31.73/4.41 thf(f472,plain,(
% 31.73/4.41 (setadjoinOr = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => ((Y1 = Y0) | (in @ Y0 @ Y2))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f471])).
% 31.73/4.41 thf(f471,plain,(
% 31.73/4.41 (setadjoinOr = ! [X0,X1,X2] : ((in @ X2 @ (setadjoin @ X1 @ X0)) => ((in @ X2 @ X0) | (X1 = X2))))),
% 31.73/4.41 inference(rectify,[],[f35])).
% 31.73/4.41 thf(f35,axiom,(
% 31.73/4.41 (setadjoinOr = ! [X3,X1,X2] : ((in @ X2 @ (setadjoin @ X1 @ X3)) => ((in @ X2 @ X3) | (X1 = X2))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinOr)).
% 31.73/4.41 thf(f791,plain,(
% 31.73/4.41 (setadjoinE = (!! @ $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))))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f306])).
% 31.73/4.41 thf(f306,plain,(
% 31.73/4.41 (setadjoinE = (!! @ $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))))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f305])).
% 31.73/4.41 thf(f305,plain,(
% 31.73/4.41 (setadjoinE = ! [X0,X1,X2] : ((in @ X2 @ (setadjoin @ X1 @ X0)) => ! [X3 : $o] : (((X1 = X2) => X3) => (((in @ X2 @ X0) => X3) => X3))))),
% 31.73/4.41 inference(rectify,[],[f34])).
% 31.73/4.41 thf(f34,axiom,(
% 31.73/4.41 (setadjoinE = ! [X3,X1,X2] : ((in @ X2 @ (setadjoin @ X1 @ X3)) => ! [X0 : $o] : (((X1 = X2) => X0) => (((in @ X2 @ X3) => X0) => X0))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinE)).
% 31.73/4.41 thf(f751,plain,(
% 31.73/4.41 (setadjoinIR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f243])).
% 31.73/4.41 thf(f243,plain,(
% 31.73/4.41 (setadjoinIR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f242])).
% 31.73/4.41 thf(f242,plain,(
% 31.73/4.41 (! [X0,X1,X2] : ((in @ X0 @ X2) => (in @ X0 @ (setadjoin @ X1 @ X2))) = setadjoinIR)),
% 31.73/4.41 inference(rectify,[],[f33])).
% 31.73/4.41 thf(f33,axiom,(
% 31.73/4.41 (! [X2,X1,X3] : ((in @ X2 @ X3) => (in @ X2 @ (setadjoin @ X1 @ X3))) = setadjoinIR)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIR)).
% 31.73/4.41 thf(f632,plain,(
% 31.73/4.41 (emptyinunitempty = (in @ emptyset @ (setadjoin @ emptyset @ emptyset)))),
% 31.73/4.41 inference(cnf_transformation,[],[f335])).
% 31.73/4.41 thf(f335,plain,(
% 31.73/4.41 (emptyinunitempty = (in @ emptyset @ (setadjoin @ emptyset @ emptyset)))),
% 31.73/4.41 inference(fool_elimination,[],[f32])).
% 31.73/4.41 thf(f32,axiom,(
% 31.73/4.41 (emptyinunitempty = (in @ emptyset @ (setadjoin @ emptyset @ emptyset)))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinunitempty)).
% 31.73/4.41 thf(f638,plain,(
% 31.73/4.41 (setadjoinIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f301])).
% 31.73/4.41 thf(f301,plain,(
% 31.73/4.41 (setadjoinIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))))),
% 31.73/4.41 inference(fool_elimination,[],[f300])).
% 31.73/4.41 thf(f300,plain,(
% 31.73/4.41 (setadjoinIL = ! [X0,X1] : (in @ X1 @ (setadjoin @ X1 @ X0)))),
% 31.73/4.41 inference(rectify,[],[f31])).
% 31.73/4.41 thf(f31,axiom,(
% 31.73/4.41 (setadjoinIL = ! [X2,X1] : (in @ X1 @ (setadjoin @ X1 @ X2)))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL)).
% 31.73/4.41 thf(f801,plain,(
% 31.73/4.41 (nonemptyI1 = (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => ((^[Y1 : $i]: (~ (emptyset = Y1))) @ Y0)))))),
% 31.73/4.41 inference(definition_unfolding,[],[f732,f648])).
