0.07/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % 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 0.12/0.34 % Computer : n017.cluster.edu 0.12/0.34 % Model : x86_64 x86_64 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.34 % Memory : 8042.1875MB 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.34 % CPULimit : 300 0.12/0.34 % WCLimit : 300 0.12/0.34 % DateTime : Fri Jul 5 04:22:39 EDT 2024 0.12/0.34 % CPUTime : 0.12/0.36 This is a THF_ problem 0.12/0.36 Running vampire_ho --cores 8 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p 0.12/0.39 % (1975)lrs+1002_1:1_au=on:s2a=on:s2agt=32:sgt=8:ss=axioms:i=385:si=on:rtra=on_0 on theBenchmark for (2999ds/385Mi) 0.12/0.39 % (1974)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=34:si=on:rtra=on_0 on theBenchmark for (2999ds/34Mi) 0.12/0.39 % (1973)lrs+10_1:2_cnfonf=off:hud=1:inj=on:i=36:si=on:rtra=on_0 on theBenchmark for (2999ds/36Mi) 0.12/0.39 % (1972)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on theBenchmark for (2999ds/96Mi) 0.12/0.39 % (1976)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on theBenchmark for (2999ds/17Mi) 0.12/0.39 % (1977)ott+1010_1:1_cnfonf=lazy_gen:fe=off:kws=inv_arity:plsq=on:plsqc=1:plsqr=32,1:prag=on:sp=const_frequency:i=74:si=on:rtra=on_0 on theBenchmark for (2999ds/74Mi) 0.12/0.39 % (1978)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi) 0.12/0.39 % (1979)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=915:si=on:rtra=on_0 on theBenchmark for (2999ds/915Mi) 0.12/0.39 % (1978)Instruction limit reached! 0.12/0.39 % (1978)------------------------------ 0.12/0.39 % (1978)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.12/0.39 % (1978)Termination reason: Unknown 0.12/0.40 % (1978)Termination phase: shuffling 0.12/0.40 0.12/0.40 % (1978)Memory used [KB]: 1407 0.12/0.40 % (1978)Time elapsed: 0.004 s 0.12/0.40 % (1978)Instructions burned: 5 (million) 0.12/0.40 % (1978)------------------------------ 0.12/0.40 % (1978)------------------------------ 0.22/0.40 % (1976)Instruction limit reached! 0.22/0.40 % (1976)------------------------------ 0.22/0.40 % (1976)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.22/0.40 % (1976)Termination reason: Unknown 0.22/0.40 % (1976)Termination phase: shuffling 0.22/0.40 0.22/0.40 % (1976)Memory used [KB]: 1663 0.22/0.40 % (1976)Time elapsed: 0.010 s 0.22/0.40 % (1976)Instructions burned: 17 (million) 0.22/0.40 % (1976)------------------------------ 0.22/0.40 % (1976)------------------------------ 0.22/0.41 % (1974)Instruction limit reached! 0.22/0.41 % (1974)------------------------------ 0.22/0.41 % (1974)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.22/0.41 % (1974)Termination reason: Unknown 0.22/0.41 % (1974)Termination phase: Property scanning 0.22/0.41 0.22/0.41 % (1974)Memory used [KB]: 1918 0.22/0.41 % (1974)Time elapsed: 0.019 s 0.22/0.41 % (1974)Instructions burned: 35 (million) 0.22/0.41 % (1974)------------------------------ 0.22/0.41 % (1974)------------------------------ 0.22/0.41 % (1980)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) 0.22/0.41 % (1973)Instruction limit reached! 0.22/0.41 % (1973)------------------------------ 0.22/0.41 % (1973)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.22/0.41 % (1973)Termination reason: Unknown 0.22/0.41 % (1973)Termination phase: Property scanning 0.22/0.41 0.22/0.41 % (1973)Memory used [KB]: 1918 0.22/0.41 % (1973)Time elapsed: 0.020 s 0.22/0.41 % (1973)Instructions burned: 37 (million) 0.22/0.41 % (1973)------------------------------ 0.22/0.41 % (1973)------------------------------ 0.22/0.42 % (1981)lrs-3_1:1024_cbe=off:chr=on:tnu=1:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi) 0.22/0.42 % (1981)Instruction limit reached! 0.22/0.42 % (1981)------------------------------ 0.22/0.42 % (1981)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.22/0.42 % (1981)Termination reason: Unknown 0.22/0.42 % (1981)Termination phase: shuffling 0.22/0.42 0.22/0.42 % (1981)Memory used [KB]: 1407 0.22/0.42 % (1981)Time elapsed: 0.005 s 0.22/0.42 % (1981)Instructions burned: 7 (million) 0.22/0.42 % (1981)------------------------------ 0.22/0.42 % (1981)------------------------------ 0.22/0.42 % (1980)Instruction limit reached! 0.22/0.42 % (1980)------------------------------ 0.22/0.42 % (1980)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.22/0.42 % (1980)Termination reason: Unknown 0.22/0.42 % (1980)Termination phase: shuffling 0.22/0.42 0.22/0.42 % (1980)Memory used [KB]: 1791 0.22/0.42 % (1980)Time elapsed: 0.013 s 0.22/0.42 % (1980)Instructions burned: 21 (million) 0.22/0.42 % (1980)------------------------------ 0.22/0.42 % (1980)------------------------------ 0.22/0.42 % (1982)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 (2999ds/1021Mi) 0.22/0.43 % (1983)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 (2999ds/71Mi) 0.22/0.43 % (1977)Instruction limit reached! 0.22/0.43 % (1977)------------------------------ 0.22/0.43 % (1977)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.22/0.43 % (1977)Termination reason: Unknown 0.22/0.43 % (1977)Termination phase: Function definition elimination 0.22/0.43 0.22/0.43 % (1977)Memory used [KB]: 2174 0.22/0.43 % (1977)Time elapsed: 0.036 s 0.22/0.43 % (1977)Instructions burned: 74 (million) 0.22/0.43 % (1977)------------------------------ 0.22/0.43 % (1977)------------------------------ 0.22/0.43 % (1984)lrs-1010_1:50_au=on:awrs=converge:awrsf=430:bet=on:cbe=off:cha=on:nm=20:sac=on:i=9:si=on:rtra=on_0 on theBenchmark for (2999ds/9Mi) 0.22/0.44 % (1985)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=1044:si=on:rtra=on_0 on theBenchmark for (2999ds/1044Mi) 0.22/0.44 % (1972)Instruction limit reached! 0.22/0.44 % (1972)------------------------------ 0.22/0.44 % (1972)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.22/0.44 % (1972)Termination reason: Unknown 0.22/0.44 % (1972)Termination phase: Saturation 0.22/0.44 0.22/0.44 % (1972)Memory used [KB]: 6780 0.22/0.44 % (1972)Time elapsed: 0.048 s 0.22/0.44 % (1972)Instructions burned: 96 (million) 0.22/0.44 % (1972)------------------------------ 0.22/0.44 % (1972)------------------------------ 0.22/0.44 % (1984)Instruction limit reached! 0.22/0.44 % (1984)------------------------------ 0.22/0.44 % (1984)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.22/0.44 % (1984)Termination reason: Unknown 0.22/0.44 % (1984)Termination phase: shuffling 0.22/0.44 0.22/0.44 % (1984)Memory used [KB]: 1535 0.22/0.44 % (1984)Time elapsed: 0.007 s 0.22/0.44 % (1984)Instructions burned: 9 (million) 0.22/0.44 % (1984)------------------------------ 0.22/0.44 % (1984)------------------------------ 0.22/0.44 % (1986)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=128:si=on:rtra=on_0 on theBenchmark for (2999ds/128Mi) 0.22/0.45 % (1987)lrs+21_1:1_cond=on:e2e=on:i=61:si=on:rtra=on_0 on theBenchmark for (2999ds/61Mi) 0.22/0.45 % (1988)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=14:si=on:rtra=on_0 on theBenchmark for (2999ds/14Mi) 0.22/0.46 % (1983)Instruction limit reached! 0.22/0.46 % (1983)------------------------------ 0.22/0.46 % (1983)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.22/0.46 % (1983)Termination reason: Unknown 0.22/0.46 % (1983)Termination phase: Function definition elimination 0.22/0.46 0.22/0.46 % (1983)Memory used [KB]: 2174 0.22/0.46 % (1983)Time elapsed: 0.037 s 0.22/0.46 % (1983)Instructions burned: 71 (million) 0.22/0.46 % (1983)------------------------------ 0.22/0.46 % (1983)------------------------------ 0.22/0.46 % (1988)Instruction limit reached! 0.22/0.46 % (1988)------------------------------ 0.22/0.46 % (1988)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.22/0.46 % (1988)Termination reason: Unknown 0.22/0.46 % (1988)Termination phase: shuffling 0.22/0.46 0.22/0.46 % (1988)Memory used [KB]: 1663 0.22/0.46 % (1988)Time elapsed: 0.011 s 0.22/0.46 % (1988)Instructions burned: 14 (million) 0.22/0.46 % (1988)------------------------------ 0.22/0.46 % (1988)------------------------------ 0.22/0.48 % (1991)lrs+2_5:1_cnfonf=lazy_not_be_gen:hud=10:inj=on:ntd=on:tnu=1:i=2:si=on:rtra=on_0 on theBenchmark for (2998ds/2Mi) 0.22/0.48 % (1991)Instruction limit reached! 0.22/0.48 % (1991)------------------------------ 0.22/0.48 % (1991)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.22/0.48 % (1991)Termination reason: Unknown 0.22/0.48 % (1991)Termination phase: shuffling 0.22/0.48 0.22/0.48 % (1991)Memory used [KB]: 1407 0.22/0.48 % (1991)Time elapsed: 0.003 s 0.22/0.48 % (1991)Instructions burned: 2 (million) 0.22/0.48 % (1991)------------------------------ 0.22/0.48 % (1991)------------------------------ 0.22/0.48 % (1994)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 (2998ds/1041Mi) 0.22/0.49 % (1987)Instruction limit reached! 0.22/0.49 % (1987)------------------------------ 0.22/0.49 % (1987)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.22/0.49 % (1987)Termination reason: Unknown 0.22/0.49 % (1987)Termination phase: Preprocessing 3 0.22/0.49 0.22/0.49 % (1987)Memory used [KB]: 3070 0.22/0.49 % (1987)Time elapsed: 0.039 s 0.22/0.49 % (1987)Instructions burned: 62 (million) 0.22/0.49 % (1987)------------------------------ 0.22/0.49 % (1987)------------------------------ 0.22/0.49 % (2000)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on theBenchmark for (2998ds/11Mi) 0.22/0.50 % (2000)Instruction limit reached! 0.22/0.50 % (2000)------------------------------ 0.22/0.50 % (2000)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.22/0.50 % (2000)Termination reason: Unknown 0.22/0.50 % (2000)Termination phase: shuffling 0.22/0.50 0.22/0.50 % (2000)Memory used [KB]: 1535 0.22/0.50 % (2000)Time elapsed: 0.007 s 0.22/0.50 % (2000)Instructions burned: 11 (million) 0.22/0.50 % (2000)------------------------------ 0.22/0.50 % (2000)------------------------------ 0.22/0.51 % (2003)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on theBenchmark for (2998ds/140Mi) 0.22/0.51 % (1986)Instruction limit reached! 0.22/0.51 % (1986)------------------------------ 0.22/0.51 % (1986)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.22/0.51 % (1986)Termination reason: Unknown 0.22/0.51 % (1986)Termination phase: Saturation 0.22/0.51 0.22/0.51 % (1986)Memory used [KB]: 6908 0.22/0.51 % (1986)Time elapsed: 0.067 s 0.22/0.51 % (1986)Instructions burned: 128 (million) 0.22/0.51 % (1986)------------------------------ 0.22/0.51 % (1986)------------------------------ 0.22/0.51 % (2004)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=26:si=on:rtra=on_0 on theBenchmark for (2998ds/26Mi) 0.22/0.52 % (2005)lrs+1002_1:4_au=on:av=off:bsr=on:cbe=off:nm=2:i=56:si=on:rtra=on_0 on theBenchmark for (2998ds/56Mi) 0.22/0.53 % (2004)Instruction limit reached! 0.22/0.53 % (2004)------------------------------ 0.22/0.53 % (2004)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.22/0.53 % (2004)Termination reason: Unknown 0.22/0.53 % (2004)Termination phase: shuffling 0.22/0.53 0.22/0.53 % (2004)Memory used [KB]: 1918 0.22/0.53 % (2004)Time elapsed: 0.017 s 0.22/0.53 % (2004)Instructions burned: 27 (million) 0.22/0.53 % (2004)------------------------------ 0.22/0.53 % (2004)------------------------------ 0.22/0.55 % (2005)Instruction limit reached! 0.22/0.55 % (2005)------------------------------ 0.22/0.55 % (2005)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.22/0.55 % (2005)Termination reason: Unknown 0.22/0.55 % (2005)Termination phase: Property scanning 0.22/0.55 0.22/0.55 % (2005)Memory used [KB]: 2046 0.22/0.55 % (2005)Time elapsed: 0.029 s 0.22/0.55 % (2005)Instructions burned: 57 (million) 0.22/0.55 % (2005)------------------------------ 0.22/0.55 % (2005)------------------------------ 0.22/0.55 % (2014)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 (2998ds/275Mi) 0.22/0.56 % (2003)Instruction limit reached! 0.22/0.56 % (2003)------------------------------ 0.22/0.56 % (2003)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.22/0.56 % (2003)Termination reason: Unknown 0.22/0.56 % (2003)Termination phase: Saturation 0.22/0.56 0.22/0.56 % (2003)Memory used [KB]: 6908 0.22/0.56 % (2003)Time elapsed: 0.055 s 0.22/0.56 % (2003)Instructions burned: 140 (million) 0.22/0.56 % (2003)------------------------------ 0.22/0.56 % (2003)------------------------------ 0.22/0.57 % (2016)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) 0.22/0.58 % (2015)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2998ds/3Mi) 0.22/0.58 % (2015)Instruction limit reached! 0.22/0.58 % (2015)------------------------------ 0.22/0.58 % (2015)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.22/0.58 % (2015)Termination reason: Unknown 0.22/0.58 % (2015)Termination phase: shuffling 0.22/0.58 0.22/0.58 % (2015)Memory used [KB]: 1407 0.22/0.58 % (2015)Time elapsed: 0.004 s 0.22/0.58 % (2015)Instructions burned: 4 (million) 0.22/0.58 % (2015)------------------------------ 0.22/0.58 % (2015)------------------------------ 0.22/0.58 % (2016)Instruction limit reached! 0.22/0.58 % (2016)------------------------------ 0.22/0.58 % (2016)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.22/0.58 % (2016)Termination reason: Unknown 0.22/0.58 % (2016)Termination phase: shuffling 0.22/0.58 0.22/0.58 % (2016)Memory used [KB]: 1791 0.22/0.58 % (2016)Time elapsed: 0.011 s 0.22/0.58 % (2016)Instructions burned: 19 (million) 0.22/0.58 % (2016)------------------------------ 0.22/0.58 % (2016)------------------------------ 0.22/0.60 % (1975)Instruction limit reached! 0.22/0.60 % (1975)------------------------------ 0.22/0.60 % (1975)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.22/0.60 % (1975)Termination reason: Unknown 0.22/0.60 % (1975)Termination phase: Saturation 0.22/0.60 0.22/0.60 % (1975)Memory used [KB]: 8443 0.22/0.60 % (1975)Time elapsed: 0.206 s 0.22/0.60 % (1975)Instructions burned: 385 (million) 0.22/0.60 % (1975)------------------------------ 0.22/0.60 % (1975)------------------------------ 0.22/0.60 % (2017)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 (2997ds/44Mi) 0.22/0.61 % (2018)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=191:si=on:rtra=on_0 on theBenchmark for (2997ds/191Mi) 1.88/0.61 % (2019)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on theBenchmark for (2997ds/62Mi) 1.88/0.62 % (2017)Instruction limit reached! 1.88/0.62 % (2017)------------------------------ 1.88/0.62 % (2017)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.88/0.62 % (2017)Termination reason: Unknown 1.88/0.62 % (2017)Termination phase: Property scanning 1.88/0.62 1.88/0.62 % (2017)Memory used [KB]: 2174 1.88/0.62 % (2017)Time elapsed: 0.023 s 1.88/0.62 % (2017)Instructions burned: 45 (million) 1.88/0.62 % (2017)------------------------------ 1.88/0.62 % (2017)------------------------------ 2.08/0.64 % (2021)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=105:si=on:rtra=on_0 on theBenchmark for (2997ds/105Mi) 2.08/0.64 % (2019)Instruction limit reached! 2.08/0.64 % (2019)------------------------------ 2.08/0.64 % (2019)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.08/0.64 % (2019)Termination reason: Unknown 2.08/0.64 % (2019)Termination phase: Property scanning 2.08/0.64 2.08/0.64 % (2019)Memory used [KB]: 2174 2.08/0.64 % (2019)Time elapsed: 0.031 s 2.08/0.64 % (2019)Instructions burned: 62 (million) 2.08/0.64 % (2019)------------------------------ 2.08/0.64 % (2019)------------------------------ 2.08/0.66 % (2014)Instruction limit reached! 2.08/0.66 % (2014)------------------------------ 2.08/0.66 % (2014)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.08/0.66 % (2014)Termination reason: Unknown 2.08/0.66 % (2014)Termination phase: Saturation 2.08/0.66 2.08/0.66 % (2014)Memory used [KB]: 8443 2.08/0.66 % (2014)Time elapsed: 0.124 s 2.08/0.66 % (2014)Instructions burned: 276 (million) 2.08/0.66 % (2014)------------------------------ 2.08/0.66 % (2014)------------------------------ 2.08/0.66 % (2022)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2997ds/3Mi) 2.08/0.66 % (2022)Instruction limit reached! 2.08/0.66 % (2022)------------------------------ 2.08/0.66 % (2022)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.08/0.66 % (2022)Termination reason: Unknown 2.08/0.66 % (2022)Termination phase: shuffling 2.08/0.66 2.08/0.66 % (2022)Memory used [KB]: 1407 2.08/0.66 % (2022)Time elapsed: 0.004 s 2.08/0.66 % (2022)Instructions burned: 4 (million) 2.08/0.66 % (2022)------------------------------ 2.08/0.66 % (2022)------------------------------ 2.08/0.67 % (2023)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=238:si=on:rtra=on_0 on theBenchmark for (2997ds/238Mi) 2.08/0.68 % (2024)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 (2997ds/3Mi) 2.08/0.68 % (2024)Instruction limit reached! 2.08/0.68 % (2024)------------------------------ 2.08/0.68 % (2024)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.08/0.68 % (2024)Termination reason: Unknown 2.08/0.68 % (2024)Termination phase: shuffling 2.08/0.68 2.08/0.68 % (2024)Memory used [KB]: 1407 2.08/0.68 % (2024)Time elapsed: 0.003 s 2.08/0.68 % (2024)Instructions burned: 3 (million) 2.08/0.68 % (2024)------------------------------ 2.08/0.68 % (2024)------------------------------ 2.08/0.69 % (2021)Instruction limit reached! 2.08/0.69 % (2021)------------------------------ 2.08/0.69 % (2021)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.08/0.69 % (2021)Termination reason: Unknown 2.08/0.69 % (2021)Termination phase: Saturation 2.08/0.69 2.08/0.69 % (2021)Memory used [KB]: 6780 2.08/0.69 % (2021)Time elapsed: 0.052 s 2.08/0.69 % (2021)Instructions burned: 106 (million) 2.08/0.69 % (2021)------------------------------ 2.08/0.69 % (2021)------------------------------ 2.08/0.70 % (2025)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 (2996ds/4Mi) 2.08/0.70 % (2018)Instruction limit reached! 2.08/0.70 % (2018)------------------------------ 2.08/0.70 % (2018)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.08/0.70 % (2018)Termination reason: Unknown 2.08/0.70 % (2018)Termination phase: Saturation 2.08/0.70 2.08/0.70 % (2018)Memory used [KB]: 7547 2.08/0.70 % (2018)Time elapsed: 0.091 s 2.08/0.70 % (2018)Instructions burned: 191 (million) 2.08/0.70 % (2018)------------------------------ 2.08/0.70 % (2018)------------------------------ 2.08/0.70 % (2025)Instruction limit reached! 2.08/0.70 % (2025)------------------------------ 2.08/0.70 % (2025)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.08/0.70 % (2025)Termination reason: Unknown 2.08/0.70 % (2025)Termination phase: shuffling 2.08/0.70 2.08/0.70 % (2025)Memory used [KB]: 1407 2.08/0.70 % (2025)Time elapsed: 0.004 s 2.08/0.70 % (2025)Instructions burned: 5 (million) 2.08/0.70 % (2025)------------------------------ 2.08/0.70 % (2025)------------------------------ 2.64/0.70 % (2026)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) 2.64/0.71 % (2027)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on theBenchmark for (2996ds/150Mi) 2.64/0.71 % (2028)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=199:si=on:rtra=on_0 on theBenchmark for (2996ds/199Mi) 2.64/0.73 % (2023)Instruction limit reached! 2.64/0.73 % (2023)------------------------------ 2.64/0.73 % (2023)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.64/0.73 % (2023)Termination reason: Unknown 2.64/0.73 % (2023)Termination phase: Saturation 2.64/0.73 2.64/0.73 % (2023)Memory used [KB]: 6908 2.64/0.73 % (2023)Time elapsed: 0.070 s 2.64/0.73 % (2023)Instructions burned: 238 (million) 2.64/0.73 % (2023)------------------------------ 2.64/0.73 % (2023)------------------------------ 2.64/0.74 % (2029)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on theBenchmark for (2996ds/39Mi) 2.64/0.76 % (2029)Instruction limit reached! 2.64/0.76 % (2029)------------------------------ 2.64/0.76 % (2029)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.64/0.76 % (2029)Termination reason: Unknown 2.64/0.76 % (2029)Termination phase: Property scanning 2.64/0.76 2.64/0.76 % (2029)Memory used [KB]: 1918 2.64/0.76 % (2029)Time elapsed: 0.014 s 2.64/0.76 % (2029)Instructions burned: 42 (million) 2.64/0.76 % (2029)------------------------------ 2.64/0.76 % (2029)------------------------------ 2.97/0.77 % (2030)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=721:si=on:rtra=on_0 on theBenchmark for (2996ds/721Mi) 2.97/0.78 % (2026)Instruction limit reached! 2.97/0.78 % (2026)------------------------------ 2.97/0.78 % (2026)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.97/0.78 % (2026)Termination reason: Unknown 2.97/0.78 % (2026)Termination phase: Saturation 2.97/0.78 2.97/0.78 % (2026)Memory used [KB]: 7419 2.97/0.78 % (2026)Time elapsed: 0.076 s 2.97/0.78 % (2026)Instructions burned: 149 (million) 2.97/0.78 % (2026)------------------------------ 2.97/0.78 % (2026)------------------------------ 2.97/0.79 % (2027)Instruction limit reached! 2.97/0.79 % (2027)------------------------------ 2.97/0.79 % (2027)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.97/0.79 % (2027)Termination reason: Unknown 2.97/0.79 % (2027)Termination phase: Saturation 2.97/0.79 2.97/0.79 % (2027)Memory used [KB]: 8187 2.97/0.79 % (2027)Time elapsed: 0.077 s 2.97/0.79 % (2027)Instructions burned: 151 (million) 2.97/0.79 % (2027)------------------------------ 2.97/0.79 % (2027)------------------------------ 2.97/0.80 % (2031)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=3:si=on:rtra=on_0 on theBenchmark for (2995ds/3Mi) 2.97/0.80 % (2031)Instruction limit reached! 2.97/0.80 % (2031)------------------------------ 2.97/0.80 % (2031)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.97/0.80 % (2031)Termination reason: Unknown 2.97/0.80 % (2031)Termination phase: shuffling 2.97/0.80 2.97/0.80 % (2031)Memory used [KB]: 1407 2.97/0.80 % (2031)Time elapsed: 0.003 s 2.97/0.80 % (2031)Instructions burned: 3 (million) 2.97/0.80 % (2031)------------------------------ 2.97/0.80 % (2031)------------------------------ 2.97/0.80 % (2032)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 (2995ds/18Mi) 2.97/0.81 % (2032)Instruction limit reached! 2.97/0.81 % (2032)------------------------------ 2.97/0.81 % (2032)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.97/0.81 % (2032)Termination reason: Unknown 2.97/0.81 % (2032)Termination phase: shuffling 2.97/0.81 2.97/0.81 % (2032)Memory used [KB]: 1791 2.97/0.81 % (2032)Time elapsed: 0.011 s 2.97/0.81 % (2032)Instructions burned: 19 (million) 2.97/0.81 % (2032)------------------------------ 2.97/0.81 % (2032)------------------------------ 2.97/0.81 % (2033)lrs+10_1:1_au=on:c=on:sac=on:slsq=on:slsqc=2:i=218:si=on:rtra=on_0 on theBenchmark for (2995ds/218Mi) 2.97/0.82 % (2028)Instruction limit reached! 2.97/0.82 % (2028)------------------------------ 2.97/0.82 % (2028)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.97/0.82 % (2028)Termination reason: Unknown 2.97/0.82 % (2028)Termination phase: Saturation 2.97/0.82 2.97/0.82 % (2028)Memory used [KB]: 7164 2.97/0.82 % (2028)Time elapsed: 0.105 s 2.97/0.82 % (2028)Instructions burned: 200 (million) 2.97/0.82 % (2028)------------------------------ 2.97/0.82 % (2028)------------------------------ 2.97/0.83 % (2034)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 (2995ds/448Mi) 2.97/0.83 % (2035)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 (2995ds/6Mi) 2.97/0.83 % (2035)Instruction limit reached! 2.97/0.83 % (2035)------------------------------ 2.97/0.83 % (2035)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.97/0.83 % (2035)Termination reason: Unknown 2.97/0.83 % (2035)Termination phase: shuffling 2.97/0.83 2.97/0.83 % (2035)Memory used [KB]: 1407 2.97/0.83 % (2035)Time elapsed: 0.005 s 2.97/0.83 % (2035)Instructions burned: 6 (million) 2.97/0.83 % (2035)------------------------------ 2.97/0.83 % (2035)------------------------------ 2.97/0.85 % (2036)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=9:si=on:rtra=on_0 on theBenchmark for (2995ds/9Mi) 2.97/0.86 % (2036)Instruction limit reached! 2.97/0.86 % (2036)------------------------------ 2.97/0.86 % (2036)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.97/0.86 % (2036)Termination reason: Unknown 2.97/0.86 % (2036)Termination phase: shuffling 2.97/0.86 2.97/0.86 % (2036)Memory used [KB]: 1535 2.97/0.86 % (2036)Time elapsed: 0.007 s 2.97/0.86 % (2036)Instructions burned: 9 (million) 2.97/0.86 % (2036)------------------------------ 2.97/0.86 % (2036)------------------------------ 2.97/0.86 % (1979)Instruction limit reached! 2.97/0.86 % (1979)------------------------------ 2.97/0.86 % (1979)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.97/0.86 % (1979)Termination reason: Unknown 2.97/0.86 % (1979)Termination phase: Saturation 2.97/0.86 2.97/0.86 % (1979)Memory used [KB]: 9594 2.97/0.86 % (1979)Time elapsed: 0.469 s 2.97/0.86 % (1979)Instructions burned: 916 (million) 2.97/0.86 % (1979)------------------------------ 2.97/0.86 % (1979)------------------------------ 3.76/0.87 % (2037)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2994ds/16Mi) 3.76/0.87 % (2038)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=40:si=on:rtra=on_0 on theBenchmark for (2994ds/40Mi) 3.76/0.88 % (2037)Instruction limit reached! 3.76/0.88 % (2037)------------------------------ 3.76/0.88 % (2037)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.76/0.88 % (2037)Termination reason: Unknown 3.76/0.88 % (2037)Termination phase: shuffling 3.76/0.88 3.76/0.88 % (2037)Memory used [KB]: 1663 3.76/0.88 % (2037)Time elapsed: 0.010 s 3.76/0.88 % (2037)Instructions burned: 16 (million) 3.76/0.88 % (2037)------------------------------ 3.76/0.88 % (2037)------------------------------ 3.87/0.89 % (2038)Instruction limit reached! 3.87/0.89 % (2038)------------------------------ 3.87/0.89 % (2038)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.87/0.89 % (2038)Termination reason: Unknown 3.87/0.89 % (2038)Termination phase: Property scanning 3.87/0.89 3.87/0.89 % (2038)Memory used [KB]: 1918 3.87/0.89 % (2038)Time elapsed: 0.020 s 3.87/0.89 % (2038)Instructions burned: 40 (million) 3.87/0.89 % (2038)------------------------------ 3.87/0.89 % (2038)------------------------------ 3.87/0.90 % (1994)Instruction limit reached! 3.87/0.90 % (1994)------------------------------ 3.87/0.90 % (1994)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.87/0.90 % (1994)Termination reason: Unknown 3.87/0.90 % (1994)Termination phase: Saturation 3.87/0.90 3.87/0.90 % (1994)Memory used [KB]: 11385 3.87/0.90 % (1994)Time elapsed: 0.424 s 3.87/0.90 % (1994)Instructions burned: 1042 (million) 3.87/0.90 % (1994)------------------------------ 3.87/0.90 % (1994)------------------------------ 3.87/0.91 % (2039)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2994ds/2Mi) 3.87/0.91 % (2039)Instruction limit reached! 3.87/0.91 % (2039)------------------------------ 3.87/0.91 % (2039)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.87/0.91 % (2039)Termination reason: Unknown 3.87/0.91 % (2039)Termination phase: shuffling 3.87/0.91 3.87/0.91 % (2039)Memory used [KB]: 1407 3.87/0.91 % (2039)Time elapsed: 0.003 s 3.87/0.91 % (2039)Instructions burned: 2 (million) 3.87/0.91 % (2039)------------------------------ 3.87/0.91 % (2039)------------------------------ 3.87/0.92 % (2041)lrs+1004_1:1_chr=on:prag=on:i=8:si=on:rtra=on_0 on theBenchmark for (2994ds/8Mi) 3.87/0.92 % (2033)Instruction limit reached! 3.87/0.92 % (2033)------------------------------ 3.87/0.92 % (2033)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.87/0.92 % (2033)Termination reason: Unknown 3.87/0.92 % (2033)Termination phase: Saturation 3.87/0.92 3.87/0.92 % (2033)Memory used [KB]: 7803 3.87/0.92 % (2033)Time elapsed: 0.105 s 3.87/0.92 % (2033)Instructions burned: 220 (million) 3.87/0.92 % (2033)------------------------------ 3.87/0.92 % (2033)------------------------------ 3.87/0.92 % (2040)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 (2994ds/98Mi) 3.87/0.92 % (2041)Instruction limit reached! 3.87/0.92 % (2041)------------------------------ 3.87/0.92 % (2041)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.87/0.92 % (2041)Termination reason: Unknown 3.87/0.92 % (2041)Termination phase: shuffling 3.87/0.92 3.87/0.92 % (2041)Memory used [KB]: 1535 3.87/0.92 % (2041)Time elapsed: 0.006 s 3.87/0.92 % (2041)Instructions burned: 9 (million) 3.87/0.92 % (2041)------------------------------ 3.87/0.92 % (2041)------------------------------ 3.87/0.92 % (2042)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 (2994ds/86Mi) 4.15/0.93 % (2043)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 (2994ds/3Mi) 4.15/0.93 % (2043)Instruction limit reached! 4.15/0.93 % (2043)------------------------------ 4.15/0.93 % (2043)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 4.15/0.93 % (2043)Termination reason: Unknown 4.15/0.93 % (2043)Termination phase: shuffling 4.15/0.93 4.15/0.93 % (2043)Memory used [KB]: 1407 4.15/0.93 % (2043)Time elapsed: 0.003 s 4.15/0.93 % (2043)Instructions burned: 3 (million) 4.15/0.93 % (2043)------------------------------ 4.15/0.93 % (2043)------------------------------ 4.15/0.94 % (2044)lrs+1010_1:1024_au=on:hud=10:ntd=on:ss=included:i=294:si=on:rtra=on_0 on theBenchmark for (2994ds/294Mi) 4.15/0.96 % (2042)Instruction limit reached! 4.15/0.96 % (2042)------------------------------ 4.15/0.96 % (2042)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 4.15/0.96 % (2042)Termination reason: Unknown 4.15/0.96 % (2042)Termination phase: Property scanning 4.15/0.96 4.15/0.96 % (2042)Memory used [KB]: 2174 4.15/0.96 % (2042)Time elapsed: 0.038 s 4.15/0.96 % (2042)Instructions burned: 86 (million) 4.15/0.96 % (2042)------------------------------ 4.15/0.96 % (2042)------------------------------ 4.15/0.96 % (2040)Instruction limit reached! 4.15/0.96 % (2040)------------------------------ 4.15/0.96 % (2040)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 4.15/0.96 % (2040)Termination reason: Unknown 4.15/0.96 % (2040)Termination phase: Saturation 4.15/0.96 4.15/0.96 % (2040)Memory used [KB]: 2302 4.15/0.96 % (2040)Time elapsed: 0.042 s 4.15/0.96 % (2040)Instructions burned: 100 (million) 4.15/0.96 % (2040)------------------------------ 4.15/0.96 % (2040)------------------------------ 4.15/0.96 % (2045)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=274:si=on:rtra=on_0 on theBenchmark for (2994ds/274Mi) 4.15/0.97 % (2046)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on theBenchmark for (2994ds/47Mi) 4.15/0.97 % (2047)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 (2994ds/37Mi) 4.15/0.98 % (1985)Instruction limit reached! 4.15/0.98 % (1985)------------------------------ 4.15/0.98 % (1985)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 4.15/0.98 % (1985)Termination reason: Unknown 4.15/0.98 % (1985)Termination phase: Saturation 4.15/0.98 4.15/0.98 % (1985)Memory used [KB]: 9083 4.15/0.98 % (1985)Time elapsed: 0.571 s 4.15/0.98 % (1985)Instructions burned: 1045 (million) 4.15/0.98 % (1985)------------------------------ 4.15/0.98 % (1985)------------------------------ 4.15/0.99 % (2047)Instruction limit reached! 4.15/0.99 % (2047)------------------------------ 4.15/0.99 % (2047)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 4.15/0.99 % (2047)Termination reason: Unknown 4.15/0.99 % (2047)Termination phase: Property scanning 4.15/0.99 4.15/0.99 % (2047)Memory used [KB]: 2046 4.15/0.99 % (2047)Time elapsed: 0.018 s 4.15/0.99 % (2047)Instructions burned: 37 (million) 4.15/0.99 % (2047)------------------------------ 4.15/0.99 % (2047)------------------------------ 4.15/0.99 % (2046)Instruction limit reached! 4.15/0.99 % (2046)------------------------------ 4.15/0.99 % (2046)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 4.15/0.99 % (2046)Termination reason: Unknown 4.15/0.99 % (2046)Termination phase: Property scanning 4.15/0.99 4.15/0.99 % (2046)Memory used [KB]: 1918 4.15/0.99 % (2046)Time elapsed: 0.021 s 4.15/0.99 % (2046)Instructions burned: 47 (million) 4.15/0.99 % (2046)------------------------------ 4.15/0.99 % (2046)------------------------------ 4.15/0.99 % (1982)Instruction limit reached! 4.15/0.99 % (1982)------------------------------ 4.15/0.99 % (1982)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 4.15/0.99 % (1982)Termination reason: Unknown 4.15/0.99 % (1982)Termination phase: Saturation 4.15/0.99 4.15/0.99 % (1982)Memory used [KB]: 10618 4.15/0.99 % (1982)Time elapsed: 0.595 s 4.15/0.99 % (1982)Instructions burned: 1022 (million) 4.15/0.99 % (1982)------------------------------ 4.15/0.99 % (1982)------------------------------ 4.15/1.00 % (2048)lrs+1002_1:16_av=off:e2e=on:fe=axiom:prag=on:sos=on:ss=axioms:i=3:si=on:rtra=on_0 on theBenchmark for (2993ds/3Mi) 4.15/1.00 % (2048)Instruction limit reached! 4.15/1.00 % (2048)------------------------------ 4.15/1.00 % (2048)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 4.15/1.00 % (2048)Termination reason: Unknown 4.15/1.00 % (2048)Termination phase: shuffling 4.15/1.00 4.15/1.00 % (2048)Memory used [KB]: 1407 4.15/1.00 % (2048)Time elapsed: 0.004 s 4.15/1.00 % (2048)Instructions burned: 4 (million) 4.15/1.00 % (2048)------------------------------ 4.15/1.00 % (2048)------------------------------ 4.48/1.00 % (2034)Instruction limit reached! 4.48/1.00 % (2034)------------------------------ 4.48/1.00 % (2034)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 4.48/1.00 % (2034)Termination reason: Unknown 4.48/1.00 % (2034)Termination phase: Saturation 4.48/1.00 4.48/1.00 % (2034)Memory used [KB]: 8059 4.48/1.00 % (2034)Time elapsed: 0.174 s 4.48/1.00 % (2034)Instructions burned: 449 (million) 4.48/1.00 % (2034)------------------------------ 4.48/1.00 % (2034)------------------------------ 4.48/1.00 % (2051)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:i=5:si=on:rtra=on_0 on theBenchmark for (2993ds/5Mi) 4.48/1.00 % (2051)Instruction limit reached! 4.48/1.00 % (2051)------------------------------ 4.48/1.00 % (2051)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 4.48/1.00 % (2051)Termination reason: Unknown 4.48/1.00 % (2051)Termination phase: shuffling 4.48/1.00 4.48/1.00 % (2051)Memory used [KB]: 1407 4.48/1.00 % (2051)Time elapsed: 0.003 s 4.48/1.00 % (2051)Instructions burned: 5 (million) 4.48/1.00 % (2051)------------------------------ 4.48/1.00 % (2051)------------------------------ 4.48/1.01 % (2050)lrs+10_8:1_au=on:e2e=on:hfsq=on:hfsqc=1:ins=3:s2a=on:s2at=3.0:ss=axioms:i=19:si=on:rtra=on_0 on theBenchmark for (2993ds/19Mi) 4.48/1.01 % (2058)ott+21_1:3_bd=off:cnfonf=lazy_gen:fe=off:hfsq=on:hfsqc=3:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=450:si=on:rtra=on_0 on theBenchmark for (2993ds/450Mi) 4.48/1.01 % (2052)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=44:si=on:rtra=on_0 on theBenchmark for (2993ds/44Mi) 4.48/1.02 % (2050)Instruction limit reached! 4.48/1.02 % (2050)------------------------------ 4.48/1.02 % (2050)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 4.48/1.02 % (2050)Termination reason: Unknown 4.48/1.02 % (2050)Termination phase: Property scanning 4.48/1.02 4.48/1.02 % (2050)Memory used [KB]: 1663 4.48/1.02 % (2050)Time elapsed: 0.011 s 4.48/1.02 % (2050)Instructions burned: 19 (million) 4.48/1.02 % (2050)------------------------------ 4.48/1.02 % (2050)------------------------------ 4.48/1.02 % (2059)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=102:si=on:rtra=on_0 on theBenchmark for (2993ds/102Mi) 4.48/1.02 % (2060)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on theBenchmark for (2993ds/134Mi) 4.48/1.03 % (2052)Instruction limit reached! 4.48/1.03 % (2052)------------------------------ 4.48/1.03 % (2052)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 4.48/1.03 % (2052)Termination reason: Unknown 4.48/1.03 % (2052)Termination phase: Property scanning 4.48/1.03 4.48/1.03 % (2052)Memory used [KB]: 2174 4.48/1.03 % (2052)Time elapsed: 0.021 s 4.48/1.03 % (2052)Instructions burned: 44 (million) 4.48/1.03 % (2052)------------------------------ 4.48/1.03 % (2052)------------------------------ 4.48/1.03 % (2061)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 (2993ds/204Mi) 4.48/1.04 % (2045)Instruction limit reached! 4.48/1.04 % (2045)------------------------------ 4.48/1.04 % (2045)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 4.48/1.04 % (2045)Termination reason: Unknown 4.48/1.04 % (2045)Termination phase: Saturation 4.48/1.04 4.48/1.04 % (2045)Memory used [KB]: 7547 4.48/1.04 % (2045)Time elapsed: 0.078 s 4.48/1.04 % (2045)Instructions burned: 277 (million) 4.48/1.04 % (2045)------------------------------ 4.48/1.04 % (2045)------------------------------ 4.48/1.05 % (2030)Instruction limit reached! 4.48/1.05 % (2030)------------------------------ 4.48/1.05 % (2030)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 4.48/1.05 % (2030)Termination reason: Unknown 4.48/1.05 % (2030)Termination phase: Saturation 4.48/1.05 4.48/1.05 % (2030)Memory used [KB]: 9722 4.48/1.05 % (2030)Time elapsed: 0.281 s 4.48/1.05 % (2030)Instructions burned: 721 (million) 4.48/1.05 % (2030)------------------------------ 4.48/1.05 % (2030)------------------------------ 4.48/1.05 % (2062)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 (2993ds/154Mi) 4.48/1.05 % (2064)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=424:si=on:rtra=on_0 on theBenchmark for (2993ds/424Mi) 4.48/1.06 % (2059)Instruction limit reached! 4.48/1.06 % (2059)------------------------------ 4.48/1.06 % (2059)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 4.48/1.06 % (2059)Termination reason: Unknown 4.48/1.06 % (2059)Termination phase: Property scanning 4.48/1.06 4.48/1.06 % (2059)Memory used [KB]: 3454 4.48/1.06 % (2059)Time elapsed: 0.047 s 4.48/1.06 % (2059)Instructions burned: 103 (million) 4.48/1.06 % (2059)------------------------------ 4.48/1.06 % (2059)------------------------------ 4.48/1.06 % (2065)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 (2993ds/41Mi) 5.17/1.07 % (2044)Instruction limit reached! 5.17/1.07 % (2044)------------------------------ 5.17/1.07 % (2044)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 5.17/1.07 % (2044)Termination reason: Unknown 5.17/1.07 % (2044)Termination phase: Saturation 5.17/1.07 5.17/1.07 % (2044)Memory used [KB]: 8059 5.17/1.07 % (2044)Time elapsed: 0.137 s 5.17/1.07 % (2044)Instructions burned: 294 (million) 5.17/1.07 % (2044)------------------------------ 5.17/1.07 % (2044)------------------------------ 5.17/1.08 % (2066)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 (2993ds/231Mi) 5.17/1.08 % (2060)Instruction limit reached! 5.17/1.08 % (2060)------------------------------ 5.17/1.08 % (2060)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 5.17/1.08 % (2060)Termination reason: Unknown 5.17/1.08 % (2060)Termination phase: Saturation 5.17/1.08 5.17/1.08 % (2060)Memory used [KB]: 7036 5.17/1.08 % (2060)Time elapsed: 0.059 s 5.17/1.08 % (2060)Instructions burned: 135 (million) 5.17/1.08 % (2060)------------------------------ 5.17/1.08 % (2060)------------------------------ 5.17/1.08 % (2065)Instruction limit reached! 5.17/1.08 % (2065)------------------------------ 5.17/1.08 % (2065)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 5.17/1.08 % (2065)Termination reason: Unknown 5.17/1.08 % (2065)Termination phase: Property scanning 5.17/1.08 5.17/1.08 % (2065)Memory used [KB]: 2046 5.17/1.08 % (2065)Time elapsed: 0.020 s 5.17/1.08 % (2065)Instructions burned: 42 (million) 5.17/1.08 % (2065)------------------------------ 5.17/1.08 % (2065)------------------------------ 5.17/1.09 % (2062)Instruction limit reached! 5.17/1.09 % (2062)------------------------------ 5.17/1.09 % (2062)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 5.17/1.09 % (2062)Termination reason: Unknown 5.17/1.09 % (2062)Termination phase: Saturation 5.17/1.09 5.17/1.09 % (2062)Memory used [KB]: 6908 5.17/1.09 % (2062)Time elapsed: 0.039 s 5.17/1.09 % (2062)Instructions burned: 156 (million) 5.17/1.09 % (2062)------------------------------ 5.17/1.09 % (2062)------------------------------ 5.17/1.09 % (2068)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=297:si=on:rtra=on_0 on theBenchmark for (2992ds/297Mi) 5.17/1.09 % (2070)lrs+1010_1:1024_au=on:fe=axiom:lwlo=on:nm=0:ntd=on:nwc=10.0:spb=non_intro:uhcvi=on:i=130:si=on:rtra=on_0 on theBenchmark for (2992ds/130Mi) 5.17/1.09 % (2067)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 (2992ds/70Mi) 5.17/1.10 % (2069)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) 5.17/1.12 % (2061)Instruction limit reached! 5.17/1.12 % (2061)------------------------------ 5.17/1.12 % (2061)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 5.17/1.12 % (2061)Termination reason: Unknown 5.17/1.12 % (2061)Termination phase: Saturation 5.17/1.12 5.17/1.12 % (2061)Memory used [KB]: 7547 5.17/1.12 % (2061)Time elapsed: 0.089 s 5.17/1.12 % (2061)Instructions burned: 204 (million) 5.17/1.12 % (2061)------------------------------ 5.17/1.12 % (2061)------------------------------ 5.17/1.12 % (2067)Instruction limit reached! 5.17/1.12 % (2067)------------------------------ 5.17/1.12 % (2067)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 5.17/1.12 % (2067)Termination reason: Unknown 5.17/1.12 % (2067)Termination phase: Function definition elimination 5.17/1.12 5.17/1.12 % (2067)Memory used [KB]: 2174 5.17/1.12 % (2067)Time elapsed: 0.032 s 5.17/1.12 % (2067)Instructions burned: 72 (million) 5.17/1.12 % (2067)------------------------------ 5.17/1.12 % (2067)------------------------------ 5.17/1.13 % (2070)Instruction limit reached! 5.17/1.13 % (2070)------------------------------ 5.17/1.13 % (2070)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 5.17/1.13 % (2070)Termination reason: Unknown 5.17/1.13 % (2070)Termination phase: Saturation 5.17/1.13 5.17/1.13 % (2070)Memory used [KB]: 7036 5.17/1.13 % (2070)Time elapsed: 0.035 s 5.17/1.13 % (2070)Instructions burned: 132 (million) 5.17/1.13 % (2070)------------------------------ 5.17/1.13 % (2070)------------------------------ 5.17/1.14 % (2072)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) 5.17/1.14 % (2071)lrs+21_1:16_au=on:cbe=off:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=7,4:i=570:si=on:rtra=on_0 on theBenchmark for (2992ds/570Mi) 5.17/1.15 % (2073)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=190:si=on:rtra=on_0 on theBenchmark for (2992ds/190Mi) 6.26/1.18 % (2069)Instruction limit reached! 6.26/1.18 % (2069)------------------------------ 6.26/1.18 % (2069)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 6.26/1.18 % (2069)Termination reason: Unknown 6.26/1.18 % (2069)Termination phase: Saturation 6.26/1.18 6.26/1.18 % (2069)Memory used [KB]: 7419 6.26/1.18 % (2069)Time elapsed: 0.082 s 6.26/1.18 % (2069)Instructions burned: 183 (million) 6.26/1.18 % (2069)------------------------------ 6.26/1.18 % (2069)------------------------------ 6.26/1.18 % (2058)Instruction limit reached! 6.26/1.18 % (2058)------------------------------ 6.26/1.18 % (2058)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 6.26/1.18 % (2058)Termination reason: Unknown 6.26/1.18 % (2058)Termination phase: Saturation 6.26/1.18 6.26/1.18 % (2058)Memory used [KB]: 8187 6.26/1.18 % (2058)Time elapsed: 0.168 s 6.26/1.18 % (2058)Instructions burned: 451 (million) 6.26/1.18 % (2058)------------------------------ 6.26/1.18 % (2058)------------------------------ 6.26/1.18 % (2066)Instruction limit reached! 6.26/1.18 % (2066)------------------------------ 6.26/1.18 % (2066)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 6.26/1.18 % (2066)Termination reason: Unknown 6.26/1.18 % (2066)Termination phase: Saturation 6.26/1.18 6.26/1.18 % (2066)Memory used [KB]: 12281 6.26/1.18 % (2066)Time elapsed: 0.106 s 6.26/1.18 % (2066)Instructions burned: 232 (million) 6.26/1.18 % (2066)------------------------------ 6.26/1.18 % (2066)------------------------------ 6.26/1.19 % (2074)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 (2991ds/96Mi) 6.26/1.19 % (2075)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on theBenchmark for (2991ds/182Mi) 6.26/1.20 % (2076)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) 6.49/1.21 % (2073)Instruction limit reached! 6.49/1.21 % (2073)------------------------------ 6.49/1.21 % (2073)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 6.49/1.21 % (2073)Termination reason: Unknown 6.49/1.21 % (2073)Termination phase: Saturation 6.49/1.21 6.49/1.21 % (2073)Memory used [KB]: 8443 6.49/1.21 % (2073)Time elapsed: 0.056 s 6.49/1.21 % (2073)Instructions burned: 190 (million) 6.49/1.21 % (2073)------------------------------ 6.49/1.21 % (2073)------------------------------ 6.49/1.22 % (2077)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=390:si=on:rtra=on_0 on theBenchmark for (2991ds/390Mi) 6.49/1.22 % (2068)Instruction limit reached! 6.49/1.22 % (2068)------------------------------ 6.49/1.22 % (2068)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 6.49/1.22 % (2068)Termination reason: Unknown 6.49/1.22 % (2068)Termination phase: Saturation 6.49/1.22 6.49/1.22 % (2068)Memory used [KB]: 8059 6.49/1.22 % (2068)Time elapsed: 0.134 s 6.49/1.22 % (2068)Instructions burned: 297 (million) 6.49/1.22 % (2068)------------------------------ 6.49/1.22 % (2068)------------------------------ 6.49/1.23 % (2074)Instruction limit reached! 6.49/1.23 % (2074)------------------------------ 6.49/1.23 % (2074)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 6.49/1.23 % (2074)Termination reason: Unknown 6.49/1.23 % (2074)Termination phase: Property scanning 6.49/1.23 6.49/1.23 % (2074)Memory used [KB]: 2302 6.49/1.23 % (2074)Time elapsed: 0.042 s 6.49/1.23 % (2074)Instructions burned: 96 (million) 6.49/1.23 % (2074)------------------------------ 6.49/1.23 % (2074)------------------------------ 6.49/1.24 % (2078)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on theBenchmark for (2991ds/192Mi) 6.70/1.24 % (2079)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=279:si=on:rtra=on_0 on theBenchmark for (2991ds/279Mi) 6.70/1.25 % (2072)Instruction limit reached! 6.70/1.25 % (2072)------------------------------ 6.70/1.25 % (2072)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 6.70/1.25 % (2072)Termination reason: Unknown 6.70/1.25 % (2072)Termination phase: Saturation 6.70/1.25 6.70/1.25 % (2072)Memory used [KB]: 8443 6.70/1.25 % (2072)Time elapsed: 0.114 s 6.70/1.25 % (2072)Instructions burned: 298 (million) 6.70/1.25 % (2072)------------------------------ 6.70/1.25 % (2072)------------------------------ 6.70/1.26 % (2080)lrs+1010_1:1024_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:ixr=off:i=25:si=on:rtra=on_0 on theBenchmark for (2991ds/25Mi) 6.70/1.27 % (2080)Instruction limit reached! 6.70/1.27 % (2080)------------------------------ 6.70/1.27 % (2080)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 6.70/1.27 % (2080)Termination reason: Unknown 6.70/1.27 % (2080)Termination phase: shuffling 6.70/1.27 6.70/1.27 % (2080)Memory used [KB]: 1918 6.70/1.27 % (2080)Time elapsed: 0.013 s 6.70/1.27 % (2080)Instructions burned: 25 (million) 6.70/1.27 % (2080)------------------------------ 6.70/1.27 % (2080)------------------------------ 6.70/1.28 % (2075)Instruction limit reached! 6.70/1.28 % (2075)------------------------------ 6.70/1.28 % (2075)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 6.70/1.28 % (2075)Termination reason: Unknown 6.70/1.28 % (2075)Termination phase: Saturation 6.70/1.28 6.70/1.28 % (2075)Memory used [KB]: 10234 6.70/1.28 % (2075)Time elapsed: 0.086 s 6.70/1.28 % (2075)Instructions burned: 182 (million) 6.70/1.28 % (2075)------------------------------ 6.70/1.28 % (2075)------------------------------ 6.70/1.28 % (2064)Instruction limit reached! 6.70/1.28 % (2064)------------------------------ 6.70/1.28 % (2064)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 6.70/1.28 % (2064)Termination reason: Unknown 6.70/1.28 % (2064)Termination phase: Saturation 6.70/1.28 6.70/1.28 % (2064)Memory used [KB]: 9466 6.70/1.28 % (2064)Time elapsed: 0.226 s 6.70/1.28 % (2064)Instructions burned: 425 (million) 6.70/1.28 % (2064)------------------------------ 6.70/1.28 % (2064)------------------------------ 6.70/1.29 % (2082)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=422:si=on:rtra=on_0 on theBenchmark for (2990ds/422Mi) 6.70/1.29 % (2083)lrs+10_1:1_cnfonf=lazy_gen:hud=7:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=103:si=on:rtra=on_0 on theBenchmark for (2990ds/103Mi) 6.70/1.30 % (2081)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=940:si=on:rtra=on_0 on theBenchmark for (2991ds/940Mi) 6.70/1.32 % (2078)Instruction limit reached! 6.70/1.32 % (2078)------------------------------ 6.70/1.32 % (2078)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 6.70/1.32 % (2078)Termination reason: Unknown 6.70/1.32 % (2078)Termination phase: Saturation 6.70/1.32 6.70/1.32 % (2078)Memory used [KB]: 7547 6.70/1.32 % (2078)Time elapsed: 0.085 s 6.70/1.32 % (2078)Instructions burned: 193 (million) 6.70/1.32 % (2078)------------------------------ 6.70/1.32 % (2078)------------------------------ 7.08/1.33 % (2083)Instruction limit reached! 7.08/1.33 % (2083)------------------------------ 7.08/1.33 % (2083)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 7.08/1.33 % (2083)Termination reason: Unknown 7.08/1.33 % (2083)Termination phase: Saturation 7.08/1.33 7.08/1.33 % (2083)Memory used [KB]: 6780 7.08/1.33 % (2083)Time elapsed: 0.044 s 7.08/1.33 % (2083)Instructions burned: 104 (million) 7.08/1.33 % (2083)------------------------------ 7.08/1.33 % (2083)------------------------------ 7.08/1.34 % (2084)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on theBenchmark for (2990ds/182Mi) 7.08/1.34 % (2077)Instruction limit reached! 7.08/1.34 % (2077)------------------------------ 7.08/1.34 % (2077)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 7.08/1.34 % (2077)Termination reason: Unknown 7.08/1.34 % (2077)Termination phase: Saturation 7.08/1.34 7.08/1.34 % (2077)Memory used [KB]: 8443 7.08/1.34 % (2077)Time elapsed: 0.125 s 7.08/1.34 % (2077)Instructions burned: 392 (million) 7.08/1.34 % (2077)------------------------------ 7.08/1.34 % (2077)------------------------------ 7.08/1.35 % (2076)Instruction limit reached! 7.08/1.35 % (2076)------------------------------ 7.08/1.35 % (2076)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 7.08/1.35 % (2076)Termination reason: Unknown 7.08/1.35 % (2076)Termination phase: Saturation 7.08/1.35 7.08/1.35 % (2076)Memory used [KB]: 8059 7.08/1.35 % (2076)Time elapsed: 0.154 s 7.08/1.35 % (2076)Instructions burned: 369 (million) 7.08/1.35 % (2076)------------------------------ 7.08/1.35 % (2076)------------------------------ 7.08/1.35 % (2071)Instruction limit reached! 7.08/1.35 % (2071)------------------------------ 7.08/1.35 % (2071)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 7.08/1.35 % (2071)Termination reason: Unknown 7.08/1.35 % (2071)Termination phase: Saturation 7.08/1.35 7.08/1.35 % (2071)Memory used [KB]: 11129 7.08/1.35 % (2071)Time elapsed: 0.213 s 7.08/1.35 % (2071)Instructions burned: 570 (million) 7.08/1.35 % (2071)------------------------------ 7.08/1.35 % (2071)------------------------------ 7.08/1.35 % (2085)lrs+10_1:5_av=off:bd=off:fd=off:kws=precedence:nwc=3.0:prag=on:rawr=on:sos=all:sp=reverse_frequency:i=230:si=on:rtra=on_0 on theBenchmark for (2990ds/230Mi) 7.08/1.35 % (2086)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on theBenchmark for (2990ds/83Mi) 7.08/1.35 % (2079)Instruction limit reached! 