% 31.73/4.41 thf(f732,plain,(
% 31.73/4.41 (nonemptyI1 = (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (nonempty @ Y0)))))),
% 31.73/4.41 inference(cnf_transformation,[],[f442])).
% 31.73/4.41 thf(f442,plain,(
% 31.73/4.41 (nonemptyI1 = (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (nonempty @ Y0)))))),
% 31.73/4.41 inference(fool_elimination,[],[f441])).
% 31.73/4.41 thf(f441,plain,(
% 31.73/4.41 (! [X0] : (? [X1] : (in @ X1 @ X0) => (nonempty @ X0)) = nonemptyI1)),
% 31.73/4.41 inference(rectify,[],[f30])).
% 31.73/4.41 thf(f30,axiom,(
% 31.73/4.41 (! [X3] : (? [X1] : (in @ X1 @ X3) => (nonempty @ X3)) = nonemptyI1)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI1)).
% 31.73/4.41 thf(f800,plain,(
% 31.73/4.41 (nonemptyI = (!! @ $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)))))))))))))),
% 31.73/4.41 inference(definition_unfolding,[],[f611,f648])).
% 31.73/4.41 thf(f611,plain,(
% 31.73/4.41 (nonemptyI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (nonempty @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f534])).
% 31.73/4.41 thf(f534,plain,(
% 31.73/4.41 (nonemptyI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (nonempty @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f533])).
% 31.73/4.41 thf(f533,plain,(
% 31.73/4.41 (nonemptyI = ! [X0 : $i > $o,X1,X2] : ((in @ X1 @ X2) => ((X0 @ X1) => (nonempty @ (dsetconstr @ X2 @ (^[X3 : $i] : (X0 @ X3)))))))),
% 31.73/4.41 inference(rectify,[],[f29])).
% 31.73/4.41 thf(f29,axiom,(
% 31.73/4.41 (nonemptyI = ! [X0 : $i > $o,X1,X3] : ((in @ X1 @ X3) => ((X0 @ X1) => (nonempty @ (dsetconstr @ X3 @ (^[X2 : $i] : (X0 @ X2)))))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI)).
% 31.73/4.41 thf(f799,plain,(
% 31.73/4.41 (nonemptyE1 = (!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (~ (emptyset = Y1))) @ Y0) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))))),
% 31.73/4.41 inference(definition_unfolding,[],[f623,f648])).
% 31.73/4.41 thf(f623,plain,(
% 31.73/4.41 (nonemptyE1 = (!! @ $i @ (^[Y0 : $i]: ((nonempty @ Y0) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f390])).
% 31.73/4.41 thf(f390,plain,(
% 31.73/4.41 (nonemptyE1 = (!! @ $i @ (^[Y0 : $i]: ((nonempty @ Y0) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))))),
% 31.73/4.41 inference(fool_elimination,[],[f389])).
% 31.73/4.41 thf(f389,plain,(
% 31.73/4.41 (nonemptyE1 = ! [X0] : ((nonempty @ X0) => ? [X1] : (in @ X1 @ X0)))),
% 31.73/4.41 inference(rectify,[],[f28])).
% 31.73/4.41 thf(f28,axiom,(
% 31.73/4.41 (nonemptyE1 = ! [X3] : ((nonempty @ X3) => ? [X1] : (in @ X1 @ X3)))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1)).
% 31.73/4.41 thf(f726,plain,(
% 31.73/4.41 (setbeta = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))) = (Y2 @ Y1))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f271])).
% 31.73/4.41 thf(f271,plain,(
% 31.73/4.41 (setbeta = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))) = (Y2 @ Y1))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f270])).
% 31.73/4.41 thf(f270,plain,(
% 31.73/4.41 (setbeta = ! [X0 : $i > $o,X1,X2] : ((in @ X1 @ X2) => ((in @ X1 @ (dsetconstr @ X2 @ (^[X3 : $i] : (X0 @ X3)))) <=> (X0 @ X1))))),
% 31.73/4.41 inference(rectify,[],[f26])).
% 31.73/4.41 thf(f26,axiom,(
% 31.73/4.41 (setbeta = ! [X0 : $i > $o,X1,X3] : ((in @ X1 @ X3) => ((in @ X1 @ (dsetconstr @ X3 @ (^[X2 : $i] : (X0 @ X2)))) <=> (X0 @ X1))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setbeta)).
% 31.73/4.41 thf(f624,plain,(
% 31.73/4.41 (noeltsimpempty = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))))),
% 31.73/4.41 inference(cnf_transformation,[],[f287])).
% 31.73/4.41 thf(f287,plain,(
% 31.73/4.41 (noeltsimpempty = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))))),
% 31.73/4.41 inference(fool_elimination,[],[f286])).
% 31.73/4.41 thf(f286,plain,(
% 31.73/4.41 (noeltsimpempty = ! [X0] : (! [X1] : ~(in @ X1 @ X0) => (emptyset = X0)))),
% 31.73/4.41 inference(rectify,[],[f25])).
% 31.73/4.41 thf(f25,axiom,(
% 31.73/4.41 (noeltsimpempty = ! [X3] : (! [X1] : ~(in @ X1 @ X3) => (emptyset = X3)))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty)).
% 31.73/4.41 thf(f634,plain,(
% 31.73/4.41 (emptyI = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))))),
% 31.73/4.41 inference(cnf_transformation,[],[f314])).
% 31.73/4.41 thf(f314,plain,(
% 31.73/4.41 (emptyI = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))))),
% 31.73/4.41 inference(fool_elimination,[],[f313])).
% 31.73/4.41 thf(f313,plain,(
% 31.73/4.41 (! [X0] : (! [X1] : ~(in @ X1 @ X0) => (emptyset = X0)) = emptyI)),
% 31.73/4.41 inference(rectify,[],[f24])).
% 31.73/4.41 thf(f24,axiom,(
% 31.73/4.41 (! [X3] : (! [X1] : ~(in @ X1 @ X3) => (emptyset = X3)) = emptyI)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyI)).
% 31.73/4.41 thf(f625,plain,(
% 31.73/4.41 (setext = (!! @ $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))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f562])).
% 31.73/4.41 thf(f562,plain,(
% 31.73/4.41 (setext = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f561])).
% 31.73/4.41 thf(f561,plain,(
% 31.73/4.41 (setext = ! [X0,X1] : (! [X2] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (! [X3] : ((in @ X3 @ X0) => (in @ X3 @ X1)) => (X0 = X1))))),
% 31.73/4.41 inference(rectify,[],[f23])).
% 31.73/4.41 thf(f23,axiom,(
% 31.73/4.41 (setext = ! [X4,X3] : (! [X1] : ((in @ X1 @ X3) => (in @ X1 @ X4)) => (! [X1] : ((in @ X1 @ X4) => (in @ X1 @ X3)) => (X3 = X4))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setext)).
% 31.73/4.41 thf(f798,plain,(
% 31.73/4.41 (exuE3e = (!! @ ($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 : $i]: (Y0 @ Y1)))))))),
% 31.73/4.41 inference(definition_unfolding,[],[f692,f598])).
% 31.73/4.41 thf(f692,plain,(
% 31.73/4.41 (exuE3e = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f408])).
% 31.73/4.41 thf(f408,plain,(
% 31.73/4.41 (exuE3e = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 31.73/4.41 inference(fool_elimination,[],[f407])).
% 31.73/4.41 thf(f407,plain,(
% 31.73/4.41 (! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ? [X2] : (X0 @ X2)) = exuE3e)),
% 31.73/4.41 inference(rectify,[],[f22])).
% 31.73/4.41 thf(f22,axiom,(
% 31.73/4.41 (! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ? [X1] : (X0 @ X1)) = exuE3e)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3e)).
% 31.73/4.41 thf(f777,plain,(
% 31.73/4.41 (notinemptyset = (!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))))),
% 31.73/4.41 inference(cnf_transformation,[],[f556])).
% 31.73/4.41 thf(f556,plain,(
% 31.73/4.41 (notinemptyset = (!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))))),
% 31.73/4.41 inference(fool_elimination,[],[f555])).
% 31.73/4.41 thf(f555,plain,(
% 31.73/4.41 (! [X0] : ~(in @ X0 @ emptyset) = notinemptyset)),
% 31.73/4.41 inference(rectify,[],[f21])).
% 31.73/4.41 thf(f21,axiom,(
% 31.73/4.41 (! [X1] : ~(in @ X1 @ emptyset) = notinemptyset)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinemptyset)).
% 31.73/4.41 thf(f653,plain,(
% 31.73/4.41 (emptysetimpfalse = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))))),
% 31.73/4.41 inference(cnf_transformation,[],[f416])).