7.08/1.35 % (2079)------------------------------ 7.08/1.35 % (2079)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 7.08/1.35 % (2079)Termination reason: Unknown 7.08/1.35 % (2079)Termination phase: Saturation 7.08/1.35 7.08/1.35 % (2079)Memory used [KB]: 6908 7.08/1.35 % (2079)Time elapsed: 0.112 s 7.08/1.35 % (2079)Instructions burned: 280 (million) 7.08/1.35 % (2079)------------------------------ 7.08/1.35 % (2079)------------------------------ 7.08/1.36 % (2088)lrs+1010_1:1_cbe=off:cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=148:si=on:rtra=on_0 on theBenchmark for (2990ds/148Mi) 7.08/1.36 % (2087)lrs+1002_1:1_anc=all:cbe=off:cnfonf=lazy_not_gen_be_off:fe=off:hud=5:nwc=10.0:plsq=on:plsqr=32,1:prag=on:sp=unary_first:i=202:si=on:rtra=on_0 on theBenchmark for (2990ds/202Mi) 7.08/1.37 % (2089)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 (2990ds/104Mi) 7.08/1.37 % (2086)Instruction limit reached! 7.08/1.37 % (2086)------------------------------ 7.08/1.37 % (2086)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 7.08/1.37 % (2086)Termination reason: Unknown 7.08/1.37 % (2086)Termination phase: Function definition elimination 7.08/1.37 7.08/1.37 % (2086)Memory used [KB]: 2046 7.08/1.37 % (2086)Time elapsed: 0.023 s 7.08/1.37 % (2086)Instructions burned: 86 (million) 7.08/1.37 % (2086)------------------------------ 7.08/1.37 % (2086)------------------------------ 7.08/1.38 % (2090)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2990ds/6Mi) 7.08/1.38 % (2090)Instruction limit reached! 7.08/1.38 % (2090)------------------------------ 7.08/1.38 % (2090)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 7.08/1.38 % (2090)Termination reason: Unknown 7.08/1.38 % (2090)Termination phase: shuffling 7.08/1.38 7.08/1.38 % (2090)Memory used [KB]: 1535 7.08/1.38 % (2090)Time elapsed: 0.004 s 7.08/1.38 % (2090)Instructions burned: 8 (million) 7.08/1.38 % (2090)------------------------------ 7.08/1.38 % (2090)------------------------------ 7.63/1.39 % (2091)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1200:si=on:rtra=on_0 on theBenchmark for (2989ds/1200Mi) 7.63/1.41 % (2084)Instruction limit reached! 7.63/1.41 % (2084)------------------------------ 7.63/1.41 % (2084)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 7.63/1.41 % (2084)Termination reason: Unknown 7.63/1.41 % (2084)Termination phase: Saturation 7.63/1.41 7.63/1.41 % (2084)Memory used [KB]: 6908 7.63/1.41 % (2084)Time elapsed: 0.074 s 7.63/1.41 % (2084)Instructions burned: 183 (million) 7.63/1.41 % (2084)------------------------------ 7.63/1.41 % (2084)------------------------------ 7.63/1.41 % (2089)Instruction limit reached! 7.63/1.41 % (2089)------------------------------ 7.63/1.41 % (2089)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 7.63/1.41 % (2089)Termination reason: Unknown 7.63/1.41 % (2089)Termination phase: Saturation 7.63/1.41 7.63/1.41 % (2089)Memory used [KB]: 6780 7.63/1.41 % (2089)Time elapsed: 0.047 s 7.63/1.41 % (2089)Instructions burned: 105 (million) 7.63/1.41 % (2089)------------------------------ 7.63/1.41 % (2089)------------------------------ 7.63/1.42 % (2088)Instruction limit reached! 7.63/1.42 % (2088)------------------------------ 7.63/1.42 % (2088)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 7.63/1.42 % (2088)Termination reason: Unknown 7.63/1.42 % (2088)Termination phase: Saturation 7.63/1.42 7.63/1.42 % (2088)Memory used [KB]: 6908 7.63/1.42 % (2088)Time elapsed: 0.061 s 7.63/1.42 % (2088)Instructions burned: 148 (million) 7.63/1.42 % (2088)------------------------------ 7.63/1.42 % (2088)------------------------------ 7.63/1.43 % (2093)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 (2989ds/164Mi) 7.63/1.43 % (2092)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 (2989ds/90Mi) 7.63/1.44 % (2094)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=392:si=on:rtra=on_0 on theBenchmark for (2989ds/392Mi) 7.63/1.44 % (2087)Instruction limit reached! 7.63/1.44 % (2087)------------------------------ 7.63/1.44 % (2087)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 7.63/1.44 % (2087)Termination reason: Unknown 7.63/1.44 % (2087)Termination phase: Saturation 7.63/1.44 7.63/1.44 % (2087)Memory used [KB]: 7164 7.63/1.44 % (2087)Time elapsed: 0.078 s 7.63/1.44 % (2087)Instructions burned: 206 (million) 7.63/1.44 % (2087)------------------------------ 7.63/1.44 % (2087)------------------------------ 7.63/1.45 % (2085)Instruction limit reached! 7.63/1.45 % (2085)------------------------------ 7.63/1.45 % (2085)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 7.63/1.45 % (2085)Termination reason: Unknown 7.63/1.45 % (2085)Termination phase: Saturation 7.63/1.45 7.63/1.45 % (2085)Memory used [KB]: 3326 7.63/1.45 % (2085)Time elapsed: 0.098 s 7.63/1.45 % (2085)Instructions burned: 233 (million) 7.63/1.45 % (2085)------------------------------ 7.63/1.45 % (2085)------------------------------ 7.63/1.45 % (2095)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on theBenchmark for (2989ds/279Mi) 8.04/1.45 % (2096)lrs+1010_1:128_au=on:av=off:bd=preordered:bs=on:chr=on:cnfonf=lazy_not_gen:ntd=on:piset=and:i=59:si=on:rtra=on_0 on theBenchmark for (2989ds/59Mi) 8.04/1.45 % (2092)Instruction limit reached! 8.04/1.45 % (2092)------------------------------ 8.04/1.45 % (2092)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 8.04/1.45 % (2092)Termination reason: Unknown 8.04/1.45 % (2092)Termination phase: Twee Goal Transformation 8.04/1.45 8.04/1.45 % (2092)Memory used [KB]: 2558 8.04/1.45 % (2092)Time elapsed: 0.027 s 8.04/1.45 % (2092)Instructions burned: 90 (million) 8.04/1.45 % (2092)------------------------------ 8.04/1.45 % (2092)------------------------------ 8.08/1.46 % (2097)lrs+10_1:1_au=on:sd=1:sgt=32:sos=on:ss=axioms:i=141:si=on:rtra=on_0 on theBenchmark for (2989ds/141Mi) 8.08/1.47 % (2096)Instruction limit reached! 8.08/1.47 % (2096)------------------------------ 8.08/1.47 % (2096)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 8.08/1.47 % (2096)Termination reason: Unknown 8.08/1.47 % (2096)Termination phase: Property scanning 8.08/1.47 8.08/1.47 % (2096)Memory used [KB]: 2174 8.08/1.47 % (2096)Time elapsed: 0.016 s 8.08/1.47 % (2096)Instructions burned: 59 (million) 8.08/1.47 % (2096)------------------------------ 8.08/1.47 % (2096)------------------------------ 8.08/1.47 % (2093)Instruction limit reached! 8.08/1.47 % (2093)------------------------------ 8.08/1.47 % (2093)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 8.08/1.47 % (2093)Termination reason: Unknown 8.08/1.47 % (2093)Termination phase: Saturation 8.08/1.47 8.08/1.47 % (2093)Memory used [KB]: 2558 8.08/1.47 % (2093)Time elapsed: 0.046 s 8.08/1.47 % (2093)Instructions burned: 164 (million) 8.08/1.47 % (2093)------------------------------ 8.08/1.47 % (2093)------------------------------ 8.08/1.48 % (2098)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=389:si=on:rtra=on_0 on theBenchmark for (2988ds/389Mi) 8.08/1.48 % (2082)Instruction limit reached! 8.08/1.48 % (2082)------------------------------ 8.08/1.48 % (2082)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 8.08/1.48 % (2082)Termination reason: Unknown 8.08/1.48 % (2082)Termination phase: Saturation 8.08/1.48 8.08/1.48 % (2082)Memory used [KB]: 9978 8.08/1.48 % (2082)Time elapsed: 0.211 s 8.08/1.48 % (2082)Instructions burned: 423 (million) 8.08/1.48 % (2082)------------------------------ 8.08/1.48 % (2082)------------------------------ 8.08/1.48 % (2099)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on theBenchmark for (2988ds/593Mi) 8.08/1.49 % (2100)ott+1010_1:20_cnfonf=lazy_pi_sigma_gen:fe=axiom:plsq=on:plsqc=2:plsqr=32,1:sac=on:sos=all:i=4759:si=on:rtra=on_0 on theBenchmark for (2988ds/4759Mi) 8.08/1.50 % (2097)Instruction limit reached! 8.08/1.50 % (2097)------------------------------ 8.08/1.50 % (2097)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 8.08/1.50 % (2097)Termination reason: Unknown 8.08/1.50 % (2097)Termination phase: Saturation 8.08/1.50 8.08/1.50 % (2097)Memory used [KB]: 7036 8.08/1.50 % (2097)Time elapsed: 0.037 s 8.08/1.50 % (2097)Instructions burned: 141 (million) 8.08/1.50 % (2097)------------------------------ 8.08/1.50 % (2097)------------------------------ 8.41/1.51 % (2106)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on theBenchmark for (2988ds/906Mi) 8.41/1.51 % (2095)Instruction limit reached! 8.41/1.51 % (2095)------------------------------ 8.41/1.51 % (2095)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 8.41/1.51 % (2095)Termination reason: Unknown 8.41/1.51 % (2095)Termination phase: Saturation 8.41/1.51 8.41/1.51 % (2095)Memory used [KB]: 6908 8.41/1.51 % (2095)Time elapsed: 0.066 s 8.41/1.51 % (2095)Instructions burned: 281 (million) 8.41/1.51 % (2095)------------------------------ 8.41/1.51 % (2095)------------------------------ 8.41/1.52 % (2113)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 (2988ds/668Mi) 8.41/1.53 % (2094)Instruction limit reached! 8.41/1.53 % (2094)------------------------------ 8.41/1.53 % (2094)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 8.41/1.53 % (2094)Termination reason: Unknown 8.41/1.53 % (2094)Termination phase: Saturation 8.41/1.53 8.41/1.53 % (2094)Memory used [KB]: 10618 8.41/1.53 % (2094)Time elapsed: 0.093 s 8.41/1.53 % (2094)Instructions burned: 393 (million) 8.41/1.53 % (2094)------------------------------ 8.41/1.53 % (2094)------------------------------ 8.41/1.54 % (2120)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on theBenchmark for (2988ds/1670Mi) 8.58/1.55 % (2081)Instruction limit reached! 8.58/1.55 % (2081)------------------------------ 8.58/1.55 % (2081)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 8.58/1.55 % (2081)Termination reason: Unknown 8.58/1.55 % (2081)Termination phase: Saturation 8.58/1.55 8.58/1.55 % (2081)Memory used [KB]: 7036 8.58/1.55 % (2081)Time elapsed: 0.258 s 8.58/1.55 % (2081)Instructions burned: 943 (million) 8.58/1.55 % (2081)------------------------------ 8.58/1.55 % (2081)------------------------------ 8.58/1.56 % (2131)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 (2988ds/794Mi) 8.58/1.60 % (2098)Instruction limit reached! 8.58/1.60 % (2098)------------------------------ 8.58/1.60 % (2098)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 8.58/1.60 % (2098)Termination reason: Unknown 8.58/1.60 % (2098)Termination phase: Saturation 8.58/1.60 8.58/1.60 % (2098)Memory used [KB]: 9210 8.58/1.60 % (2098)Time elapsed: 0.122 s 8.58/1.60 % (2098)Instructions burned: 391 (million) 8.58/1.60 % (2098)------------------------------ 8.58/1.60 % (2098)------------------------------ 8.58/1.61 % (2151)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 (2987ds/294Mi) 8.98/1.66 % (2099)Instruction limit reached! 8.98/1.66 % (2099)------------------------------ 8.98/1.66 % (2099)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 8.98/1.66 % (2099)Termination reason: Unknown 8.98/1.66 % (2099)Termination phase: Saturation 8.98/1.66 8.98/1.66 % (2099)Memory used [KB]: 8571 8.98/1.66 % (2099)Time elapsed: 0.182 s 8.98/1.66 % (2099)Instructions burned: 593 (million) 8.98/1.66 % (2099)------------------------------ 8.98/1.66 % (2099)------------------------------ 8.98/1.67 % (2177)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=970:si=on:rtra=on_0 on theBenchmark for (2987ds/970Mi) 8.98/1.67 % (2113)Instruction limit reached! 8.98/1.67 % (2113)------------------------------ 8.98/1.67 % (2113)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 8.98/1.67 % (2113)Termination reason: Unknown 8.98/1.67 % (2113)Termination phase: Saturation 8.98/1.67 8.98/1.67 % (2113)Memory used [KB]: 13048 8.98/1.67 % (2113)Time elapsed: 0.155 s 8.98/1.67 % (2113)Instructions burned: 670 (million) 8.98/1.67 % (2113)------------------------------ 8.98/1.67 % (2113)------------------------------ 8.98/1.67 % (2151)Instruction limit reached! 8.98/1.67 % (2151)------------------------------ 8.98/1.67 % (2151)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 8.98/1.67 % (2151)Termination reason: Unknown 8.98/1.67 % (2151)Termination phase: Saturation 8.98/1.67 8.98/1.67 % (2151)Memory used [KB]: 6908 8.98/1.67 % (2151)Time elapsed: 0.071 s 8.98/1.67 % (2151)Instructions burned: 294 (million) 8.98/1.67 % (2151)------------------------------ 8.98/1.67 % (2151)------------------------------ 8.98/1.68 % (2188)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=383:si=on:rtra=on_0 on theBenchmark for (2986ds/383Mi) 8.98/1.68 % (2189)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 (2986ds/961Mi) 11.06/1.78 % (2091)Instruction limit reached! 11.06/1.78 % (2091)------------------------------ 11.06/1.78 % (2091)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 11.06/1.78 % (2091)Termination reason: Unknown 11.06/1.78 % (2091)Termination phase: Saturation 11.06/1.78 11.06/1.78 % (2091)Memory used [KB]: 11897 11.06/1.78 % (2091)Time elapsed: 0.413 s 11.06/1.78 % (2091)Instructions burned: 1200 (million) 11.06/1.78 % (2091)------------------------------ 11.06/1.78 % (2091)------------------------------ 11.06/1.79 % (2252)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=1083:si=on:rtra=on_0 on theBenchmark for (2985ds/1083Mi) 11.06/1.80 % (2188)Instruction limit reached! 11.06/1.80 % (2188)------------------------------ 11.06/1.80 % (2188)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 11.06/1.80 % (2188)Termination reason: Unknown 11.06/1.80 % (2188)Termination phase: Saturation 11.06/1.80 11.06/1.80 % (2188)Memory used [KB]: 10490 11.06/1.80 % (2188)Time elapsed: 0.124 s 11.06/1.80 % (2188)Instructions burned: 384 (million) 11.06/1.80 % (2188)------------------------------ 11.06/1.80 % (2188)------------------------------ 11.06/1.80 % (2131)Instruction limit reached! 11.06/1.80 % (2131)------------------------------ 11.06/1.80 % (2131)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 11.06/1.80 % (2131)Termination reason: Unknown 11.06/1.80 % (2131)Termination phase: Saturation 11.06/1.80 11.06/1.80 % (2131)Memory used [KB]: 4477 11.06/1.80 % (2131)Time elapsed: 0.246 s 11.06/1.80 % (2131)Instructions burned: 794 (million) 11.06/1.80 % (2131)------------------------------ 11.06/1.80 % (2131)------------------------------ 11.06/1.81 % (2106)Instruction limit reached! 11.06/1.81 % (2106)------------------------------ 11.06/1.81 % (2106)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 11.06/1.81 % (2106)Termination reason: Unknown 11.06/1.81 % (2106)Termination phase: Saturation 11.06/1.81 11.06/1.81 % (2106)Memory used [KB]: 9850 11.06/1.81 % (2106)Time elapsed: 0.301 s 11.06/1.81 % (2106)Instructions burned: 907 (million) 11.06/1.81 % (2106)------------------------------ 11.06/1.81 % (2106)------------------------------ 11.06/1.81 % (2262)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=1398:si=on:rtra=on_0 on theBenchmark for (2985ds/1398Mi) 11.06/1.81 % (2263)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 (2985ds/562Mi) 11.37/1.82 % (2265)lrs+1010_1:2_au=on:e2e=on:sd=3:ss=axioms:st=3.0:i=1208:si=on:rtra=on_0 on theBenchmark for (2985ds/1208Mi) 11.45/1.86 % (2177)First to succeed. 11.45/1.92 % (2120)Instruction limit reached! 11.45/1.92 % (2120)------------------------------ 11.45/1.92 % (2120)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 11.45/1.92 % (2120)Termination reason: Unknown 11.45/1.92 % (2120)Termination phase: Saturation 11.45/1.92 11.45/1.92 % (2120)Memory used [KB]: 12025 11.45/1.92 % (2120)Time elapsed: 0.382 s 11.45/1.92 % (2120)Instructions burned: 1672 (million) 11.45/1.92 % (2120)------------------------------ 11.45/1.92 % (2120)------------------------------ 11.79/1.92 % (2279)lrs+1010_1:7_bd=off:cnfonf=lazy_not_be_gen:fe=off:hud=10:tnu=1:i=348:si=on:rtra=on_0 on theBenchmark for (2984ds/348Mi) 11.79/1.94 % (2263)Instruction limit reached! 11.79/1.94 % (2263)------------------------------ 11.79/1.94 % (2263)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 11.79/1.94 % (2263)Termination reason: Unknown 11.79/1.94 % (2263)Termination phase: Saturation 11.79/1.94 11.79/1.94 % (2263)Memory used [KB]: 7164 11.79/1.94 % (2263)Time elapsed: 0.131 s 11.79/1.94 % (2263)Instructions burned: 566 (million) 11.79/1.94 % (2263)------------------------------ 11.79/1.94 % (2263)------------------------------ 11.79/1.95 % (2286)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 (2984ds/343Mi) 12.09/1.98 % (2189)Instruction limit reached! 12.09/1.98 % (2189)------------------------------ 12.09/1.98 % (2189)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 12.09/1.98 % (2189)Termination reason: Unknown 12.09/1.98 % (2189)Termination phase: Saturation 12.09/1.98 12.09/1.98 % (2189)Memory used [KB]: 8827 12.09/1.98 % (2189)Time elapsed: 0.300 s 12.09/1.98 % (2189)Instructions burned: 963 (million) 12.09/1.98 % (2189)------------------------------ 12.09/1.98 % (2189)------------------------------ 12.09/1.99 % (2298)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=1655:si=on:rtra=on_0 on theBenchmark for (2983ds/1655Mi) 12.09/2.01 % (2279)Instruction limit reached! 12.09/2.01 % (2279)------------------------------ 12.09/2.01 % (2279)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 12.09/2.01 % (2279)Termination reason: Unknown 12.09/2.01 % (2279)Termination phase: Saturation 12.09/2.01 12.09/2.01 % (2279)Memory used [KB]: 7547 12.09/2.01 % (2279)Time elapsed: 0.083 s 12.09/2.01 % (2279)Instructions burned: 348 (million) 12.09/2.01 % (2279)------------------------------ 12.09/2.01 % (2279)------------------------------ 12.09/2.01 % (2306)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on theBenchmark for (2983ds/6454Mi) 12.09/2.05 % (2286)Instruction limit reached! 12.09/2.05 % (2286)------------------------------ 12.09/2.05 % (2286)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 12.09/2.05 % (2286)Termination reason: Unknown 12.09/2.05 % (2286)Termination phase: Saturation 12.09/2.05 12.09/2.05 % (2286)Memory used [KB]: 8315 12.09/2.05 % (2286)Time elapsed: 0.098 s 12.09/2.05 % (2286)Instructions burned: 346 (million) 12.09/2.05 % (2286)------------------------------ 12.09/2.05 % (2286)------------------------------ 12.45/2.06 % (2314)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 (2983ds/1539Mi) 12.57/2.13 % (2252)Instruction limit reached! 12.57/2.13 % (2252)------------------------------ 12.57/2.13 % (2252)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 12.57/2.13 % (2252)Termination reason: Unknown 12.57/2.13 % (2252)Termination phase: Saturation 12.57/2.13 12.57/2.13 % (2252)Memory used [KB]: 9850 12.57/2.13 % (2252)Time elapsed: 0.340 s 12.57/2.13 % (2252)Instructions burned: 1085 (million) 12.57/2.13 % (2252)------------------------------ 12.57/2.13 % (2252)------------------------------ 12.57/2.13 % (2351)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 (2982ds/501Mi) 12.96/2.21 % (2265)Instruction limit reached! 12.96/2.21 % (2265)------------------------------ 12.96/2.21 % (2265)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 12.96/2.21 % (2265)Termination reason: Unknown 12.96/2.21 % (2265)Termination phase: Saturation 12.96/2.21 12.96/2.21 % (2265)Memory used [KB]: 11385 12.96/2.21 % (2265)Time elapsed: 0.399 s 12.96/2.21 % (2265)Instructions burned: 1210 (million) 12.96/2.21 % (2265)------------------------------ 12.96/2.21 % (2265)------------------------------ 13.54/2.22 % (2358)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=277:si=on:rtra=on_0 on theBenchmark for (2981ds/277Mi) 13.54/2.22 % (2262)Instruction limit reached! 13.54/2.22 % (2262)------------------------------ 13.54/2.22 % (2262)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 13.54/2.22 % (2262)Termination reason: Unknown 13.54/2.22 % (2262)Termination phase: Saturation 13.54/2.22 13.54/2.22 % (2262)Memory used [KB]: 10106 13.54/2.22 % (2262)Time elapsed: 0.413 s 13.54/2.22 % (2262)Instructions burned: 1400 (million) 13.54/2.22 % (2262)------------------------------ 13.54/2.22 % (2262)------------------------------ 13.54/2.23 % (2359)lrs+21_1:1_cha=on:cnfonf=off:hud=10:kws=inv_frequency:lcm=predicate:sgt=32:sos=on:sp=occurrence:ss=axioms:i=136:si=on:rtra=on_0 on theBenchmark for (2981ds/136Mi) 13.54/2.27 % (2359)Instruction limit reached! 13.54/2.27 % (2359)------------------------------ 13.54/2.27 % (2359)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 13.54/2.27 % (2359)Termination reason: Unknown 13.54/2.27 % (2359)Termination phase: Saturation 13.54/2.27 13.54/2.27 % (2359)Memory used [KB]: 6908 13.54/2.27 % (2359)Time elapsed: 0.037 s 13.54/2.27 % (2359)Instructions burned: 139 (million) 13.54/2.27 % (2359)------------------------------ 13.54/2.27 % (2359)------------------------------ 13.54/2.28 % (2360)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on theBenchmark for (2981ds/401Mi) 13.54/2.29 % (2358)Instruction limit reached! 13.54/2.29 % (2358)------------------------------ 13.54/2.29 % (2358)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 13.54/2.29 % (2358)Termination reason: Unknown 13.54/2.29 % (2358)Termination phase: Saturation 13.54/2.29 13.54/2.29 % (2358)Memory used [KB]: 7291 13.54/2.29 % (2358)Time elapsed: 0.065 s 13.54/2.29 % (2358)Instructions burned: 277 (million) 13.54/2.29 % (2358)------------------------------ 13.54/2.29 % (2358)------------------------------ 15.14/2.29 % (2351)Instruction limit reached! 15.14/2.29 % (2351)------------------------------ 15.14/2.29 % (2351)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 15.14/2.29 % (2351)Termination reason: Unknown 15.14/2.29 % (2351)Termination phase: Saturation 15.14/2.29 15.14/2.29 % (2351)Memory used [KB]: 9338 15.14/2.29 % (2351)Time elapsed: 0.181 s 15.14/2.29 % (2351)Instructions burned: 503 (million) 15.14/2.29 % (2351)------------------------------ 15.14/2.29 % (2351)------------------------------ 15.14/2.30 % (2361)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=4810:si=on:rtra=on_0 on theBenchmark for (2980ds/4810Mi) 15.14/2.30 % (2362)lrs+1002_1:128_atotf=0.1:au=on:cbe=off:ntd=on:sp=const_frequency:i=2020:si=on:rtra=on_0 on theBenchmark for (2980ds/2020Mi) 15.62/2.37 % (2360)Instruction limit reached! 15.62/2.37 % (2360)------------------------------ 15.62/2.37 % (2360)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 15.62/2.37 % (2360)Termination reason: Unknown 15.62/2.37 % (2360)Termination phase: Saturation 15.62/2.37 15.62/2.37 % (2360)Memory used [KB]: 6908 15.62/2.37 % (2360)Time elapsed: 0.091 s 15.62/2.37 % (2360)Instructions burned: 401 (million) 15.62/2.37 % (2360)------------------------------ 15.62/2.37 % (2360)------------------------------ 15.62/2.37 % (2363)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=375:si=on:rtra=on_0 on theBenchmark for (2979ds/375Mi) 15.72/2.38 % (2177)Refutation found. Thanks to Tanya! 15.72/2.38 % SZS status Theorem for theBenchmark 15.72/2.38 % SZS output start Proof for theBenchmark 15.72/2.38 thf(func_def_0, type, in: $i > $i > $o). 15.72/2.38 thf(func_def_1, type, exu: ($i > $o) > $o). 15.72/2.38 thf(func_def_6, type, setadjoin: $i > $i > $i). 15.72/2.38 thf(func_def_8, type, powerset: $i > $i). 15.72/2.38 thf(func_def_10, type, setunion: $i > $i). 15.72/2.38 thf(func_def_19, type, descr: ($i > $o) > $i). 15.72/2.38 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i). 15.72/2.38 thf(func_def_26, type, prop2set: $o > $i). 15.72/2.38 thf(func_def_36, type, nonempty: $i > $o). 15.72/2.38 thf(func_def_69, type, set2prop: $i > $o). 15.72/2.38 thf(func_def_88, type, subset: $i > $i > $o). 15.72/2.38 thf(func_def_89, type, disjoint: $i > $i > $o). 15.72/2.38 thf(func_def_90, type, setsmeet: $i > $i > $o). 15.72/2.38 thf(func_def_114, type, binunion: $i > $i > $i). 15.72/2.38 thf(func_def_122, type, binintersect: $i > $i > $i). 15.72/2.38 thf(func_def_135, type, regular: $i > $o). 15.72/2.38 thf(func_def_136, type, setminus: $i > $i > $i). 15.72/2.38 thf(func_def_147, type, symdiff: $i > $i > $i). 15.72/2.38 thf(func_def_153, type, iskpair: $i > $o). 15.72/2.38 thf(func_def_158, type, kpair: $i > $i > $i). 15.72/2.38 thf(func_def_160, type, cartprod: $i > $i > $i). 15.72/2.38 thf(func_def_177, type, singleton: $i > $o). 15.72/2.38 thf(func_def_179, type, ex1: $i > ($i > $o) > $o). 15.72/2.38 thf(func_def_184, type, atmost1p: $i > $o). 15.72/2.38 thf(func_def_185, type, atleast2p: $i > $o). 15.72/2.38 thf(func_def_186, type, atmost2p: $i > $o). 15.72/2.38 thf(func_def_187, type, upairsetp: $i > $o). 15.72/2.38 thf(func_def_191, type, kfst: $i > $i). 15.72/2.38 thf(func_def_203, type, ksnd: $i > $i). 15.72/2.38 thf(func_def_213, type, breln: $i > $i > $i > $o). 15.72/2.38 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 15.72/2.38 thf(func_def_222, type, func: $i > $i > $i > $o). 15.72/2.38 thf(func_def_223, type, funcSet: $i > $i > $i). 15.72/2.38 thf(func_def_226, type, ap: $i > $i > $i > $i > $i). 15.72/2.38 thf(f1017,plain,( 15.72/2.38 $false), 15.72/2.38 inference(trivial_inequality_removal,[],[f1016])). 15.72/2.38 thf(f1016,plain,( 15.72/2.38 ($false = $true)), 15.72/2.38 inference(boolean_simplification,[],[f1015])). 15.72/2.38 thf(f1015,plain,( 15.72/2.38 ($true = (~ $true))), 15.72/2.38 inference(boolean_simplification,[],[f1014])). 15.72/2.38 thf(f1014,plain,( 15.72/2.38 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => $true)))), 15.72/2.38 inference(boolean_simplification,[],[f1013])). 15.72/2.38 thf(f1013,plain,( 15.72/2.38 ((~ ((!! @ $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)), 15.72/2.38 inference(boolean_simplification,[],[f1012])). 15.72/2.38 thf(f1012,plain,( 15.72/2.38 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => $true)))) = $true)), 15.72/2.38 inference(boolean_simplification,[],[f1011])). 15.72/2.38 thf(f1011,plain,( 15.72/2.38 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => $true))))) = $true)), 15.72/2.38 inference(boolean_simplification,[],[f1010])). 15.72/2.38 thf(f1010,plain,( 15.72/2.38 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => $true)))))) = $true)), 15.72/2.38 inference(boolean_simplification,[],[f1009])). 