% 31.73/4.41 thf(f416,plain,(
% 31.73/4.41 (emptysetimpfalse = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))))),
% 31.73/4.41 inference(fool_elimination,[],[f415])).
% 31.73/4.41 thf(f415,plain,(
% 31.73/4.41 (emptysetimpfalse = ! [X0] : ((in @ X0 @ emptyset) => $false))),
% 31.73/4.41 inference(rectify,[],[f20])).
% 31.73/4.41 thf(f20,axiom,(
% 31.73/4.41 (emptysetimpfalse = ! [X1] : ((in @ X1 @ emptyset) => $false))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse)).
% 31.73/4.41 thf(f645,plain,(
% 31.73/4.41 (emptysetE = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f576])).
% 31.73/4.41 thf(f576,plain,(
% 31.73/4.41 (emptysetE = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))))),
% 31.73/4.41 inference(fool_elimination,[],[f575])).
% 31.73/4.41 thf(f575,plain,(
% 31.73/4.41 (! [X0] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1) = emptysetE)),
% 31.73/4.41 inference(rectify,[],[f19])).
% 31.73/4.41 thf(f19,axiom,(
% 31.73/4.41 (! [X1] : ((in @ X1 @ emptyset) => ! [X0 : $o] : X0) = emptysetE)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE)).
% 31.73/4.41 thf(f600,plain,(
% 31.73/4.41 (prop2setE = (!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f456])).
% 31.73/4.41 thf(f456,plain,(
% 31.73/4.41 (prop2setE = (!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))))),
% 31.73/4.41 inference(fool_elimination,[],[f455])).
% 31.73/4.41 thf(f455,plain,(
% 31.73/4.41 (prop2setE = ! [X0 : $o,X1] : ((in @ X1 @ (prop2set @ X0)) => X0))),
% 31.73/4.41 inference(rectify,[],[f18])).
% 31.73/4.41 thf(f18,axiom,(
% 31.73/4.41 (prop2setE = ! [X0 : $o,X1] : ((in @ X1 @ (prop2set @ X0)) => X0))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setE)).
% 31.73/4.41 thf(f797,plain,(
% 31.73/4.41 (exuE1 = (!! @ ($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 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))))),
% 31.73/4.41 inference(definition_unfolding,[],[f661,f598])).
% 31.73/4.41 thf(f661,plain,(
% 31.73/4.41 (exuE1 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f364])).
% 31.73/4.41 thf(f364,plain,(
% 31.73/4.41 (exuE1 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f363])).
% 31.73/4.41 thf(f363,plain,(
% 31.73/4.41 (! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ? [X2] : ((X0 @ X2) & ! [X3] : ((X0 @ X3) => (X2 = X3)))) = exuE1)),
% 31.73/4.41 inference(rectify,[],[f17])).
% 31.73/4.41 thf(f17,axiom,(
% 31.73/4.41 (! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ? [X1] : ((X0 @ X1) & ! [X2] : ((X0 @ X2) => (X1 = X2)))) = exuE1)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE1)).
% 31.73/4.41 thf(f766,plain,(
% 31.73/4.41 (dsetconstrER = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3)))) => (Y0 @ Y1)))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f295])).
% 31.73/4.41 thf(f295,plain,(
% 31.73/4.41 (dsetconstrER = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3)))) => (Y0 @ Y1)))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f294])).
% 31.73/4.41 thf(f294,plain,(
% 31.73/4.41 (! [X0,X1,X2 : $i > $o] : ((in @ X1 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X2 @ X3)))) => (X2 @ X1)) = dsetconstrER)),
% 31.73/4.41 inference(rectify,[],[f16])).
% 31.73/4.41 thf(f16,axiom,(
% 31.73/4.41 (! [X3,X1,X0 : $i > $o] : ((in @ X1 @ (dsetconstr @ X3 @ (^[X2 : $i] : (X0 @ X2)))) => (X0 @ X1)) = dsetconstrER)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER)).
% 31.73/4.41 thf(f621,plain,(
% 31.73/4.41 (dsetconstrEL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (in @ Y0 @ Y1)))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f540])).
% 31.73/4.41 thf(f540,plain,(
% 31.73/4.41 (dsetconstrEL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (in @ Y0 @ Y1)))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f539])).