15.72/2.38 thf(f1009,plain,( 15.72/2.38 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((in @ emptyset @ omega) => $true))))))) = $true)), 15.72/2.38 inference(boolean_simplification,[],[f1008])). 15.72/2.38 thf(f1008,plain,( 15.72/2.38 ($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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => $true)))))))))), 15.72/2.38 inference(boolean_simplification,[],[f1007])). 15.72/2.38 thf(f1007,plain,( 15.72/2.38 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => $true))))))))) = $true)), 15.72/2.38 inference(boolean_simplification,[],[f1006])). 15.72/2.38 thf(f1006,plain,( 15.72/2.38 ($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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => $true)))))))))))), 15.72/2.38 inference(boolean_simplification,[],[f1005])). 15.72/2.38 thf(f1005,plain,( 15.72/2.38 ($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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => $true))))))))))))), 15.72/2.38 inference(boolean_simplification,[],[f1004])). 15.72/2.38 thf(f1004,plain,( 15.72/2.38 ($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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => $true)))))))))))))), 15.72/2.38 inference(boolean_simplification,[],[f1003])). 15.72/2.38 thf(f1003,plain,( 15.72/2.38 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => $true))))))))))))) = $true)), 15.72/2.38 inference(boolean_simplification,[],[f1002])). 15.72/2.38 thf(f1002,plain,( 15.72/2.38 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => $true)))))))))))))) = $true)), 15.72/2.38 inference(boolean_simplification,[],[f1001])). 15.72/2.38 thf(f1001,plain,( 15.72/2.38 ($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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => $true))))))))))))))))), 15.72/2.38 inference(boolean_simplification,[],[f1000])). 15.72/2.38 thf(f1000,plain,( 15.72/2.38 ($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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => $true)))))))))))))))))), 15.72/2.38 inference(boolean_simplification,[],[f999])). 15.72/2.38 thf(f999,plain,( 15.72/2.38 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => $true))))))))))))))))) = $true)), 15.72/2.38 inference(boolean_simplification,[],[f998])). 15.72/2.38 thf(f998,plain,( 15.72/2.38 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => $true)))))))))))))))))) = $true)), 15.72/2.38 inference(boolean_simplification,[],[f997])). 15.72/2.38 thf(f997,plain,( 15.72/2.38 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => $true))))))))))))))))))) = $true)), 15.72/2.38 inference(boolean_simplification,[],[f996])). 15.72/2.38 thf(f996,plain,( 15.72/2.38 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => $true)))))))))))))))))))) = $true)), 15.72/2.38 inference(boolean_simplification,[],[f995])). 15.72/2.38 thf(f995,plain,( 15.72/2.38 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => $true))))))))))))))))))))) = $true)), 15.72/2.38 inference(boolean_simplification,[],[f994])). 15.72/2.38 thf(f994,plain,( 15.72/2.38 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => $true)))))))))))))))))))))) = $true)), 15.72/2.38 inference(boolean_simplification,[],[f993])). 15.72/2.38 thf(f993,plain,( 15.72/2.38 ($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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => $true))))))))))))))))))))))))), 15.72/2.38 inference(boolean_simplification,[],[f992])). 15.72/2.38 thf(f992,plain,( 15.72/2.38 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => $true)))))))))))))))))))))))) = $true)), 15.72/2.38 inference(boolean_simplification,[],[f991])). 15.72/2.38 thf(f991,plain,( 15.72/2.38 ($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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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))))))))))))))))))))))))))), 15.72/2.38 inference(boolean_simplification,[],[f990])). 15.72/2.38 thf(f990,plain,( 15.72/2.38 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => $true)))))))))))))))))))))))))) = $true)), 15.72/2.38 inference(boolean_simplification,[],[f989])). 15.72/2.38 thf(f989,plain,( 15.72/2.38 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => $true))))))))))))))))))))))))))) = $true)), 15.72/2.38 inference(boolean_simplification,[],[f988])). 15.72/2.38 thf(f988,plain,( 15.72/2.38 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => $true)))))))))))))))))))))))))))) = $true)), 15.72/2.38 inference(boolean_simplification,[],[f987])). 15.72/2.38 thf(f987,plain,( 15.72/2.38 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => $true))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f986])). 15.72/2.39 thf(f986,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))) => $true)))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f985])). 15.72/2.39 thf(f985,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f984])). 15.72/2.39 thf(f984,plain,( 15.72/2.39 ($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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => $true)))))))))))))))))))))))))))))))))), 15.72/2.39 inference(boolean_simplification,[],[f983])). 15.72/2.39 thf(f983,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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)), 15.72/2.39 inference(boolean_simplification,[],[f982])). 15.72/2.39 thf(f982,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => $true)))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f981])). 15.72/2.39 thf(f981,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => $true))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f980])). 15.72/2.39 thf(f980,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => $true)))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f979])). 15.72/2.39 thf(f979,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => $true))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f978])). 15.72/2.39 thf(f978,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => $true)))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f977])). 15.72/2.39 thf(f977,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => $true))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f976])). 15.72/2.39 thf(f976,plain,( 15.72/2.39 ($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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))), 15.72/2.39 inference(boolean_simplification,[],[f975])). 15.72/2.39 thf(f975,plain,( 15.72/2.39 ($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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => $true))))))))))))))))))))))))))))))))))))))))))), 15.72/2.39 inference(boolean_simplification,[],[f974])). 15.72/2.39 thf(f974,plain,( 15.72/2.39 ($true = (~ ((!! 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@ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => $true)))))))))))))))))))))))))))))))))))))))))))), 15.72/2.39 inference(boolean_simplification,[],[f973])). 15.72/2.39 thf(f973,plain,( 15.72/2.39 ($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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! 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@ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))), 15.72/2.39 inference(boolean_simplification,[],[f972])). 15.72/2.39 thf(f972,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))) => $true)))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f971])). 15.72/2.39 thf(f971,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => $true))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f970])). 15.72/2.39 thf(f970,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f969])). 15.72/2.39 thf(f969,plain,( 15.72/2.39 ($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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))), 15.72/2.39 inference(boolean_simplification,[],[f968])). 15.72/2.39 thf(f968,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f967])). 15.72/2.39 thf(f967,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f966])). 15.72/2.39 thf(f966,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f965])). 15.72/2.39 thf(f965,plain,( 15.72/2.39 ($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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))), 15.72/2.39 inference(boolean_simplification,[],[f964])). 15.72/2.39 thf(f964,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => ((emptyset = (dsetconstr @ Y1 @ Y0)) => $false)))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f963])). 15.72/2.39 thf(f963,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => ((emptyset = (dsetconstr @ Y1 @ Y0)) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f962])). 15.72/2.39 thf(f962,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => ((emptyset = (dsetconstr @ Y1 @ Y0)) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f961])). 15.72/2.39 thf(f961,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => ((emptyset = (dsetconstr @ Y1 @ Y0)) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($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)), 15.72/2.39 inference(boolean_simplification,[],[f960])). 15.72/2.39 thf(f960,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => ((emptyset = (dsetconstr @ Y1 @ Y0)) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))))))))) => ((!! @ ($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)), 15.72/2.39 inference(boolean_simplification,[],[f959])). 15.72/2.39 thf(f959,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => ((emptyset = (dsetconstr @ Y1 @ Y0)) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ $i @ (^[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)), 15.72/2.39 inference(boolean_simplification,[],[f958])). 15.72/2.39 thf(f958,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => ((emptyset = (dsetconstr @ Y1 @ Y0)) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f957])). 15.72/2.39 thf(f957,plain,( 15.72/2.39 ($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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => ((emptyset = (dsetconstr @ Y1 @ Y0)) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 15.72/2.39 inference(boolean_simplification,[],[f956])). 15.72/2.39 thf(f956,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => ((emptyset = (dsetconstr @ Y1 @ Y0)) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f955])). 15.72/2.39 thf(f955,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => ((emptyset = (dsetconstr @ Y1 @ Y0)) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))) => (!! @ $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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f954])). 15.72/2.39 thf(f954,plain,( 15.72/2.39 ($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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! 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@ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => ((emptyset = (dsetconstr @ Y1 @ Y0)) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))) => (!! @ $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 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $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 > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f952])). 15.72/2.39 thf(f952,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => ((emptyset = (dsetconstr @ Y1 @ Y0)) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))) => (!! @ $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 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $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 > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f951])). 15.72/2.39 thf(f951,plain,( 15.72/2.39 ($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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))) => (!! @ $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 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $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 > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f949])). 15.72/2.39 thf(f949,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! 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@ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => ((emptyset = (dsetconstr @ Y1 @ Y0)) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))) => (!! @ $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 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $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 > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f948])). 15.72/2.39 thf(f948,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => ((emptyset = (dsetconstr @ Y1 @ Y0)) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))) => (!! @ $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 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $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 > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) = (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f947])). 15.72/2.39 thf(f947,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => ((emptyset = (dsetconstr @ Y1 @ Y0)) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))) => (!! @ $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 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $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 > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) = (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((emptyset = emptyset) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f946])). 15.72/2.39 thf(f946,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! 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@ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) = (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f945])). 15.72/2.39 thf(f945,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! 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@ $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 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $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 > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) = (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f944])). 15.72/2.39 thf(f944,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! 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@ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) = (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f943])). 15.72/2.39 thf(f943,plain,( 15.72/2.39 ((~ ((!! 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@ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))) => (!! @ $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 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $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 > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) = (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f942])). 15.72/2.39 thf(f942,plain,( 15.72/2.39 ((~ ((!! 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@ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) = (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f941])). 15.72/2.39 thf(f941,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! 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@ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) => ((descr @ Y0) = (descr @ Y1))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f940])). 15.72/2.39 thf(f940,plain,( 15.72/2.39 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! 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@ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y3) = (dsetconstr @ Y0 @ Y2)))))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f939])). 15.72/2.39 thf(f939,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => ((emptyset = (dsetconstr @ Y1 @ Y0)) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))) => (!! @ $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 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $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 > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) = (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y3) = (dsetconstr @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f938])). 15.72/2.39 thf(f938,plain,( 15.72/2.39 ($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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => ((emptyset = (dsetconstr @ Y1 @ Y0)) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))) => (!! @ $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 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $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 > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) = (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y3) = (dsetconstr @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 15.72/2.39 inference(boolean_simplification,[],[f937])). 15.72/2.39 thf(f937,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => ((emptyset = (dsetconstr @ Y1 @ Y0)) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))) => (!! @ $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 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $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 > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) = (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y3) = (dsetconstr @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f936])). 15.72/2.39 thf(f936,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => ((emptyset = (dsetconstr @ Y1 @ Y0)) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! 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@ ($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]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) = (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y3) = (dsetconstr @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f935])). 15.72/2.39 thf(f935,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => ((emptyset = (dsetconstr @ Y1 @ Y0)) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))) => (!! @ $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 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $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 > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) = (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y3) = (dsetconstr @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f934])). 15.72/2.39 thf(f934,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => ((emptyset = (dsetconstr @ Y1 @ Y0)) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))) => (!! @ $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 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $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 > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) = (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y3) = (dsetconstr @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f933])). 15.72/2.39 thf(f933,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! 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@ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => ((emptyset = (dsetconstr @ Y1 @ Y0)) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))))))))) => ((!! 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@ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) = (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y3) = (dsetconstr @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f932])). 15.72/2.39 thf(f932,plain,( 15.72/2.39 ((~ ((!! @ $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 : $i]: (((in @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! 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@ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) = (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y3) = (dsetconstr @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (subset @ Y2 @ Y0)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f931])). 15.72/2.39 thf(f931,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! 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@ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => ((emptyset = (dsetconstr @ Y1 @ Y0)) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))) => (!! @ $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 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $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 > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) = (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y3) = (dsetconstr @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (subset @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f930])). 15.72/2.39 thf(f930,plain,( 15.72/2.39 ($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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! 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@ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => ((emptyset = (dsetconstr @ Y1 @ Y0)) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))) => (!! @ $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 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $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 > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) = (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y3) = (dsetconstr @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (subset @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f928])). 15.72/2.39 thf(f928,plain,( 15.72/2.39 ($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]: (!! 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@ $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 @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (subset @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (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 @ Y1) => ((subset @ Y1 @ Y2) => (subset @ Y0 @ Y2))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 15.72/2.39 inference(boolean_simplification,[],[f927])). 15.72/2.39 thf(f927,plain,( 15.72/2.39 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! 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@ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => ((emptyset = (dsetconstr @ Y1 @ Y0)) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))) => (!! @ $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 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $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 > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) = (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y3) = (dsetconstr @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (subset @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (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 @ Y1) => ((subset @ Y1 @ Y2) => (subset @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f926])). 15.72/2.39 thf(f926,plain,( 15.72/2.39 ((~ ((!! 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@ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y3) = (dsetconstr @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (subset @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (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 @ Y1) => ((subset @ Y1 @ Y2) => (subset @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f922])). 15.72/2.39 thf(f922,plain,( 15.72/2.39 ($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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! 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@ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) = (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y3) = (dsetconstr @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (subset @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (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 @ Y1) => ((subset @ Y1 @ Y2) => (subset @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f920])). 15.72/2.39 thf(f920,plain,( 15.72/2.39 ($true = (~ ((!! 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@ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => ((emptyset = (dsetconstr @ Y1 @ Y0)) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))))))))) => ((!! 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@ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) = (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y3) = (dsetconstr @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (subset @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (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 @ Y1) => ((subset @ Y1 @ Y2) => (subset @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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)), 15.72/2.39 inference(boolean_simplification,[],[f917])). 15.72/2.39 thf(f917,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => ((emptyset = (dsetconstr @ Y1 @ Y0)) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))) => (!! @ $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 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $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 > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) = (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y3) = (dsetconstr @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (subset @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (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 @ Y1) => ((subset @ Y1 @ Y2) => (subset @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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)), 15.72/2.39 inference(boolean_simplification,[],[f916])). 