% 31.73/4.41 thf(f539,plain,(
% 31.73/4.41 (! [X0 : $i > $o,X1,X2] : ((in @ X2 @ (dsetconstr @ X1 @ (^[X3 : $i] : (X0 @ X3)))) => (in @ X2 @ X1)) = dsetconstrEL)),
% 31.73/4.41 inference(rectify,[],[f15])).
% 31.73/4.41 thf(f15,axiom,(
% 31.73/4.41 (! [X0 : $i > $o,X3,X1] : ((in @ X1 @ (dsetconstr @ X3 @ (^[X2 : $i] : (X0 @ X2)))) => (in @ X1 @ X3)) = dsetconstrEL)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL)).
% 31.73/4.41 thf(f615,plain,(
% 31.73/4.41 (dsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f574])).
% 31.73/4.41 thf(f574,plain,(
% 31.73/4.41 (dsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ Y0) => ((Y2 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f573])).
% 31.73/4.41 thf(f573,plain,(
% 31.73/4.41 (dsetconstrI = ! [X0 : $i > $o,X1,X2] : ((in @ X1 @ X2) => ((X0 @ X1) => (in @ X1 @ (dsetconstr @ X2 @ (^[X3 : $i] : (X0 @ X3)))))))),
% 31.73/4.41 inference(rectify,[],[f14])).
% 31.73/4.41 thf(f14,axiom,(
% 31.73/4.41 (dsetconstrI = ! [X0 : $i > $o,X1,X3] : ((in @ X1 @ X3) => ((X0 @ X1) => (in @ X1 @ (dsetconstr @ X3 @ (^[X2 : $i] : (X0 @ X2)))))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI)).
% 31.73/4.41 thf(f796,plain,(
% 31.73/4.41 (descrp = (!! @ ($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 : $i]: (Y0 @ Y1))))))))),
% 31.73/4.41 inference(definition_unfolding,[],[f743,f598])).
% 31.73/4.41 thf(f743,plain,(
% 31.73/4.41 (descrp = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (Y0 @ (descr @ (^[Y1 : $i]: (Y0 @ Y1))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f354])).
% 31.73/4.41 thf(f354,plain,(
% 31.73/4.41 (descrp = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (Y0 @ (descr @ (^[Y1 : $i]: (Y0 @ Y1))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f353])).
% 31.73/4.41 thf(f353,plain,(
% 31.73/4.41 (! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => (X0 @ (descr @ (^[X2 : $i] : (X0 @ X2))))) = descrp)),
% 31.73/4.41 inference(rectify,[],[f13])).
% 31.73/4.41 thf(f13,axiom,(
% 31.73/4.41 (! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => (X0 @ (descr @ (^[X1 : $i] : (X0 @ X1))))) = descrp)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',descrp)).
% 31.73/4.41 thf(f776,plain,(
% 31.73/4.41 (wellorderingAx = (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f436])).
% 31.73/4.41 thf(f436,plain,(
% 31.73/4.41 (wellorderingAx = (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ 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 @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (in @ Y5 @ Y3))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3)))) | (in @ Y4 @ Y5)))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f435])).
% 31.73/4.41 thf(f435,plain,(
% 31.73/4.41 (wellorderingAx = ! [X0] : ? [X1] : (! [X2] : ((in @ X2 @ X1) => ! [X3] : ((in @ X3 @ X2) => (in @ X3 @ X0))) & ! [X4,X5] : (((in @ X5 @ X0) & (in @ X4 @ X0)) => (! [X6] : ((in @ X6 @ X1) => ((in @ X4 @ X6) <=> (in @ X5 @ X6))) => (X4 = X5))) & ! [X7] : ((? [X8] : (in @ X8 @ X7) & ! [X9] : ((in @ X9 @ X7) => (in @ X9 @ X0))) => ? [X10,X11] : ((in @ X11 @ X1) & (in @ X10 @ X7) & ! [X12] : ((in @ X12 @ X1) => ((in @ X10 @ X12) | ! [X13] : ((in @ X13 @ X12) => (in @ X13 @ X11)))) & ~? [X14] : ((in @ X14 @ X11) & (in @ X14 @ X7)))) & ! [X15,X16] : (((in @ X15 @ X1) & (in @ X16 @ X1)) => (! [X17] : ((in @ X17 @ X16) => (in @ X17 @ X15)) | ! [X18] : ((in @ X18 @ X15) => (in @ X18 @ X16))))))),
% 31.73/4.41 inference(rectify,[],[f12])).