15.72/2.39 thf(f916,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $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 @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => ((emptyset = (dsetconstr @ Y1 @ Y0)) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))) => (!! @ $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 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $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 > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) = (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y3) = (dsetconstr @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (subset @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (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 @ Y1) => ((subset @ Y1 @ Y2) => (subset @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ (binunion @ Y0 @ Y1))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f915])). 15.72/2.39 thf(f915,plain,( 15.72/2.39 ((~ ((!! 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@ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y2) => (subset @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f914])). 15.72/2.39 thf(f914,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! 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@ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y3) = (dsetconstr @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (subset @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (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 @ Y1) => ((subset @ Y1 @ Y2) => (subset @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f913])). 15.72/2.39 thf(f913,plain,( 15.72/2.39 ($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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! 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@ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ Y2)) => (!! @ $o @ (^[Y3 : $o]: (((Y1 = Y0) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => ((emptyset = (dsetconstr @ Y1 @ Y0)) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))) => (!! @ $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 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $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 > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) = (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y3) = (dsetconstr @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (subset @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (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 @ Y1) => ((subset @ Y1 @ Y2) => (subset @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: ((in @ Y0 @ (binunion @ Y1 @ Y2)) => (((in @ Y0 @ Y1) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binunion @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1)))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f910])). 15.72/2.39 thf(f910,plain,( 15.72/2.39 ((~ ((!! 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@ $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 @ Y1) => ((subset @ Y1 @ Y2) => (subset @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: ((in @ Y0 @ (binunion @ Y1 @ Y2)) => (((in @ Y0 @ Y1) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binunion @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f908])). 15.72/2.39 thf(f908,plain,( 15.72/2.39 ($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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! 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@ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! 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@ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))) => (!! @ $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 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $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 > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) = (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y3) = (dsetconstr @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (subset @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (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 @ Y1) => ((subset @ Y1 @ Y2) => (subset @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: ((in @ Y0 @ (binunion @ Y1 @ Y2)) => (((in @ Y0 @ Y1) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binunion @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $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 @ Y2 @ Y1) => ((subset @ Y2 @ Y0) => (subset @ Y2 @ (binintersect @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f906])). 15.72/2.39 thf(f906,plain,( 15.72/2.39 ($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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! 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@ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y3) = (dsetconstr @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (subset @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (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 @ Y1) => ((subset @ Y1 @ Y2) => (subset @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: ((in @ Y0 @ (binunion @ Y1 @ Y2)) => (((in @ Y0 @ Y1) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binunion @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $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 @ Y2 @ Y1) => ((subset @ Y2 @ Y0) => (subset @ Y2 @ (binintersect @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f903])). 15.72/2.39 thf(f903,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! 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@ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! 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@ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))) => (!! @ $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 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $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 > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) = (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y3) = (dsetconstr @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (subset @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (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 @ Y1) => ((subset @ Y1 @ Y2) => (subset @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: ((in @ Y0 @ (binunion @ Y1 @ Y2)) => (((in @ Y0 @ Y1) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binunion @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $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 @ Y2 @ Y1) => ((subset @ Y2 @ Y0) => (subset @ Y2 @ (binintersect @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1)))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f902])). 15.72/2.39 thf(f902,plain,( 15.72/2.39 ($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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))) => (emptyset = (binintersect @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f900])). 15.72/2.39 thf(f900,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! 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@ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y3) = (dsetconstr @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (subset @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (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 @ Y1) => ((subset @ Y1 @ Y2) => (subset @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: ((in @ Y0 @ (binunion @ Y1 @ Y2)) => (((in @ Y0 @ Y1) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binunion @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $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 @ Y2 @ Y1) => ((subset @ Y2 @ Y0) => (subset @ Y2 @ (binintersect @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))) => (emptyset = (binintersect @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f899])). 15.72/2.39 thf(f899,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! 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@ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! 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@ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))) => (!! @ $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 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $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 > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) = (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y3) = (dsetconstr @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (subset @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (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 @ Y1) => ((subset @ Y1 @ Y2) => (subset @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: ((in @ Y0 @ (binunion @ Y1 @ Y2)) => (((in @ Y0 @ Y1) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binunion @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $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 @ Y2 @ Y1) => ((subset @ Y2 @ Y0) => (subset @ Y2 @ (binintersect @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))) => (emptyset = (binintersect @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f898])). 15.72/2.39 thf(f898,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! 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@ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! 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@ $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]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))) => (!! @ $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 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $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 > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) = (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y3) = (dsetconstr @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (subset @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (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 @ Y1) => ((subset @ Y1 @ Y2) => (subset @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: ((in @ Y0 @ (binunion @ Y1 @ Y2)) => (((in @ Y0 @ Y1) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binunion @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $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 @ Y2 @ Y1) => ((subset @ Y2 @ Y0) => (subset @ Y2 @ (binintersect @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))) => (emptyset = (binintersect @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0)) = (binintersect @ Y2 @ (binunion @ Y1 @ Y0))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f897])). 15.72/2.39 thf(f897,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((in @ emptyset @ omega) => ((!! 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@ $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 @ Y0) => (in @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: ((in @ Y0 @ (binunion @ Y1 @ Y2)) => (((in @ Y0 @ Y1) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binunion @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $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 @ Y2 @ Y1) => ((subset @ Y2 @ Y0) => (subset @ Y2 @ (binintersect @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))) => (emptyset = (binintersect @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0)) = (binintersect @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f896])). 15.72/2.39 thf(f896,plain,( 15.72/2.39 ((~ ((!! 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@ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (?? @ $i @ (^[Y3 : $i]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! 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@ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) = (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y3) = (dsetconstr @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (subset @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (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 @ Y1) => ((subset @ Y1 @ Y2) => (subset @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: ((in @ Y0 @ (binunion @ Y1 @ Y2)) => (((in @ Y0 @ Y1) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binunion @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $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 @ Y2 @ Y1) => ((subset @ Y2 @ Y0) => (subset @ Y2 @ (binintersect @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))) => (emptyset = (binintersect @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0)) = (binintersect @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f895])). 15.72/2.39 thf(f895,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! 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@ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ 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 @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => ((emptyset = (dsetconstr @ Y1 @ Y0)) => $false)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))) => (!! @ $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 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $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 > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) = (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y3) = (dsetconstr @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (subset @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (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 @ Y1) => ((subset @ Y1 @ Y2) => (subset @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: ((in @ Y0 @ (binunion @ Y1 @ Y2)) => (((in @ Y0 @ Y1) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binunion @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $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 @ Y2 @ Y1) => ((subset @ Y2 @ Y0) => (subset @ Y2 @ (binintersect @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))) => (emptyset = (binintersect @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0)) = (binintersect @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y1 @ Y0)) => (~ (in @ Y2 @ Y0))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f894])). 15.72/2.39 thf(f894,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! 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@ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binunion @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $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 @ Y2 @ Y1) => ((subset @ Y2 @ Y0) => (subset @ Y2 @ (binintersect @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))) => (emptyset = (binintersect @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0)) = (binintersect @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y1 @ Y0)) => (~ (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f893])). 15.72/2.39 thf(f893,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! 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@ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) = (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y3) = (dsetconstr @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (subset @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (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 @ Y1) => ((subset @ Y1 @ Y2) => (subset @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: ((in @ Y0 @ (binunion @ Y1 @ Y2)) => (((in @ Y0 @ Y1) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binunion @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $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 @ Y2 @ Y1) => ((subset @ Y2 @ Y0) => (subset @ Y2 @ (binintersect @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))) => (emptyset = (binintersect @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0)) = (binintersect @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y1 @ Y0)) => (~ (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y2 @ Y0))) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f892])). 15.72/2.39 thf(f892,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $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 @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! 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@ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) = (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y3) = (dsetconstr @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (subset @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (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 @ Y1) => ((subset @ Y1 @ Y2) => (subset @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: ((in @ Y0 @ (binunion @ Y1 @ Y2)) => (((in @ Y0 @ Y1) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binunion @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $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 @ Y2 @ Y1) => ((subset @ Y2 @ Y0) => (subset @ Y2 @ (binintersect @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))) => (emptyset = (binintersect @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0)) = (binintersect @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y1 @ Y0)) => (~ (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y2 @ Y0))) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y0 @ Y1))) => ((~ (in @ Y2 @ Y1)) => (~ (in @ Y2 @ Y0)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f891])). 15.72/2.39 thf(f891,plain,( 15.72/2.39 ((~ ((!! @ $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]: (!! 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@ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: ((in @ Y0 @ (binunion @ Y1 @ Y2)) => (((in @ Y0 @ Y1) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binunion @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $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 @ Y2 @ Y1) => ((subset @ Y2 @ Y0) => (subset @ Y2 @ (binintersect @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))) => (emptyset = (binintersect @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0)) = (binintersect @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y1 @ Y0)) => (~ (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y2 @ Y0))) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y0 @ Y1))) => ((~ (in @ Y2 @ Y1)) => (~ (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (setminus @ Y0 @ Y1)))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f890])). 15.72/2.39 thf(f890,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! 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@ $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 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $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 > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) = (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y3) = (dsetconstr @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (subset @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (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 @ Y1) => ((subset @ Y1 @ Y2) => (subset @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: ((in @ Y0 @ (binunion @ Y1 @ Y2)) => (((in @ Y0 @ Y1) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binunion @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $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 @ Y2 @ Y1) => ((subset @ Y2 @ Y0) => (subset @ Y2 @ (binintersect @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))) => (emptyset = (binintersect @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0)) = (binintersect @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y1 @ Y0)) => (~ (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y2 @ Y0))) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y0 @ Y1))) => ((~ (in @ Y2 @ Y1)) => (~ (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (setminus @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (in @ Y2 @ (setminus @ Y1 @ Y0)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f889])). 15.72/2.39 thf(f889,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y1 @ Y0)) => (~ (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y2 @ Y0))) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y0 @ Y1))) => ((~ (in @ Y2 @ Y1)) => (~ (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (setminus @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (in @ Y2 @ (setminus @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f888])). 15.72/2.39 thf(f888,plain,( 15.72/2.39 ($true = (~ ((!! 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@ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) = (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y3) = (dsetconstr @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (subset @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (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 @ Y1) => ((subset @ Y1 @ Y2) => (subset @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: ((in @ Y0 @ (binunion @ Y1 @ Y2)) => (((in @ Y0 @ Y1) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binunion @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $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 @ Y2 @ Y1) => ((subset @ Y2 @ Y0) => (subset @ Y2 @ (binintersect @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))) => (emptyset = (binintersect @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0)) = (binintersect @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y1 @ Y0)) => (~ (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y2 @ Y0))) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y0 @ Y1))) => ((~ (in @ Y2 @ Y1)) => (~ (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (setminus @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (in @ Y2 @ (setminus @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (symdiff @ Y2 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => Y3)) => (((~ (in @ Y1 @ Y2)) => ((in @ Y1 @ Y0) => Y3)) => Y3))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f886])). 15.72/2.39 thf(f886,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0)) = (binintersect @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y1 @ Y0)) => (~ (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y2 @ Y0))) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y0 @ Y1))) => ((~ (in @ Y2 @ Y1)) => (~ (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (setminus @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (in @ Y2 @ (setminus @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (symdiff @ Y2 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => Y3)) => (((~ (in @ Y1 @ Y2)) => ((in @ Y1 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f885])). 15.72/2.39 thf(f885,plain,( 15.72/2.39 ($true = (~ ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (symdiff @ Y2 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => Y3)) => (((~ (in @ Y1 @ Y2)) => ((in @ Y1 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 15.72/2.39 inference(boolean_simplification,[],[f884])). 15.72/2.39 thf(f884,plain,( 15.72/2.39 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! 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@ $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 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $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 > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) = (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y3) = (dsetconstr @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (subset @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (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 @ Y1) => ((subset @ Y1 @ Y2) => (subset @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: ((in @ Y0 @ (binunion @ Y1 @ Y2)) => (((in @ Y0 @ Y1) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binunion @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $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 @ Y2 @ Y1) => ((subset @ Y2 @ Y0) => (subset @ Y2 @ (binintersect @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))) => (emptyset = (binintersect @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0)) = (binintersect @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y1 @ Y0)) => (~ (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y2 @ Y0))) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y0 @ Y1))) => ((~ (in @ Y2 @ Y1)) => (~ (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (setminus @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (in @ Y2 @ (setminus @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (symdiff @ Y2 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => Y3)) => (((~ (in @ Y1 @ Y2)) => ((in @ Y1 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y1 @ Y0) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ Y2)) => ((~ (in @ Y1 @ Y0)) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f882])). 15.72/2.39 thf(f882,plain,( 15.72/2.39 ((~ ((!! 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@ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y1 @ Y0)) => (~ (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y2 @ Y0))) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y0 @ Y1))) => ((~ (in @ Y2 @ Y1)) => (~ (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (setminus @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (in @ Y2 @ (setminus @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (symdiff @ Y2 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => Y3)) => (((~ (in @ Y1 @ Y2)) => ((in @ Y1 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y1 @ Y0) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ Y2)) => ((~ (in @ Y1 @ Y0)) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f881])). 15.72/2.39 thf(f881,plain,( 15.72/2.39 ((~ ((!! 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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 @ Y2 @ Y1) => ((subset @ Y2 @ Y0) => (subset @ Y2 @ (binintersect @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))) => (emptyset = (binintersect @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0)) = (binintersect @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y1 @ Y0)) => (~ (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y2 @ Y0))) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y0 @ Y1))) => ((~ (in @ Y2 @ Y1)) => (~ (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (setminus @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (in @ Y2 @ (setminus @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (symdiff @ Y2 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => Y3)) => (((~ (in @ Y1 @ Y2)) => ((in @ Y1 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y1 @ Y0) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ Y2)) => ((~ (in @ Y1 @ Y0)) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f880])). 15.72/2.39 thf(f880,plain,( 15.72/2.39 ($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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((in @ emptyset @ omega) => ((!! 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@ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) = (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y3) = (dsetconstr @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (subset @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (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 @ Y1) => ((subset @ Y1 @ Y2) => (subset @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: ((in @ Y0 @ (binunion @ Y1 @ Y2)) => (((in @ Y0 @ Y1) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binunion @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $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 @ Y2 @ Y1) => ((subset @ Y2 @ Y0) => (subset @ Y2 @ (binintersect @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))) => (emptyset = (binintersect @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0)) = (binintersect @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y1 @ Y0)) => (~ (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y2 @ Y0))) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y0 @ Y1))) => ((~ (in @ Y2 @ Y1)) => (~ (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (setminus @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (in @ Y2 @ (setminus @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (symdiff @ Y2 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => Y3)) => (((~ (in @ Y1 @ Y2)) => ((in @ Y1 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y1 @ Y0) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ Y2)) => ((~ (in @ Y1 @ Y0)) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ 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 @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f878])). 15.72/2.39 thf(f878,plain,( 15.72/2.39 ((~ ((!! 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@ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y3) = (dsetconstr @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (subset @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (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 @ Y1) => ((subset @ Y1 @ Y2) => (subset @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: ((in @ Y0 @ (binunion @ Y1 @ Y2)) => (((in @ Y0 @ Y1) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binunion @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $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 @ Y2 @ Y1) => ((subset @ Y2 @ Y0) => (subset @ Y2 @ (binintersect @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))) => (emptyset = (binintersect @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0)) = (binintersect @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y1 @ Y0)) => (~ (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y2 @ Y0))) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y0 @ Y1))) => ((~ (in @ Y2 @ Y1)) => (~ (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (setminus @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (in @ Y2 @ (setminus @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (symdiff @ Y2 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => Y3)) => (((~ (in @ Y1 @ Y2)) => ((in @ Y1 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y1 @ Y0) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ Y2)) => ((~ (in @ Y1 @ Y0)) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ 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 @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f876])). 15.72/2.39 thf(f876,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! 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@ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) = (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (!! @ $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]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2)))) => ((?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3)))) & (Y0 @ Y2)))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ Y3) = (dsetconstr @ Y0 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (subset @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (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 @ Y1) => ((subset @ Y1 @ Y2) => (subset @ Y0 @ Y2))))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $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 @ Y0) => (in @ Y2 @ (binunion @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: ((in @ Y0 @ (binunion @ Y1 @ Y2)) => (((in @ Y0 @ Y1) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binunion @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $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 @ Y2 @ Y1) => ((subset @ Y2 @ Y0) => (subset @ Y2 @ (binintersect @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))) => (emptyset = (binintersect @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0)) = (binintersect @ Y2 @ (binunion @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y1 @ Y0)) => (~ (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y2 @ Y0))) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y0 @ Y1))) => ((~ (in @ Y2 @ Y1)) => (~ (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (setminus @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (in @ Y2 @ (setminus @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (symdiff @ Y2 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => Y3)) => (((~ (in @ Y1 @ Y2)) => ((in @ Y1 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y1 @ Y0) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ Y2)) => ((~ (in @ Y1 @ Y0)) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ 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 @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y1)))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f874])). 15.72/2.39 thf(f874,plain,( 15.72/2.39 ((~ ((!! 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@ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y1 @ Y0)) => (~ (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y2 @ Y0))) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y0 @ Y1))) => ((~ (in @ Y2 @ Y1)) => (~ (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (setminus @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (in @ Y2 @ (setminus @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (symdiff @ Y2 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => Y3)) => (((~ (in @ Y1 @ Y2)) => ((in @ Y1 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y1 @ Y0) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ Y2)) => ((~ (in @ Y1 @ Y0)) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ 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 @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f873])). 15.72/2.39 thf(f873,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! 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@ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (~ (emptyset = (dsetconstr @ Y1 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y2)))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f872])). 15.72/2.39 thf(f872,plain,( 15.72/2.39 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! 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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 @ Y2 @ Y1) => ((subset @ Y2 @ Y0) => (subset @ Y2 @ (binintersect @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1)))))))) => ((!! 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@ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y1 @ Y0)) => (~ (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y2 @ Y0))) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y0 @ Y1))) => ((~ (in @ Y2 @ Y1)) => (~ (in @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (setminus @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (in @ Y2 @ (setminus @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (symdiff @ Y2 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => Y3)) => (((~ (in @ Y1 @ Y2)) => ((in @ Y1 @ Y0) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y1 @ Y0) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ Y2)) => ((~ (in @ Y1 @ Y0)) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ 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 @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y0 @ Y2))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y1)))))))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f869])). 15.72/2.39 thf(f869,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f868])). 15.72/2.39 thf(f868,plain,( 15.72/2.39 ((~ ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y0 @ Y2))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y2)))) & (in @ Y3 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (iskpair @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f862])). 15.72/2.39 thf(f862,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y2)))) & (in @ Y3 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (iskpair @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ $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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f861])). 15.72/2.39 thf(f861,plain,( 15.72/2.39 ($true = (~ ((!! 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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 @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y0 @ Y2))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y2)))) & (in @ Y3 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (iskpair @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ $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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $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)), 15.72/2.39 inference(boolean_simplification,[],[f859])). 15.72/2.39 thf(f859,plain,( 15.72/2.39 ((~ ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ $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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)))))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f858])). 15.72/2.39 thf(f858,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! 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@ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)))))))))))))) => ((!! @ $i @ (^[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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f857])). 15.72/2.39 thf(f857,plain,( 15.72/2.39 ((~ ((!! 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@ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y2)))) & (in @ Y3 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (iskpair @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ $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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)))))))))))))) => ((!! @ $i @ (^[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 @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f856])). 15.72/2.39 thf(f856,plain,( 15.72/2.39 ((~ ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y2)))) & (in @ Y3 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (iskpair @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ $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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y1 @ Y0) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ Y2)) => ((~ (in @ Y1 @ Y0)) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ 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 @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y0 @ Y2))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y2)))) & (in @ Y3 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (iskpair @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ $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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)))))))))))))) => ((!! @ $i @ (^[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 @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (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 @ Y1 @ Y0)) = Y1))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f852])). 15.72/2.39 thf(f852,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! 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@ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ (setunion @ Y0) @ (^[Y2 : $i]: (in @ (setadjoin @ Y2 @ emptyset) @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0)))) => (in @ (setunion @ Y0) @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y1 @ Y0)) = Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (in @ (kfst @ Y0) @ Y1)))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f851])). 15.72/2.39 thf(f851,plain,( 15.72/2.39 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! 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@ $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 @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (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 @ Y1 @ Y0)) = Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (in @ (kfst @ Y0) @ Y1)))))))) => ((!! @ $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 @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => (Y3 = Y2)))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f850])). 15.72/2.39 thf(f850,plain,( 15.72/2.39 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))) => ((!! 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@ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y2)))) & (in @ Y3 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (iskpair @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ $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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)))))))))))))) => ((!! @ $i @ (^[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 @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (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 @ Y1 @ Y0)) = Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (in @ (kfst @ Y0) @ Y1)))))))) => ((!! @ $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 @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => (Y3 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y0 @ Y3)) => (Y2 = Y0)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f849])). 15.72/2.39 thf(f849,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! 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@ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y0)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y0)))))))))))))) => ((!! @ $i @ (^[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 @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (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 @ Y1 @ Y0)) = Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (in @ (kfst @ Y0) @ Y1)))))))) => ((!! @ $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 @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => (Y3 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y0 @ Y3)) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f848])). 15.72/2.39 thf(f848,plain,( 15.72/2.39 ($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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! 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@ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! 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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 @ Y1 @ Y0)) = Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (in @ (kfst @ Y0) @ Y1)))))))) => ((!! @ $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 @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => (Y3 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y0 @ Y3)) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ 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 @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => ((Y2 = Y0) => (Y3 = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) = (setadjoin @ Y2 @ emptyset)) => (Y1 = Y0)))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f845])). 15.72/2.39 thf(f845,plain,( 15.72/2.39 ((~ ((!! 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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 @ Y1 @ Y0)) = Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (in @ (kfst @ Y0) @ Y1)))))))) => ((!! @ $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 @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => (Y3 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y0 @ Y3)) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ 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 @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => ((Y2 = Y0) => (Y3 = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) = (setadjoin @ Y2 @ emptyset)) => (Y1 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f844])). 15.72/2.39 thf(f844,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y0 @ Y3)) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ 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 @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => ((Y2 = Y0) => (Y3 = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) = (setadjoin @ Y2 @ emptyset)) => (Y1 = Y0)))))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y0 @ Y3)) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ 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 @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => ((Y2 = Y0) => (Y3 = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) = (setadjoin @ Y2 @ emptyset)) => (Y1 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y0 @ Y1) = (kpair @ Y3 @ Y2)) => (Y2 = Y1)))))))))) => ((!! @ $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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f842])). 15.72/2.39 thf(f842,plain,( 15.72/2.39 ((~ ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y0 @ Y3)) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ 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 @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => ((Y2 = Y0) => (Y3 = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) = (setadjoin @ Y2 @ emptyset)) => (Y1 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y0 @ Y1) = (kpair @ Y3 @ Y2)) => (Y2 = Y1)))))))))) => ((!! @ $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 @ Y0 @ Y1)) = Y1))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f841])). 15.72/2.39 thf(f841,plain,( 15.72/2.39 ((~ ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y0 @ Y1) = (kpair @ Y3 @ Y2)) => (Y2 = Y1)))))))))) => ((!! @ $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 @ Y0 @ Y1)) = Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => ((kpair @ (kfst @ Y0) @ (ksnd @ Y0)) = Y0)))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f840])). 15.72/2.39 thf(f840,plain,( 15.72/2.39 ((~ ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y0 @ Y3)) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ 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 @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => ((Y2 = Y0) => (Y3 = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) = (setadjoin @ Y2 @ emptyset)) => (Y1 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y0 @ Y1) = (kpair @ Y3 @ Y2)) => (Y2 = Y1)))))))))) => ((!! @ $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 @ Y0 @ Y1)) = Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => ((kpair @ (kfst @ Y0) @ (ksnd @ Y0)) = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y0 @ Y1)) => (in @ (ksnd @ Y2) @ Y1)))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f839])). 15.72/2.39 thf(f839,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y0 @ Y3)) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ 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 @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => ((Y2 = Y0) => (Y3 = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) = (setadjoin @ Y2 @ emptyset)) => (Y1 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y0 @ Y1) = (kpair @ Y3 @ Y2)) => (Y2 = Y1)))))))))) => ((!! @ $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 @ Y0 @ Y1)) = Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => ((kpair @ (kfst @ Y0) @ (ksnd @ Y0)) = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y0 @ Y1)) => (in @ (ksnd @ Y2) @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y0 @ Y1) @ (cartprod @ Y3 @ Y2)) => (in @ Y0 @ Y3)))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f838])). 15.72/2.39 thf(f838,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y0 @ Y3)) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ 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 @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => ((Y2 = Y0) => (Y3 = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) = (setadjoin @ Y2 @ emptyset)) => (Y1 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y0 @ Y1) = (kpair @ Y3 @ Y2)) => (Y2 = Y1)))))))))) => ((!! @ $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 @ Y0 @ Y1)) = Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => ((kpair @ (kfst @ Y0) @ (ksnd @ Y0)) = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y0 @ Y1)) => (in @ (ksnd @ Y2) @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y0 @ Y1) @ (cartprod @ Y3 @ Y2)) => (in @ Y0 @ Y3)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y1) @ (cartprod @ Y0 @ Y2)) => (in @ Y1 @ Y2)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f837])). 15.72/2.39 thf(f837,plain,( 15.72/2.39 ($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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))) => ((!! 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@ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y0 @ Y1)) => (in @ (ksnd @ Y2) @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y0 @ Y1) @ (cartprod @ Y3 @ Y2)) => (in @ Y0 @ Y3)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y1) @ (cartprod @ Y0 @ Y2)) => (in @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kpair @ Y2 @ Y3) = (kpair @ Y2 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((kfst @ (kpair @ Y1 @ Y3)) = Y1))))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f835])). 15.72/2.39 thf(f835,plain,( 15.72/2.39 ((~ ((!! 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@ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y0 @ Y1)) => (in @ (ksnd @ Y2) @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y0 @ Y1) @ (cartprod @ Y3 @ Y2)) => (in @ Y0 @ Y3)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y1) @ (cartprod @ Y0 @ Y2)) => (in @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kpair @ Y2 @ Y3) = (kpair @ Y2 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((kfst @ (kpair @ Y1 @ Y3)) = Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((ksnd @ (kpair @ Y2 @ Y3)) = Y3))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f834])). 15.72/2.39 thf(f834,plain,( 15.72/2.39 ((~ ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y2)))) & (in @ Y3 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (iskpair @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((!! @ $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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $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 @ Y1 @ Y0)) = Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (in @ (kfst @ Y0) @ Y1)))))))) => ((!! @ $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 @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => (Y3 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y0 @ Y3)) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ 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 @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => ((Y2 = Y0) => (Y3 = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) = (setadjoin @ Y2 @ emptyset)) => (Y1 = Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y0 @ Y1) = (kpair @ Y3 @ Y2)) => (Y2 = Y1)))))))))) => ((!! @ $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 @ Y0 @ Y1)) = Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => ((kpair @ (kfst @ Y0) @ (ksnd @ Y0)) = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y0 @ Y1)) => (in @ (ksnd @ Y2) @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y0 @ Y1) @ (cartprod @ Y3 @ Y2)) => (in @ Y0 @ Y3)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y1) @ (cartprod @ Y0 @ Y2)) => (in @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kpair @ Y2 @ Y3) = (kpair @ Y2 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((kfst @ (kpair @ Y1 @ Y3)) = Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((ksnd @ (kpair @ Y2 @ Y3)) = Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => ((kpair @ (kfst @ Y1) @ (ksnd @ Y1)) = Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y3 @ Y1 @ Y4) => (in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y0 @ Y2 @ Y3))))))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f832])). 