% 31.73/4.41 thf(f12,axiom,(
% 31.73/4.41 (wellorderingAx = ! [X3] : ? [X4] : (! [X5] : ((in @ X5 @ X4) => ! [X1] : ((in @ X1 @ X5) => (in @ X1 @ X3))) & ! [X2,X1] : (((in @ X1 @ X3) & (in @ X2 @ X3)) => (! [X5] : ((in @ X5 @ X4) => ((in @ X2 @ X5) <=> (in @ X1 @ X5))) => (X1 = X2))) & ! [X5] : ((? [X1] : (in @ X1 @ X5) & ! [X1] : ((in @ X1 @ X5) => (in @ X1 @ X3))) => ? [X1,X6] : ((in @ X6 @ X4) & (in @ X1 @ X5) & ! [X7] : ((in @ X7 @ X4) => ((in @ X1 @ X7) | ! [X2] : ((in @ X2 @ X7) => (in @ X2 @ X6)))) & ~? [X2] : ((in @ X2 @ X6) & (in @ X2 @ X5)))) & ! [X6,X5] : (((in @ X6 @ X4) & (in @ X5 @ X4)) => (! [X1] : ((in @ X1 @ X5) => (in @ X1 @ X6)) | ! [X1] : ((in @ X1 @ X6) => (in @ X1 @ X5))))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderingAx)).
% 31.73/4.41 thf(f789,plain,(
% 31.73/4.41 (foundationAx = (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f584])).
% 31.73/4.41 thf(f584,plain,(
% 31.73/4.41 (foundationAx = (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f583])).
% 31.73/4.41 thf(f583,plain,(
% 31.73/4.41 (foundationAx = ! [X0] : (? [X1] : (in @ X1 @ X0) => ? [X2] : (~? [X3] : ((in @ X3 @ X0) & (in @ X3 @ X2)) & (in @ X2 @ X0))))),
% 31.73/4.41 inference(rectify,[],[f11])).
% 31.73/4.41 thf(f11,axiom,(
% 31.73/4.41 (foundationAx = ! [X3] : (? [X1] : (in @ X1 @ X3) => ? [X4] : (~? [X1] : ((in @ X1 @ X3) & (in @ X1 @ X4)) & (in @ X4 @ X3))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',foundationAx)).
% 31.73/4.41 thf(f795,plain,(
% 31.73/4.41 (replAx = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5) => (Y4 = Y5)))))))) @ (^[Y3 : $i]: (Y1 @ Y2 @ Y3)))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))))),
% 31.73/4.41 inference(definition_unfolding,[],[f768,f598])).
% 31.73/4.41 thf(f768,plain,(
% 31.73/4.41 (replAx = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (exu @ (^[Y3 : $i]: (Y1 @ Y2 @ Y3)))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f506])).
% 31.73/4.41 thf(f506,plain,(
% 31.73/4.41 (replAx = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (exu @ (^[Y3 : $i]: (Y1 @ Y2 @ Y3)))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f505])).
% 31.73/4.41 thf(f505,plain,(
% 31.73/4.41 (replAx = ! [X0 : $i > $i > $o,X1] : (! [X2] : ((in @ X2 @ X1) => (exu @ (^[X3 : $i] : (X0 @ X2 @ X3)))) => ? [X4] : ! [X5] : ((in @ X5 @ X4) <=> ? [X6] : ((X0 @ X6 @ X5) & (in @ X6 @ X1)))))),
% 31.73/4.41 inference(rectify,[],[f10])).
% 31.73/4.41 thf(f10,axiom,(
% 31.73/4.41 (replAx = ! [X0 : $i > $i > $o,X3] : (! [X1] : ((in @ X1 @ X3) => (exu @ (^[X2 : $i] : (X0 @ X1 @ X2)))) => ? [X4] : ! [X1] : ((in @ X1 @ X4) <=> ? [X2] : ((X0 @ X2 @ X1) & (in @ X2 @ X3)))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',replAx)).
% 31.73/4.41 thf(f695,plain,(
% 31.73/4.41 (omegaIndAx = (!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f265])).
% 31.73/4.41 thf(f265,plain,(
% 31.73/4.41 (omegaIndAx = (!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f264])).