15.72/2.39 thf(f832,plain,( 15.72/2.39 ($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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))) => ((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 @ omega) & (in @ Y1 @ Y0)) => (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]: ((!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y2 @ Y4) => (Y3 = Y4)))) & (Y1 @ Y2 @ Y3))))))) => (?? @ $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]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y0) & (in @ Y2 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! 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@ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y0 @ Y1)) => (in @ (ksnd @ Y2) @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y0 @ Y1) @ (cartprod @ Y3 @ Y2)) => (in @ Y0 @ Y3)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y1) @ (cartprod @ Y0 @ Y2)) => (in @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kpair @ Y2 @ Y3) = (kpair @ Y2 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((kfst @ (kpair @ Y1 @ Y3)) = Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((ksnd @ (kpair @ Y2 @ Y3)) = Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => ((kpair @ (kfst @ Y1) @ (ksnd @ Y1)) = Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y3 @ Y1 @ Y4) => (in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y0 @ Y2 @ Y3))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y0 @ Y1 @ Y2) @ (cartprod @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y1 @ Y0 @ Y2) @ (cartprod @ Y1 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y3 @ Y0 @ Y2)) => (Y2 @ Y1 @ Y4)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: ((in @ (kpair @ Y1 @ Y3) @ (dpsetconstr @ Y0 @ Y2 @ Y4)) => (in @ Y1 @ Y0)))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f828])). 15.72/2.39 thf(f828,plain,( 15.72/2.39 ((~ ((!! @ $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 @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => ((!! 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@ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ Y0)) => (Y0 @ Y2)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1)))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => ((kpair @ (kfst @ Y1) @ (ksnd @ Y1)) = Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y3 @ Y1 @ Y4) => (in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y0 @ Y2 @ Y3))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y0 @ Y1 @ Y2) @ (cartprod @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y1 @ Y0 @ Y2) @ (cartprod @ Y1 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y3 @ Y0 @ Y2)) => (Y2 @ Y1 @ Y4)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: ((in @ (kpair @ Y1 @ Y3) @ (dpsetconstr @ Y0 @ Y2 @ Y4)) => (in @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y1 @ Y2) @ (dpsetconstr @ Y4 @ Y0 @ Y3)) => (in @ Y2 @ Y0)))))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f827])). 15.72/2.39 thf(f827,plain,( 15.72/2.39 ($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]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y1 @ Y0 @ Y2) @ (cartprod @ Y1 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y3 @ Y0 @ Y2)) => (Y2 @ Y1 @ Y4)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: ((in @ (kpair @ Y1 @ Y3) @ (dpsetconstr @ Y0 @ Y2 @ Y4)) => (in @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y1 @ Y2) @ (dpsetconstr @ Y4 @ Y0 @ Y3)) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y2 @ Y3 @ Y1)) => (Y1 @ Y0 @ Y4)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1)))))))))) & (subset @ Y1 @ (cartprod @ Y2 @ Y0))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1)))) & ((setadjoin @ Y4 @ emptyset) = (dsetconstr @ Y0 @ (^[Y5 : $i]: (in @ (kpair @ Y3 @ Y5) @ Y1))))))))))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(boolean_simplification,[],[f825])). 15.72/2.39 thf(f825,plain,( 15.72/2.39 ((~ ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y3 @ Y1 @ Y4) => (in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y0 @ Y2 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y3 @ Y5 @ Y6))))))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y2 @ Y3 @ Y4))))) @ (cartprod @ Y0 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y1 @ Y0 @ (dpsetconstr @ Y1 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y2 @ Y3 @ Y4)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y3 @ Y0 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y2 @ Y5 @ Y6)))))) => (Y2 @ Y1 @ Y4)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: ((in @ (kpair @ Y1 @ Y3) @ (dpsetconstr @ Y0 @ Y2 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y4 @ Y5 @ Y6)))))) => (in @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y1 @ Y2) @ (dpsetconstr @ Y4 @ Y0 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y3 @ Y5 @ Y6)))))) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y2 @ Y3 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y1 @ Y5 @ Y6)))))) => (Y1 @ Y0 @ Y4)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((!! @ $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)))))) & ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (subset @ Y8 @ (cartprod @ Y6 @ Y7))))))) @ Y3 @ Y4 @ Y5))))))) @ Y2 @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & ((setadjoin @ Y5 @ emptyset) = Y4))))) @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((!! @ $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)))))) & ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (subset @ Y8 @ (cartprod @ Y6 @ Y7))))))) @ Y3 @ Y4 @ Y5))))))) @ Y2 @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setunion @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y0)))) @ Y1))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((!! @ $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)))))) & ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (subset @ Y8 @ (cartprod @ Y6 @ Y7))))))) @ Y3 @ Y4 @ Y5))))))) @ Y2 @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (setunion @ (dsetconstr @ Y5 @ (^[Y8 : $i]: (in @ (kpair @ Y7 @ Y8) @ Y6))))))))))) @ Y2 @ Y1 @ Y0 @ Y3) @ Y1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.39 inference(definition_unfolding,[],[f642,f766,f757,f730,f644,f727,f613,f616,f678,f795,f781,f632,f796,f600,f598,f786,f797,f721,f709,f778,f688,f798,f695,f728,f690,f752,f799,f800,f801,f775,f636,f692,f703,f617,f596,f792,f793,f627,f630,f622,f723,f633,f802,f803,f785,f673,f660,f790,f612,f674,f733,f621,f735,f780,f736,f631,f751,f687,f791,f711,f663,f804,f805,f806,f743,f753,f807,f808,f643,f667,f771,f657,f787,f809,f810,f754,f724,f629,f747,f607,f655,f702,f671,f737,f664,f748,f668,f603,f716,f694,f734,f713,f739,f675,f684,f742,f732,f706,f682,f637,f683,f776,f650,f615,f774,f693,f681,f720,f623,f717,f599,f651,f611,f656,f718,f691,f697,f712,f659,f738,f719,f726,f653,f634,f669,f699,f768,f662,f756,f708,f762,f602,f605,f714,f784,f645,f744,f626,f755,f685,f624,f769,f640,f764,f707,f705,f749,f777,f788,f638,f746,f620,f745,f770,f811,f813,f814,f815,f760,f609,f816,f817,f652,f661,f783,f710,f641,f767,f618,f680,f686,f670,f818,f689,f763,f635,f698,f639,f619,f608,f794,f741,f701,f654,f819,f789,f773,f625,f658,f822,f823,f820,f722])). 15.72/2.39 thf(f722,plain,( 15.72/2.39 (ap = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (setunion @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2))))))))))))), 15.72/2.39 inference(cnf_transformation,[],[f401])). 15.72/2.39 thf(f401,plain,( 15.72/2.39 (ap = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (setunion @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2))))))))))))), 15.72/2.39 inference(fool_elimination,[],[f400])). 15.72/2.39 thf(f400,plain,( 15.72/2.39 (ap = (^[X0 : $i, X1 : $i, X2 : $i, X3 : $i] : (setunion @ (dsetconstr @ X1 @ (^[X4 : $i] : (in @ (kpair @ X3 @ X4) @ X2))))))), 15.72/2.39 inference(rectify,[],[f198])). 15.72/2.39 thf(f198,axiom,( 15.72/2.39 (ap = (^[X3 : $i, X4 : $i, X13 : $i, X1 : $i] : (setunion @ (dsetconstr @ X4 @ (^[X2 : $i] : (in @ (kpair @ X1 @ X2) @ X13))))))), 15.72/2.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap)). 15.72/2.39 thf(f820,plain,( 15.72/2.39 (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $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)))))) & ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y0 @ Y1 @ Y2))))))))), 15.72/2.39 inference(definition_unfolding,[],[f700,f812,f779])). 15.72/2.39 thf(f779,plain,( 15.72/2.39 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))), 15.72/2.39 inference(cnf_transformation,[],[f431])). 15.72/2.39 thf(f431,plain,( 15.72/2.39 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))), 15.72/2.39 inference(fool_elimination,[],[f430])). 15.72/2.39 thf(f430,plain,( 15.72/2.39 (breln = (^[X0 : $i, X1 : $i, X2 : $i] : (subset @ X2 @ (cartprod @ X0 @ X1))))), 15.72/2.39 inference(rectify,[],[f186])). 15.72/2.39 thf(f186,axiom,( 15.72/2.39 (breln = (^[X3 : $i, X4 : $i, X5 : $i] : (subset @ X5 @ (cartprod @ X3 @ X4))))), 15.72/2.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln)). 15.72/2.39 thf(f812,plain,( 15.72/2.39 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) & ((setadjoin @ Y3 @ emptyset) = Y2))))) @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))), 15.72/2.39 inference(definition_unfolding,[],[f648,f750])). 15.72/2.39 thf(f750,plain,( 15.72/2.39 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0))))))), 15.72/2.39 inference(cnf_transformation,[],[f407])). 15.72/2.39 thf(f407,plain,( 15.72/2.39 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0))))))), 15.72/2.39 inference(fool_elimination,[],[f406])). 15.72/2.39 thf(f406,plain,( 15.72/2.39 ((^[X0 : $i] : (? [X1] : (((setadjoin @ X1 @ emptyset) = X0) & (in @ X1 @ X0)))) = singleton)), 15.72/2.39 inference(rectify,[],[f156])). 15.72/2.39 thf(f156,axiom,( 15.72/2.39 ((^[X3 : $i] : (? [X1] : (((setadjoin @ X1 @ emptyset) = X3) & (in @ X1 @ X3)))) = singleton)), 15.72/2.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton)). 15.72/2.39 thf(f648,plain,( 15.72/2.39 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))), 15.72/2.39 inference(cnf_transformation,[],[f421])). 15.72/2.39 thf(f421,plain,( 15.72/2.39 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))), 15.72/2.39 inference(fool_elimination,[],[f420])). 15.72/2.39 thf(f420,plain,( 15.72/2.39 (ex1 = (^[X0 : $i, X1 : $i > $o] : (singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))))))), 15.72/2.39 inference(rectify,[],[f158])). 15.72/2.39 thf(f158,axiom,( 15.72/2.39 (ex1 = (^[X3 : $i, X0 : $i > $o] : (singleton @ (dsetconstr @ X3 @ (^[X1 : $i] : (X0 @ X1))))))), 15.72/2.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1)). 15.72/2.39 thf(f700,plain,( 15.72/2.39 (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (ex1 @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))) & (breln @ Y0 @ Y1 @ Y2))))))))), 15.72/2.39 inference(cnf_transformation,[],[f287])). 15.72/2.39 thf(f287,plain,( 15.72/2.39 (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (ex1 @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))) & (breln @ Y0 @ Y1 @ Y2))))))))), 15.72/2.39 inference(fool_elimination,[],[f286])). 15.72/2.39 thf(f286,plain,( 15.72/2.39 ((^[X0 : $i, X1 : $i, X2 : $i] : ((breln @ X0 @ X1 @ X2) & ! [X3] : ((in @ X3 @ X0) => (ex1 @ X1 @ (^[X4 : $i] : (in @ (kpair @ X3 @ X4) @ X2)))))) = func)), 15.72/2.39 inference(rectify,[],[f194])). 15.72/2.39 thf(f194,axiom,( 15.72/2.39 ((^[X3 : $i, X4 : $i, X12 : $i] : ((breln @ X3 @ X4 @ X12) & ! [X1] : ((in @ X1 @ X3) => (ex1 @ X4 @ (^[X2 : $i] : (in @ (kpair @ X1 @ X2) @ X12)))))) = func)), 15.72/2.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',func)). 15.72/2.39 thf(f823,plain,( 15.72/2.39 (apProp = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((!! @ $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)))))) & ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (subset @ Y8 @ (cartprod @ Y6 @ Y7))))))) @ Y3 @ Y4 @ Y5))))))) @ Y2 @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setunion @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y0)))) @ Y1))))))))))))), 15.72/2.39 inference(definition_unfolding,[],[f772,f820])). 15.72/2.39 thf(f772,plain,( 15.72/2.39 (apProp = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setunion @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y0)))) @ Y1))))))))))))), 15.72/2.39 inference(cnf_transformation,[],[f341])). 15.72/2.39 thf(f341,plain,( 15.72/2.39 (apProp = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setunion @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y0)))) @ Y1))))))))))))), 15.72/2.39 inference(fool_elimination,[],[f340])). 15.72/2.39 thf(f340,plain,( 15.72/2.39 (! [X0,X1,X2] : ((func @ X0 @ X1 @ X2) => ! [X3] : ((in @ X3 @ X0) => (in @ (setunion @ (dsetconstr @ X1 @ (^[X4 : $i] : (in @ (kpair @ X3 @ X4) @ X2)))) @ X1))) = apProp)), 15.72/2.39 inference(rectify,[],[f197])). 15.72/2.39 thf(f197,axiom,( 15.72/2.39 (! [X3,X4,X13] : ((func @ X3 @ X4 @ X13) => ! [X1] : ((in @ X1 @ X3) => (in @ (setunion @ (dsetconstr @ X4 @ (^[X2 : $i] : (in @ (kpair @ X1 @ X2) @ X13)))) @ X4))) = apProp)), 15.72/2.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',apProp)). 15.72/2.39 thf(f822,plain,( 15.72/2.39 (funcImageSingleton = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((!! @ $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)))))) & ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (subset @ Y8 @ (cartprod @ Y6 @ Y7))))))) @ Y3 @ Y4 @ Y5))))))) @ Y2 @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & ((setadjoin @ Y5 @ emptyset) = Y4))))) @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y1)))))))))))))))), 15.72/2.39 inference(definition_unfolding,[],[f610,f820,f750])). 15.72/2.39 thf(f610,plain,( 15.72/2.39 (funcImageSingleton = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (singleton @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y1)))))))))))))))), 15.72/2.39 inference(cnf_transformation,[],[f524])). 15.72/2.39 thf(f524,plain,( 15.72/2.39 (funcImageSingleton = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (singleton @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y1)))))))))))))))), 15.72/2.39 inference(fool_elimination,[],[f523])). 15.72/2.39 thf(f523,plain,( 15.72/2.39 (! [X0,X1,X2] : ((func @ X0 @ X2 @ X1) => ! [X3] : ((in @ X3 @ X0) => (singleton @ (dsetconstr @ X2 @ (^[X4 : $i] : (in @ (kpair @ X3 @ X4) @ X1)))))) = funcImageSingleton)), 15.72/2.39 inference(rectify,[],[f196])). 15.72/2.39 thf(f196,axiom,( 15.72/2.39 (! [X3,X13,X4] : ((func @ X3 @ X4 @ X13) => ! [X1] : ((in @ X1 @ X3) => (singleton @ (dsetconstr @ X4 @ (^[X2 : $i] : (in @ (kpair @ X1 @ X2) @ X13)))))) = funcImageSingleton)), 15.72/2.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcImageSingleton)). 15.72/2.39 thf(f658,plain,( 15.72/2.39 (dpsetconstrER = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y2 @ Y3 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y1 @ Y5 @ Y6)))))) => (Y1 @ Y0 @ Y4)))))))))))))), 15.72/2.39 inference(cnf_transformation,[],[f289])). 15.72/2.39 thf(f289,plain,( 15.72/2.39 (dpsetconstrER = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y0 @ Y4) @ (dpsetconstr @ Y2 @ Y3 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y1 @ Y5 @ Y6)))))) => (Y1 @ Y0 @ Y4)))))))))))))), 15.72/2.39 inference(fool_elimination,[],[f288])). 15.72/2.39 thf(f288,plain,( 15.72/2.39 (dpsetconstrER = ! [X0,X1,X2,X3 : $i > $i > $o,X4] : ((in @ (kpair @ X4 @ X0) @ (dpsetconstr @ X2 @ X1 @ (^[X5 : $i, X6 : $i] : (X3 @ X5 @ X6)))) => (X3 @ X4 @ X0)))), 15.72/2.39 inference(rectify,[],[f193])). 15.72/2.39 thf(f193,axiom,( 15.72/2.39 (dpsetconstrER = ! [X2,X4,X3,X0 : $i > $i > $o,X1] : ((in @ (kpair @ X1 @ X2) @ (dpsetconstr @ X3 @ X4 @ (^[X8 : $i, X10 : $i] : (X0 @ X8 @ X10)))) => (X0 @ X1 @ X2)))), 15.72/2.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrER)). 15.72/2.39 thf(f625,plain,( 15.72/2.39 (dpsetconstrEL2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y1 @ Y2) @ (dpsetconstr @ Y4 @ Y0 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y3 @ Y5 @ Y6)))))) => (in @ Y2 @ Y0)))))))))))))), 15.72/2.39 inference(cnf_transformation,[],[f231])). 15.72/2.39 thf(f231,plain,( 15.72/2.39 (dpsetconstrEL2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: ((in @ (kpair @ Y1 @ Y2) @ (dpsetconstr @ Y4 @ Y0 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y3 @ Y5 @ Y6)))))) => (in @ Y2 @ Y0)))))))))))))), 15.72/2.39 inference(fool_elimination,[],[f230])). 15.72/2.39 thf(f230,plain,( 15.72/2.39 (dpsetconstrEL2 = ! [X0,X1 : $i > $i > $o,X2,X3,X4] : ((in @ (kpair @ X3 @ X2) @ (dpsetconstr @ X0 @ X4 @ (^[X5 : $i, X6 : $i] : (X1 @ X5 @ X6)))) => (in @ X2 @ X4)))), 15.72/2.39 inference(rectify,[],[f192])). 15.72/2.39 thf(f192,axiom,( 15.72/2.39 (dpsetconstrEL2 = ! [X3,X0 : $i > $i > $o,X2,X1,X4] : ((in @ (kpair @ X1 @ X2) @ (dpsetconstr @ X3 @ X4 @ (^[X8 : $i, X10 : $i] : (X0 @ X8 @ X10)))) => (in @ X2 @ X4)))), 15.72/2.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL2)). 15.72/2.39 thf(f773,plain,( 15.72/2.39 (dpsetconstrEL1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: ((in @ (kpair @ Y1 @ Y3) @ (dpsetconstr @ Y0 @ Y2 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y4 @ Y5 @ Y6)))))) => (in @ Y1 @ Y0)))))))))))))), 15.72/2.39 inference(cnf_transformation,[],[f271])). 15.72/2.39 thf(f271,plain,( 15.72/2.39 (dpsetconstrEL1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: ((in @ (kpair @ Y1 @ Y3) @ (dpsetconstr @ Y0 @ Y2 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y4 @ Y5 @ Y6)))))) => (in @ Y1 @ Y0)))))))))))))), 15.72/2.39 inference(fool_elimination,[],[f270])). 15.72/2.39 thf(f270,plain,( 15.72/2.39 (! [X0 : $i > $i > $o,X1,X2,X3,X4] : ((in @ (kpair @ X3 @ X1) @ (dpsetconstr @ X4 @ X2 @ (^[X5 : $i, X6 : $i] : (X0 @ X5 @ X6)))) => (in @ X3 @ X4)) = dpsetconstrEL1)), 15.72/2.39 inference(rectify,[],[f191])). 15.72/2.39 thf(f191,axiom,( 15.72/2.39 (! [X0 : $i > $i > $o,X2,X4,X1,X3] : ((in @ (kpair @ X1 @ X2) @ (dpsetconstr @ X3 @ X4 @ (^[X8 : $i, X10 : $i] : (X0 @ X8 @ X10)))) => (in @ X1 @ X3)) = dpsetconstrEL1)), 15.72/2.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL1)). 15.72/2.39 thf(f789,plain,( 15.72/2.39 (dpsetconstrERa = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y3 @ Y0 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y2 @ Y5 @ Y6)))))) => (Y2 @ Y1 @ Y4)))))))))))))))), 15.72/2.39 inference(cnf_transformation,[],[f211])). 15.72/2.39 thf(f211,plain,( 15.72/2.39 (dpsetconstrERa = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y3) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y3 @ Y0 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y2 @ Y5 @ Y6)))))) => (Y2 @ Y1 @ Y4)))))))))))))))), 15.72/2.39 inference(fool_elimination,[],[f210])). 15.72/2.39 thf(f210,plain,( 15.72/2.39 (dpsetconstrERa = ! [X0,X1 : $i > $i > $o,X2,X3] : ((in @ X2 @ X0) => ! [X4] : ((in @ X4 @ X3) => ((in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X0 @ X3 @ (^[X5 : $i, X6 : $i] : (X1 @ X5 @ X6)))) => (X1 @ X2 @ X4)))))), 15.72/2.39 inference(rectify,[],[f190])). 15.72/2.39 thf(f190,axiom,( 15.72/2.39 (dpsetconstrERa = ! [X3,X0 : $i > $i > $o,X1,X4] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => ((in @ (kpair @ X1 @ X2) @ (dpsetconstr @ X3 @ X4 @ (^[X8 : $i, X10 : $i] : (X0 @ X8 @ X10)))) => (X0 @ X1 @ X2)))))), 15.72/2.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrERa)). 15.72/2.39 thf(f819,plain,( 15.72/2.39 (setOfPairsIsBReln = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y1 @ Y0 @ (dpsetconstr @ Y1 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y2 @ Y3 @ Y4)))))))))))))), 15.72/2.39 inference(definition_unfolding,[],[f646,f779])). 15.72/2.39 thf(f646,plain,( 15.72/2.39 (setOfPairsIsBReln = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (breln @ Y1 @ Y0 @ (dpsetconstr @ Y1 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y2 @ Y3 @ Y4)))))))))))))), 15.72/2.39 inference(cnf_transformation,[],[f299])). 15.72/2.39 thf(f299,plain,( 15.72/2.39 (setOfPairsIsBReln = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (breln @ Y1 @ Y0 @ (dpsetconstr @ Y1 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y2 @ Y3 @ Y4)))))))))))))), 15.72/2.39 inference(fool_elimination,[],[f298])). 15.72/2.39 thf(f298,plain,( 15.72/2.39 (! [X0 : $i > $i > $o,X1,X2] : (breln @ X1 @ X2 @ (dpsetconstr @ X1 @ X2 @ (^[X3 : $i, X4 : $i] : (X0 @ X3 @ X4)))) = setOfPairsIsBReln)), 15.72/2.39 inference(rectify,[],[f189])). 15.72/2.39 thf(f189,axiom,( 15.72/2.39 (! [X0 : $i > $i > $o,X3,X4] : (breln @ X3 @ X4 @ (dpsetconstr @ X3 @ X4 @ (^[X1 : $i, X2 : $i] : (X0 @ X1 @ X2)))) = setOfPairsIsBReln)), 15.72/2.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setOfPairsIsBReln)). 15.72/2.39 thf(f654,plain,( 15.72/2.39 (dpsetconstrSub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y2 @ Y3 @ Y4))))) @ (cartprod @ Y0 @ Y1)))))))))), 15.72/2.39 inference(cnf_transformation,[],[f429])). 15.72/2.39 thf(f429,plain,( 15.72/2.39 (dpsetconstrSub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y2 @ Y3 @ Y4))))) @ (cartprod @ Y0 @ Y1)))))))))), 15.72/2.39 inference(fool_elimination,[],[f428])). 15.72/2.39 thf(f428,plain,( 15.72/2.39 (! [X0 : $i > $i > $o,X1,X2] : (subset @ (dpsetconstr @ X2 @ X1 @ (^[X3 : $i, X4 : $i] : (X0 @ X3 @ X4))) @ (cartprod @ X2 @ X1)) = dpsetconstrSub)), 15.72/2.39 inference(rectify,[],[f188])). 15.72/2.39 thf(f188,axiom,( 15.72/2.39 (! [X0 : $i > $i > $o,X4,X3] : (subset @ (dpsetconstr @ X3 @ X4 @ (^[X1 : $i, X2 : $i] : (X0 @ X1 @ X2))) @ (cartprod @ X3 @ X4)) = dpsetconstrSub)), 15.72/2.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrSub)). 15.72/2.39 thf(f701,plain,( 15.72/2.39 (dpsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y3 @ Y1 @ Y4) => (in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y0 @ Y2 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y3 @ Y5 @ Y6))))))))))))))))))))), 15.72/2.39 inference(cnf_transformation,[],[f319])). 15.72/2.39 thf(f319,plain,( 15.72/2.39 (dpsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => ((Y3 @ Y1 @ Y4) => (in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y0 @ Y2 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y3 @ Y5 @ Y6))))))))))))))))))))), 15.72/2.39 inference(fool_elimination,[],[f318])). 15.72/2.39 thf(f318,plain,( 15.72/2.39 (! [X0 : $i > $i > $o,X1,X2,X3] : ((in @ X2 @ X3) => ! [X4] : ((in @ X4 @ X1) => ((X0 @ X2 @ X4) => (in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X3 @ X1 @ (^[X5 : $i, X6 : $i] : (X0 @ X5 @ X6))))))) = dpsetconstrI)), 15.72/2.39 inference(rectify,[],[f187])). 15.72/2.39 thf(f187,axiom,( 15.72/2.39 (! [X0 : $i > $i > $o,X4,X1,X3] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => ((X0 @ X1 @ X2) => (in @ (kpair @ X1 @ X2) @ (dpsetconstr @ X3 @ X4 @ (^[X8 : $i, X10 : $i] : (X0 @ X8 @ X10))))))) = dpsetconstrI)), 15.72/2.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrI)). 15.72/2.39 thf(f741,plain,( 15.72/2.39 (cartprodpairsurjEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => ((kpair @ (kfst @ Y1) @ (ksnd @ Y1)) = Y1)))))))))), 15.72/2.39 inference(cnf_transformation,[],[f504])). 15.72/2.39 thf(f504,plain,( 15.72/2.39 (cartprodpairsurjEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => ((kpair @ (kfst @ Y1) @ (ksnd @ Y1)) = Y1)))))))))), 15.72/2.39 inference(fool_elimination,[],[f503])). 15.72/2.39 thf(f503,plain,( 15.72/2.39 (! [X0,X1,X2] : ((in @ X1 @ (cartprod @ X0 @ X2)) => ((kpair @ (kfst @ X1) @ (ksnd @ X1)) = X1)) = cartprodpairsurjEq)), 15.72/2.39 inference(rectify,[],[f185])). 15.72/2.39 thf(f185,axiom,( 15.72/2.39 (! [X3,X10,X4] : ((in @ X10 @ (cartprod @ X3 @ X4)) => ((kpair @ (kfst @ X10) @ (ksnd @ X10)) = X10)) = cartprodpairsurjEq)), 15.72/2.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairsurjEq)). 15.72/2.39 thf(f794,plain,( 15.72/2.39 (cartprodsndpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((ksnd @ (kpair @ Y2 @ Y3)) = Y3))))))))))))), 15.72/2.39 inference(cnf_transformation,[],[f415])). 15.72/2.39 thf(f415,plain,( 15.72/2.39 (cartprodsndpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((ksnd @ (kpair @ Y2 @ Y3)) = Y3))))))))))))), 15.72/2.39 inference(fool_elimination,[],[f414])). 15.72/2.39 thf(f414,plain,( 15.72/2.39 (! [X0,X1,X2] : ((in @ X0 @ X2) => ! [X3] : ((in @ X3 @ X1) => ((ksnd @ (kpair @ X0 @ X3)) = X3))) = cartprodsndpairEq)), 15.72/2.39 inference(rectify,[],[f184])). 15.72/2.39 thf(f184,axiom,( 15.72/2.39 (! [X1,X4,X3] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => ((ksnd @ (kpair @ X1 @ X2)) = X2))) = cartprodsndpairEq)), 15.72/2.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndpairEq)). 15.72/2.39 thf(f608,plain,( 15.72/2.39 (cartprodfstpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((kfst @ (kpair @ Y1 @ Y3)) = Y1))))))))))))), 15.72/2.39 inference(cnf_transformation,[],[f510])). 15.72/2.39 thf(f510,plain,( 15.72/2.39 (cartprodfstpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((kfst @ (kpair @ Y1 @ Y3)) = Y1))))))))))))), 15.72/2.39 inference(fool_elimination,[],[f509])). 15.72/2.39 thf(f509,plain,( 15.72/2.39 (! [X0,X1,X2] : ((in @ X1 @ X0) => ! [X3] : ((in @ X3 @ X2) => ((kfst @ (kpair @ X1 @ X3)) = X1))) = cartprodfstpairEq)), 15.72/2.39 inference(rectify,[],[f183])). 15.72/2.39 thf(f183,axiom,( 15.72/2.39 (! [X3,X1,X4] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => ((kfst @ (kpair @ X1 @ X2)) = X1))) = cartprodfstpairEq)), 15.72/2.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstpairEq)). 15.72/2.39 thf(f619,plain,( 15.72/2.39 (cartprodmempaircEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kpair @ Y2 @ Y3) = (kpair @ Y2 @ Y3)))))))))))))), 15.72/2.39 inference(cnf_transformation,[],[f423])). 