% 31.73/4.41 thf(f264,plain,(
% 31.73/4.41 (omegaIndAx = ! [X0] : ((! [X1] : (((in @ X1 @ omega) & (in @ X1 @ X0)) => (in @ (setadjoin @ X1 @ X1) @ X0)) & (in @ emptyset @ X0)) => ! [X2] : ((in @ X2 @ omega) => (in @ X2 @ X0))))),
% 31.73/4.41 inference(rectify,[],[f9])).
% 31.73/4.41 thf(f9,axiom,(
% 31.73/4.41 (omegaIndAx = ! [X3] : ((! [X1] : (((in @ X1 @ omega) & (in @ X1 @ X3)) => (in @ (setadjoin @ X1 @ X1) @ X3)) & (in @ emptyset @ X3)) => ! [X1] : ((in @ X1 @ omega) => (in @ X1 @ X3))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaIndAx)).
% 31.73/4.41 thf(f641,plain,(
% 31.73/4.41 (omegaSAx = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))))),
% 31.73/4.41 inference(cnf_transformation,[],[f518])).
% 31.73/4.41 thf(f518,plain,(
% 31.73/4.41 (omegaSAx = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))))),
% 31.73/4.41 inference(fool_elimination,[],[f517])).
% 31.73/4.41 thf(f517,plain,(
% 31.73/4.41 (omegaSAx = ! [X0] : ((in @ X0 @ omega) => (in @ (setadjoin @ X0 @ X0) @ omega)))),
% 31.73/4.41 inference(rectify,[],[f8])).
% 31.73/4.41 thf(f8,axiom,(
% 31.73/4.41 (omegaSAx = ! [X1] : ((in @ X1 @ omega) => (in @ (setadjoin @ X1 @ X1) @ omega)))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx)).
% 31.73/4.41 thf(f689,plain,(
% 31.73/4.41 (omega0Ax = (in @ emptyset @ omega))),
% 31.73/4.41 inference(cnf_transformation,[],[f595])).
% 31.73/4.41 thf(f595,plain,(
% 31.73/4.41 (omega0Ax = (in @ emptyset @ omega))),
% 31.73/4.41 inference(fool_elimination,[],[f7])).
% 31.73/4.41 thf(f7,axiom,(
% 31.73/4.41 (omega0Ax = (in @ emptyset @ omega))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega0Ax)).
% 31.73/4.41 thf(f606,plain,(
% 31.73/4.41 (setunionAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f269])).
% 31.73/4.41 thf(f269,plain,(
% 31.73/4.41 (setunionAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))) = (in @ Y1 @ (setunion @ Y0))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f268])).
% 31.73/4.41 thf(f268,plain,(
% 31.73/4.41 (! [X0,X1] : (? [X2] : ((in @ X0 @ X2) & (in @ X2 @ X1)) <=> (in @ X0 @ (setunion @ X1))) = setunionAx)),
% 31.73/4.41 inference(rectify,[],[f6])).
% 31.73/4.41 thf(f6,axiom,(
% 31.73/4.41 (! [X1,X3] : (? [X4] : ((in @ X1 @ X4) & (in @ X4 @ X3)) <=> (in @ X1 @ (setunion @ X3))) = setunionAx)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionAx)).
% 31.73/4.41 thf(f764,plain,(
% 31.73/4.41 (powersetAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f590])).
% 31.73/4.41 thf(f590,plain,(
% 31.73/4.41 (powersetAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) = (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f589])).
% 31.73/4.41 thf(f589,plain,(
% 31.73/4.41 (! [X0,X1] : ((in @ X0 @ (powerset @ X1)) <=> ! [X2] : ((in @ X2 @ X0) => (in @ X2 @ X1))) = powersetAx)),
% 31.73/4.41 inference(rectify,[],[f5])).
% 31.73/4.41 thf(f5,axiom,(
% 31.73/4.41 (! [X4,X3] : ((in @ X4 @ (powerset @ X3)) <=> ! [X1] : ((in @ X1 @ X4) => (in @ X1 @ X3))) = powersetAx)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetAx)).
% 31.73/4.41 thf(f665,plain,(
% 31.73/4.41 (setadjoinAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f412])).
% 31.73/4.41 thf(f412,plain,(
% 31.73/4.41 (setadjoinAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y0 @ Y1) | (Y2 = Y0)) = (in @ Y0 @ (setadjoin @ Y2 @ Y1))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f411])).
% 31.73/4.41 thf(f411,plain,(
% 31.73/4.41 (! [X0,X1,X2] : (((X0 = X2) | (in @ X2 @ X1)) <=> (in @ X2 @ (setadjoin @ X0 @ X1))) = setadjoinAx)),
% 31.73/4.41 inference(rectify,[],[f4])).
% 31.73/4.41 thf(f4,axiom,(
% 31.73/4.41 (! [X1,X3,X2] : (((X1 = X2) | (in @ X2 @ X3)) <=> (in @ X2 @ (setadjoin @ X1 @ X3))) = setadjoinAx)),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinAx)).
% 31.73/4.41 thf(f603,plain,(
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% 31.73/4.41 inference(cnf_transformation,[],[f426])).
% 31.73/4.41 thf(f426,plain,(
% 31.73/4.41 (emptysetAx = (!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))))),
% 31.73/4.41 inference(fool_elimination,[],[f425])).
% 31.73/4.41 thf(f425,plain,(
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% 31.73/4.41 inference(rectify,[],[f3])).
% 31.73/4.41 thf(f3,axiom,(
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% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx)).
% 31.73/4.41 thf(f612,plain,(
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% 31.73/4.41 inference(cnf_transformation,[],[f470])).
% 31.73/4.41 thf(f470,plain,(
% 31.73/4.41 (setextAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))))),
% 31.73/4.41 inference(fool_elimination,[],[f469])).
% 31.73/4.41 thf(f469,plain,(
% 31.73/4.41 (setextAx = ! [X0,X1] : (! [X2] : ((in @ X2 @ X0) <=> (in @ X2 @ X1)) => (X0 = X1)))),
% 31.73/4.41 inference(rectify,[],[f2])).
% 31.73/4.41 thf(f2,axiom,(
% 31.73/4.41 (setextAx = ! [X3,X4] : (! [X1] : ((in @ X1 @ X3) <=> (in @ X1 @ X4)) => (X3 = X4)))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextAx)).
% 31.73/4.41 thf(f748,plain,(
% 31.73/4.41 ($true = (~ (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 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y1 @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (ap @ Y1 @ Y2 @ Y0 @ Y3) @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.41 inference(cnf_transformation,[],[f460])).
% 31.73/4.41 thf(f460,plain,(
% 31.73/4.41 ($true = (~ (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 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y1 @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (ap @ Y1 @ Y2 @ Y0 @ Y3) @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.41 inference(fool_elimination,[],[f459])).
% 31.73/4.41 thf(f459,plain,(
% 31.73/4.41 ~(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 => ! [X0,X1,X2] : ((func @ X1 @ X0 @ X2) => ! [X3] : ((in @ X3 @ X1) => (in @ (ap @ X1 @ X0 @ X2 @ X3) @ X0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.41 inference(rectify,[],[f200])).
% 31.73/4.41 thf(f200,negated_conjecture,(
% 31.73/4.41 ~(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 => ! [X4,X3,X13] : ((func @ X3 @ X4 @ X13) => ! [X1] : ((in @ X1 @ X3) => (in @ (ap @ X3 @ X4 @ X13 @ X1) @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.41 inference(negated_conjecture,[],[f199])).
% 31.73/4.41 thf(f199,conjecture,(
% 31.73/4.41 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 => ! [X4,X3,X13] : ((func @ X3 @ X4 @ X13) => ! [X1] : ((in @ X1 @ X3) => (in @ (ap @ X3 @ X4 @ X13 @ X1) @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.73/4.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',app)).
% 31.73/4.41 % SZS output end Proof for theBenchmark
% 31.73/4.41 % (32125)------------------------------
% 31.73/4.41 % (32125)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 31.73/4.41 % (32125)Termination reason: Refutation
% 31.73/4.41
% 31.73/4.41 % (32125)Memory used [KB]: 199954
% 31.73/4.41 % (32125)Time elapsed: 1.129 s
% 31.73/4.41 % (32125)Instructions burned: 915 (million)
% 31.73/4.41 % (32125)------------------------------
% 31.73/4.41 % (32125)------------------------------
% 31.73/4.41 % (31990)Success in time 4.06 s
% 31.73/4.41 % Vampire---4.8 exiting
%------------------------------------------------------------------------------