15.72/2.39 thf(f423,plain,( 15.72/2.39 (cartprodmempaircEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((kpair @ Y2 @ Y3) = (kpair @ Y2 @ Y3)))))))))))))), 15.72/2.39 inference(fool_elimination,[],[f422])). 15.72/2.39 thf(f422,plain,( 15.72/2.39 (! [X0,X1,X2] : ((in @ X0 @ X2) => ! [X3] : ((in @ X3 @ X1) => ((kpair @ X0 @ X3) = (kpair @ X0 @ X3)))) = cartprodmempaircEq)), 15.72/2.39 inference(rectify,[],[f182])). 15.72/2.39 thf(f182,axiom,( 15.72/2.39 (! [X1,X4,X3] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => ((kpair @ X1 @ X2) = (kpair @ X1 @ X2)))) = cartprodmempaircEq)), 15.72/2.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempaircEq)). 15.72/2.39 thf(f639,plain,( 15.72/2.39 (cartprodpairmemER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y1) @ (cartprod @ Y0 @ Y2)) => (in @ Y1 @ Y2)))))))))))), 15.72/2.39 inference(cnf_transformation,[],[f358])). 15.72/2.39 thf(f358,plain,( 15.72/2.39 (cartprodpairmemER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y3 @ Y1) @ (cartprod @ Y0 @ Y2)) => (in @ Y1 @ Y2)))))))))))), 15.72/2.39 inference(fool_elimination,[],[f357])). 15.72/2.39 thf(f357,plain,( 15.72/2.39 (! [X0,X1,X2,X3] : ((in @ (kpair @ X0 @ X2) @ (cartprod @ X3 @ X1)) => (in @ X2 @ X1)) = cartprodpairmemER)), 15.72/2.39 inference(rectify,[],[f181])). 15.72/2.39 thf(f181,axiom,( 15.72/2.39 (! [X1,X4,X2,X3] : ((in @ (kpair @ X1 @ X2) @ (cartprod @ X3 @ X4)) => (in @ X2 @ X4)) = cartprodpairmemER)), 15.72/2.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemER)). 15.72/2.39 thf(f698,plain,( 15.72/2.39 (cartprodpairmemEL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y0 @ Y1) @ (cartprod @ Y3 @ Y2)) => (in @ Y0 @ Y3)))))))))))), 15.72/2.39 inference(cnf_transformation,[],[f259])). 15.72/2.39 thf(f259,plain,( 15.72/2.39 (cartprodpairmemEL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y0 @ Y1) @ (cartprod @ Y3 @ Y2)) => (in @ Y0 @ Y3)))))))))))), 15.72/2.39 inference(fool_elimination,[],[f258])). 15.72/2.39 thf(f258,plain,( 15.72/2.39 (! [X0,X1,X2,X3] : ((in @ (kpair @ X3 @ X2) @ (cartprod @ X0 @ X1)) => (in @ X3 @ X0)) = cartprodpairmemEL)), 15.72/2.39 inference(rectify,[],[f180])). 15.72/2.39 thf(f180,axiom,( 15.72/2.39 (! [X3,X4,X2,X1] : ((in @ (kpair @ X1 @ X2) @ (cartprod @ X3 @ X4)) => (in @ X1 @ X3)) = cartprodpairmemEL)), 15.72/2.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemEL)). 15.72/2.39 thf(f635,plain,( 15.72/2.39 (cartprodsndin = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y0 @ Y1)) => (in @ (ksnd @ Y2) @ Y1)))))))))), 15.72/2.39 inference(cnf_transformation,[],[f397])). 15.72/2.39 thf(f397,plain,( 15.72/2.39 (cartprodsndin = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y0 @ Y1)) => (in @ (ksnd @ Y2) @ Y1)))))))))), 15.72/2.39 inference(fool_elimination,[],[f396])). 15.72/2.39 thf(f396,plain,( 15.72/2.39 (! [X0,X1,X2] : ((in @ X0 @ (cartprod @ X2 @ X1)) => (in @ (ksnd @ X0) @ X1)) = cartprodsndin)), 15.72/2.39 inference(rectify,[],[f179])). 15.72/2.39 thf(f179,axiom,( 15.72/2.39 (! [X10,X4,X3] : ((in @ X10 @ (cartprod @ X3 @ X4)) => (in @ (ksnd @ X10) @ X4)) = cartprodsndin)), 15.72/2.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndin)). 15.72/2.39 thf(f763,plain,( 15.72/2.39 (kpairsurjEq = (!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => ((kpair @ (kfst @ Y0) @ (ksnd @ Y0)) = Y0)))))), 15.72/2.39 inference(cnf_transformation,[],[f546])). 15.72/2.39 thf(f546,plain,( 15.72/2.39 (kpairsurjEq = (!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => ((kpair @ (kfst @ Y0) @ (ksnd @ Y0)) = Y0)))))), 15.72/2.39 inference(fool_elimination,[],[f545])). 15.72/2.39 thf(f545,plain,( 15.72/2.39 (! [X0] : ((iskpair @ X0) => ((kpair @ (kfst @ X0) @ (ksnd @ X0)) = X0)) = kpairsurjEq)), 15.72/2.39 inference(rectify,[],[f178])). 15.72/2.39 thf(f178,axiom,( 15.72/2.39 (! [X10] : ((iskpair @ X10) => ((kpair @ (kfst @ X10) @ (ksnd @ X10)) = X10)) = kpairsurjEq)), 15.72/2.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairsurjEq)). 15.72/2.39 thf(f689,plain,( 15.72/2.39 (ksndpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y0 @ Y1)) = Y1))))))), 15.72/2.39 inference(cnf_transformation,[],[f516])). 15.72/2.39 thf(f516,plain,( 15.72/2.39 (ksndpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y0 @ Y1)) = Y1))))))), 15.72/2.39 inference(fool_elimination,[],[f515])). 15.72/2.39 thf(f515,plain,( 15.72/2.39 (ksndpairEq = ! [X0,X1] : ((ksnd @ (kpair @ X1 @ X0)) = X0))), 15.72/2.39 inference(rectify,[],[f177])). 15.72/2.39 thf(f177,axiom,( 15.72/2.39 (ksndpairEq = ! [X2,X1] : ((ksnd @ (kpair @ X1 @ X2)) = X2))), 15.72/2.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndpairEq)). 15.72/2.39 thf(f818,plain,( 15.72/2.39 (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))))))))), 15.72/2.39 inference(definition_unfolding,[],[f725,f750])). 15.72/2.39 thf(f725,plain,( 15.72/2.39 (ksndsingleton = (!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (singleton @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: ((kpair @ (kfst @ Y0) @ Y1) = Y0))))))))), 15.72/2.39 inference(cnf_transformation,[],[f591])). 15.72/2.39 thf(f591,plain,( 15.72/2.39 (ksndsingleton = (!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (singleton @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: ((kpair @ (kfst @ Y0) @ Y1) = Y0))))))))), 15.72/2.39 inference(fool_elimination,[],[f590])). 15.72/2.39 thf(f590,plain,( 15.72/2.39 (ksndsingleton = ! [X0] : ((iskpair @ X0) => (singleton @ (dsetconstr @ (setunion @ X0) @ (^[X1 : $i] : (((kpair @ (kfst @ X0) @ X1) = X0)))))))), 15.72/2.39 inference(rectify,[],[f176])). 15.72/2.39 thf(f176,axiom,( 15.72/2.39 (ksndsingleton = ! [X10] : ((iskpair @ X10) => (singleton @ (dsetconstr @ (setunion @ X10) @ (^[X1 : $i] : (((kpair @ (kfst @ X10) @ X1) = X10)))))))), 15.72/2.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndsingleton)). 15.72/2.39 thf(f670,plain,( 15.72/2.39 (setukpairinjR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y0 @ Y1) = (kpair @ Y3 @ Y2)) => (Y2 = Y1)))))))))))), 15.72/2.39 inference(cnf_transformation,[],[f514])). 15.72/2.39 thf(f514,plain,( 15.72/2.39 (setukpairinjR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y0 @ Y1) = (kpair @ Y3 @ Y2)) => (Y2 = Y1)))))))))))), 15.72/2.39 inference(fool_elimination,[],[f513])). 15.72/2.39 thf(f513,plain,( 15.72/2.39 (setukpairinjR = ! [X0,X1,X2,X3] : (((kpair @ X3 @ X2) = (kpair @ X0 @ X1)) => (X1 = X2)))), 15.72/2.39 inference(rectify,[],[f175])). 15.72/2.39 thf(f175,axiom,( 15.72/2.39 (setukpairinjR = ! [X1,X2,X10,X8] : (((kpair @ X1 @ X2) = (kpair @ X8 @ X10)) => (X2 = X10)))), 15.72/2.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR)). 15.72/2.39 thf(f686,plain,( 15.72/2.39 (setukpairinjR2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))))), 15.72/2.39 inference(cnf_transformation,[],[f339])). 15.72/2.39 thf(f339,plain,( 15.72/2.39 (setukpairinjR2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y2 = Y0)))))))))))), 15.72/2.39 inference(fool_elimination,[],[f338])). 15.72/2.39 thf(f338,plain,( 15.72/2.39 (! [X0,X1,X2,X3] : (((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) => (X1 = X3)) = setukpairinjR2)), 15.72/2.39 inference(rectify,[],[f174])). 15.72/2.39 thf(f174,axiom,( 15.72/2.39 (! [X8,X2,X1,X10] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X8 @ emptyset) @ (setadjoin @ (setadjoin @ X8 @ (setadjoin @ X10 @ emptyset)) @ emptyset))) => (X2 = X10)) = setukpairinjR2)), 15.72/2.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR2)). 15.72/2.39 thf(f680,plain,( 15.72/2.39 (upairequniteq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) = (setadjoin @ Y2 @ emptyset)) => (Y1 = Y0)))))))))), 15.72/2.39 inference(cnf_transformation,[],[f235])). 15.72/2.39 thf(f235,plain,( 15.72/2.39 (upairequniteq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) = (setadjoin @ Y2 @ emptyset)) => (Y1 = Y0)))))))))), 15.72/2.39 inference(fool_elimination,[],[f234])). 15.72/2.39 thf(f234,plain,( 15.72/2.39 (! [X0,X1,X2] : (((setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)) = (setadjoin @ X0 @ emptyset)) => (X1 = X2)) = upairequniteq)), 15.72/2.39 inference(rectify,[],[f173])). 15.72/2.39 thf(f173,axiom,( 15.72/2.39 (! [X8,X2,X1] : (((setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) = (setadjoin @ X8 @ emptyset)) => (X1 = X2)) = upairequniteq)), 15.72/2.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairequniteq)). 15.72/2.39 thf(f618,plain,( 15.72/2.39 (setukpairinjR1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => ((Y2 = Y0) => (Y3 = Y0))))))))))))), 15.72/2.39 inference(cnf_transformation,[],[f468])). 15.72/2.39 thf(f468,plain,( 15.72/2.39 (setukpairinjR1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => ((Y2 = Y0) => (Y3 = Y0))))))))))))), 15.72/2.39 inference(fool_elimination,[],[f467])). 15.72/2.39 thf(f467,plain,( 15.72/2.39 (setukpairinjR1 = ! [X0,X1,X2,X3] : (((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset)) @ emptyset))) => ((X1 = X3) => (X0 = X3))))), 15.72/2.39 inference(rectify,[],[f172])). 15.72/2.39 thf(f172,axiom,( 15.72/2.39 (setukpairinjR1 = ! [X2,X8,X1,X10] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X8 @ emptyset) @ (setadjoin @ (setadjoin @ X8 @ (setadjoin @ X10 @ emptyset)) @ emptyset))) => ((X8 = X10) => (X2 = X10))))), 15.72/2.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR1)). 15.72/2.39 thf(f767,plain,( 15.72/2.39 (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)))))))))), 15.72/2.39 inference(cnf_transformation,[],[f389])). 15.72/2.39 thf(f389,plain,( 15.72/2.39 (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)))))))))), 15.72/2.39 inference(fool_elimination,[],[f388])). 15.72/2.39 thf(f388,plain,( 15.72/2.39 (! [X0,X1] : ((X0 = X1) => ((setadjoin @ (setadjoin @ X1 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset)))) = setukpairinjR12)), 15.72/2.39 inference(rectify,[],[f171])). 15.72/2.39 thf(f171,axiom,( 15.72/2.39 (! [X2,X1] : ((X1 = X2) => ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X1 @ emptyset) @ emptyset))) = setukpairinjR12)), 15.72/2.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR12)). 15.72/2.39 thf(f641,plain,( 15.72/2.39 (setukpairinjR11 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))))), 15.72/2.39 inference(cnf_transformation,[],[f554])). 15.72/2.39 thf(f554,plain,( 15.72/2.39 (setukpairinjR11 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))))), 15.72/2.39 inference(fool_elimination,[],[f553])). 15.72/2.39 thf(f553,plain,( 15.72/2.39 (! [X0,X1] : ((X0 = X1) => ((setadjoin @ X1 @ emptyset) = (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)))) = setukpairinjR11)), 15.72/2.39 inference(rectify,[],[f170])). 15.72/2.39 thf(f170,axiom,( 15.72/2.39 (! [X2,X1] : ((X1 = X2) => ((setadjoin @ X1 @ emptyset) = (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)))) = setukpairinjR11)), 15.72/2.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR11)). 15.72/2.40 thf(f710,plain,( 15.72/2.40 (setukpairinjL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y0 @ Y3)) => (Y2 = Y0)))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f439])). 15.72/2.40 thf(f439,plain,( 15.72/2.40 (setukpairinjL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y0 @ Y3)) => (Y2 = Y0)))))))))))), 15.72/2.40 inference(fool_elimination,[],[f438])). 15.72/2.40 thf(f438,plain,( 15.72/2.40 (setukpairinjL = ! [X0,X1,X2,X3] : (((kpair @ X1 @ X2) = (kpair @ X3 @ X0)) => (X1 = X3)))), 15.72/2.40 inference(rectify,[],[f169])). 15.72/2.40 thf(f169,axiom,( 15.72/2.40 (setukpairinjL = ! [X10,X1,X2,X8] : (((kpair @ X1 @ X2) = (kpair @ X8 @ X10)) => (X1 = X8)))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL)). 15.72/2.40 thf(f783,plain,( 15.72/2.40 (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 @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => (Y3 = Y2)))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f237])). 15.72/2.40 thf(f237,plain,( 15.72/2.40 (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 @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => (Y3 = Y2)))))))))))), 15.72/2.40 inference(fool_elimination,[],[f236])). 15.72/2.40 thf(f236,plain,( 15.72/2.40 (! [X0,X1,X2,X3] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X3 @ emptyset)) @ emptyset))) => (X0 = X1)) = setukpairinjL2)), 15.72/2.40 inference(rectify,[],[f168])). 15.72/2.40 thf(f168,axiom,( 15.72/2.40 (! [X8,X1,X2,X10] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X8 @ emptyset) @ (setadjoin @ (setadjoin @ X8 @ (setadjoin @ X10 @ emptyset)) @ emptyset))) => (X1 = X8)) = setukpairinjL2)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL2)). 15.72/2.40 thf(f661,plain,( 15.72/2.40 (cartprodfstin = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (in @ (kfst @ Y0) @ Y1)))))))))), 15.72/2.40 inference(cnf_transformation,[],[f536])). 15.72/2.40 thf(f536,plain,( 15.72/2.40 (cartprodfstin = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (in @ (kfst @ Y0) @ Y1)))))))))), 15.72/2.40 inference(fool_elimination,[],[f535])). 15.72/2.40 thf(f535,plain,( 15.72/2.40 (! [X0,X1,X2] : ((in @ X2 @ (cartprod @ X1 @ X0)) => (in @ (kfst @ X2) @ X1)) = cartprodfstin)), 15.72/2.40 inference(rectify,[],[f167])). 15.72/2.40 thf(f167,axiom,( 15.72/2.40 (! [X4,X3,X10] : ((in @ X10 @ (cartprod @ X3 @ X4)) => (in @ (kfst @ X10) @ X3)) = cartprodfstin)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstin)). 15.72/2.40 thf(f652,plain,( 15.72/2.40 (kfstpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y1 @ Y0)) = Y1))))))), 15.72/2.40 inference(cnf_transformation,[],[f585])). 15.72/2.40 thf(f585,plain,( 15.72/2.40 (kfstpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y1 @ Y0)) = Y1))))))), 15.72/2.40 inference(fool_elimination,[],[f584])). 15.72/2.40 thf(f584,plain,( 15.72/2.40 (kfstpairEq = ! [X0,X1] : ((kfst @ (kpair @ X0 @ X1)) = X0))), 15.72/2.40 inference(rectify,[],[f166])). 15.72/2.40 thf(f166,axiom,( 15.72/2.40 (kfstpairEq = ! [X1,X2] : ((kfst @ (kpair @ X1 @ X2)) = X1))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstpairEq)). 15.72/2.40 thf(f817,plain,( 15.72/2.40 (theprop = (!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & ((setadjoin @ Y2 @ emptyset) = Y1))))) @ Y0) => (in @ (setunion @ Y0) @ Y0)))))), 15.72/2.40 inference(definition_unfolding,[],[f677,f750])). 15.72/2.40 thf(f677,plain,( 15.72/2.40 (theprop = (!! @ $i @ (^[Y0 : $i]: ((singleton @ Y0) => (in @ (setunion @ Y0) @ Y0)))))), 15.72/2.40 inference(cnf_transformation,[],[f207])). 15.72/2.40 thf(f207,plain,( 15.72/2.40 (theprop = (!! @ $i @ (^[Y0 : $i]: ((singleton @ Y0) => (in @ (setunion @ Y0) @ Y0)))))), 15.72/2.40 inference(fool_elimination,[],[f206])). 15.72/2.40 thf(f206,plain,( 15.72/2.40 (! [X0] : ((singleton @ X0) => (in @ (setunion @ X0) @ X0)) = theprop)), 15.72/2.40 inference(rectify,[],[f165])). 15.72/2.40 thf(f165,axiom,( 15.72/2.40 (! [X11] : ((singleton @ X11) => (in @ (setunion @ X11) @ X11)) = theprop)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',theprop)). 15.72/2.40 thf(f816,plain,( 15.72/2.40 (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))))))))), 15.72/2.40 inference(definition_unfolding,[],[f597,f750])). 15.72/2.40 thf(f597,plain,( 15.72/2.40 (kfstsingleton = (!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (singleton @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: (in @ (setadjoin @ Y1 @ emptyset) @ Y0))))))))), 15.72/2.40 inference(cnf_transformation,[],[f239])). 15.72/2.40 thf(f239,plain,( 15.72/2.40 (kfstsingleton = (!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (singleton @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: (in @ (setadjoin @ Y1 @ emptyset) @ Y0))))))))), 15.72/2.40 inference(fool_elimination,[],[f238])). 15.72/2.40 thf(f238,plain,( 15.72/2.40 (! [X0] : ((iskpair @ X0) => (singleton @ (dsetconstr @ (setunion @ X0) @ (^[X1 : $i] : (in @ (setadjoin @ X1 @ emptyset) @ X0))))) = kfstsingleton)), 15.72/2.40 inference(rectify,[],[f164])). 15.72/2.40 thf(f164,axiom,( 15.72/2.40 (! [X10] : ((iskpair @ X10) => (singleton @ (dsetconstr @ (setunion @ X10) @ (^[X1 : $i] : (in @ (setadjoin @ X1 @ emptyset) @ X10))))) = kfstsingleton)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstsingleton)). 15.72/2.40 thf(f609,plain,( 15.72/2.40 (setukpairinjL1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = Y0)))))))))), 15.72/2.40 inference(cnf_transformation,[],[f550])). 15.72/2.40 thf(f550,plain,( 15.72/2.40 (setukpairinjL1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = Y0)))))))))), 15.72/2.40 inference(fool_elimination,[],[f549])). 15.72/2.40 thf(f549,plain,( 15.72/2.40 (! [X0,X1,X2] : ((in @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset))) => (X1 = X2)) = setukpairinjL1)), 15.72/2.40 inference(rectify,[],[f163])). 15.72/2.40 thf(f163,axiom,( 15.72/2.40 (! [X2,X1,X8] : ((in @ (setadjoin @ X8 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset))) => (X1 = X8)) = setukpairinjL1)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL1)). 15.72/2.40 thf(f760,plain,( 15.72/2.40 (singletonsuniq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))))), 15.72/2.40 inference(cnf_transformation,[],[f253])). 15.72/2.40 thf(f253,plain,( 15.72/2.40 (singletonsuniq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))))), 15.72/2.40 inference(fool_elimination,[],[f252])). 15.72/2.40 thf(f252,plain,( 15.72/2.40 (! [X0,X1] : (((setadjoin @ X1 @ emptyset) = (setadjoin @ X0 @ emptyset)) => (X0 = X1)) = singletonsuniq)), 15.72/2.40 inference(rectify,[],[f162])). 15.72/2.40 thf(f162,axiom,( 15.72/2.40 (! [X1,X2] : (((setadjoin @ X2 @ emptyset) = (setadjoin @ X1 @ emptyset)) => (X1 = X2)) = singletonsuniq)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsuniq)). 15.72/2.40 thf(f815,plain,( 15.72/2.40 (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]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => ((^[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))))))))))), 15.72/2.40 inference(definition_unfolding,[],[f601,f812])). 15.72/2.40 thf(f601,plain,( 15.72/2.40 (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]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (ex1 @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f405])). 15.72/2.40 thf(f405,plain,( 15.72/2.40 (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]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) => (ex1 @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))))), 15.72/2.40 inference(fool_elimination,[],[f404])). 15.72/2.40 thf(f404,plain,( 15.72/2.40 (! [X0 : $i > $o,X1] : (! [X2] : ((in @ X2 @ X1) => ! [X3] : ((in @ X3 @ X1) => ((X0 @ X2) => ((X0 @ X3) => (X2 = X3))))) => (? [X4] : ((X0 @ X4) & (in @ X4 @ X1)) => (ex1 @ X1 @ (^[X5 : $i] : (X0 @ X5))))) = ex1I2)), 15.72/2.40 inference(rectify,[],[f161])). 15.72/2.40 thf(f161,axiom,( 15.72/2.40 (! [X0 : $i > $o,X3] : (! [X1] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X3) => ((X0 @ X1) => ((X0 @ X2) => (X1 = X2))))) => (? [X1] : ((X0 @ X1) & (in @ X1 @ X3)) => (ex1 @ X3 @ (^[X1 : $i] : (X0 @ X1))))) = ex1I2)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I2)). 15.72/2.40 thf(f814,plain,( 15.72/2.40 (ex1I = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => ((^[Y3 : $i]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) & ((setadjoin @ Y6 @ emptyset) = Y5))))) @ (dsetconstr @ Y3 @ (^[Y5 : $i]: (Y4 @ Y5))))))) @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))), 15.72/2.40 inference(definition_unfolding,[],[f765,f812])). 15.72/2.40 thf(f765,plain,( 15.72/2.40 (ex1I = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (ex1 @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f502])). 15.72/2.40 thf(f502,plain,( 15.72/2.40 (ex1I = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y0 @ Y3) => (Y2 = Y3))))) => (ex1 @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))), 15.72/2.40 inference(fool_elimination,[],[f501])). 15.72/2.40 thf(f501,plain,( 15.72/2.40 (! [X0,X1,X2 : $i > $o] : ((in @ X0 @ X1) => ((X2 @ X0) => (! [X3] : ((in @ X3 @ X1) => ((X2 @ X3) => (X0 = X3))) => (ex1 @ X1 @ (^[X4 : $i] : (X2 @ X4)))))) = ex1I)), 15.72/2.40 inference(rectify,[],[f160])). 15.72/2.40 thf(f160,axiom,( 15.72/2.40 (! [X1,X3,X0 : $i > $o] : ((in @ X1 @ X3) => ((X0 @ X1) => (! [X2] : ((in @ X2 @ X3) => ((X0 @ X2) => (X1 = X2))) => (ex1 @ X3 @ (^[X2 : $i] : (X0 @ X2)))))) = ex1I)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I)). 15.72/2.40 thf(f813,plain,( 15.72/2.40 (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))))))))))), 15.72/2.40 inference(definition_unfolding,[],[f696,f812])). 15.72/2.40 thf(f696,plain,( 15.72/2.40 (ex1E1 = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((ex1 @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f564])). 15.72/2.40 thf(f564,plain,( 15.72/2.40 (ex1E1 = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((ex1 @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))))))))), 15.72/2.40 inference(fool_elimination,[],[f563])). 15.72/2.40 thf(f563,plain,( 15.72/2.40 (! [X0 : $i > $o,X1] : ((ex1 @ X1 @ (^[X2 : $i] : (X0 @ X2))) => ? [X3] : ((X0 @ X3) & (in @ X3 @ X1))) = ex1E1)), 15.72/2.40 inference(rectify,[],[f159])). 15.72/2.40 thf(f159,axiom,( 15.72/2.40 (! [X0 : $i > $o,X3] : ((ex1 @ X3 @ (^[X1 : $i] : (X0 @ X1))) => ? [X1] : ((X0 @ X1) & (in @ X1 @ X3))) = ex1E1)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E1)). 15.72/2.40 thf(f811,plain,( 15.72/2.40 (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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) & ((setadjoin @ Y3 @ emptyset) = Y2))))) @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2)))))))))))), 15.72/2.40 inference(definition_unfolding,[],[f715,f750])). 15.72/2.40 thf(f715,plain,( 15.72/2.40 (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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2)))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f333])). 15.72/2.40 thf(f333,plain,( 15.72/2.40 (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]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2)))))))))))), 15.72/2.40 inference(fool_elimination,[],[f332])). 15.72/2.40 thf(f332,plain,( 15.72/2.40 (singletonprop = ! [X0 : $i > $o,X1] : (! [X2] : ((in @ X2 @ X1) => ! [X3] : ((in @ X3 @ X1) => ((X0 @ X2) => ((X0 @ X3) => (X2 = X3))))) => (? [X4] : ((in @ X4 @ X1) & (X0 @ X4)) => (singleton @ (dsetconstr @ X1 @ (^[X5 : $i] : (X0 @ X5)))))))), 15.72/2.40 inference(rectify,[],[f157])). 15.72/2.40 thf(f157,axiom,( 15.72/2.40 (singletonprop = ! [X0 : $i > $o,X3] : (! [X1] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X3) => ((X0 @ X1) => ((X0 @ X2) => (X1 = X2))))) => (? [X1] : ((in @ X1 @ X3) & (X0 @ X1)) => (singleton @ (dsetconstr @ X3 @ (^[X1 : $i] : (X0 @ X1)))))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonprop)). 15.72/2.40 thf(f770,plain,( 15.72/2.40 (setunionsingleton = (!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))))), 15.72/2.40 inference(cnf_transformation,[],[f552])). 15.72/2.40 thf(f552,plain,( 15.72/2.40 (setunionsingleton = (!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))))), 15.72/2.40 inference(fool_elimination,[],[f551])). 15.72/2.40 thf(f551,plain,( 15.72/2.40 (setunionsingleton = ! [X0] : ((setunion @ (setadjoin @ X0 @ emptyset)) = X0))), 15.72/2.40 inference(rectify,[],[f155])). 15.72/2.40 thf(f155,axiom,( 15.72/2.40 (setunionsingleton = ! [X1] : ((setunion @ (setadjoin @ X1 @ emptyset)) = X1))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton)). 15.72/2.40 thf(f745,plain,( 15.72/2.40 (setunionsingleton2 = (!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))))), 15.72/2.40 inference(cnf_transformation,[],[f498])). 15.72/2.40 thf(f498,plain,( 15.72/2.40 (setunionsingleton2 = (!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))))), 15.72/2.40 inference(fool_elimination,[],[f497])). 15.72/2.40 thf(f497,plain,( 15.72/2.40 (setunionsingleton2 = ! [X0] : (subset @ X0 @ (setunion @ (setadjoin @ X0 @ emptyset))))), 15.72/2.40 inference(rectify,[],[f154])). 15.72/2.40 thf(f154,axiom,( 15.72/2.40 (setunionsingleton2 = ! [X3] : (subset @ X3 @ (setunion @ (setadjoin @ X3 @ emptyset))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton2)). 15.72/2.40 thf(f620,plain,( 15.72/2.40 (setunionsingleton1 = (!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))))), 15.72/2.40 inference(cnf_transformation,[],[f221])). 15.72/2.40 thf(f221,plain,( 15.72/2.40 (setunionsingleton1 = (!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))))), 15.72/2.40 inference(fool_elimination,[],[f220])). 15.72/2.40 thf(f220,plain,( 15.72/2.40 (setunionsingleton1 = ! [X0] : (subset @ (setunion @ (setadjoin @ X0 @ emptyset)) @ X0))), 15.72/2.40 inference(rectify,[],[f153])). 15.72/2.40 thf(f153,axiom,( 15.72/2.40 (setunionsingleton1 = ! [X3] : (subset @ (setunion @ (setadjoin @ X3 @ emptyset)) @ X3))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton1)). 15.72/2.40 thf(f746,plain,( 15.72/2.40 (setunionE2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f307])). 15.72/2.40 thf(f307,plain,( 15.72/2.40 (setunionE2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))))), 15.72/2.40 inference(fool_elimination,[],[f306])). 15.72/2.40 thf(f306,plain,( 15.72/2.40 (! [X0,X1] : ((in @ X1 @ (setunion @ X0)) => ? [X2] : ((in @ X2 @ X0) & (in @ X1 @ X2))) = setunionE2)), 15.72/2.40 inference(rectify,[],[f152])). 15.72/2.40 thf(f152,axiom,( 15.72/2.40 (! [X3,X1] : ((in @ X1 @ (setunion @ X3)) => ? [X11] : ((in @ X11 @ X3) & (in @ X1 @ X11))) = setunionE2)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE2)). 15.72/2.40 thf(f638,plain,( 15.72/2.40 (cartprodmempair = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (iskpair @ Y1)))))))))), 15.72/2.40 inference(cnf_transformation,[],[f345])). 15.72/2.40 thf(f345,plain,( 15.72/2.40 (cartprodmempair = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (iskpair @ Y1)))))))))), 15.72/2.40 inference(fool_elimination,[],[f344])). 15.72/2.40 thf(f344,plain,( 15.72/2.40 (cartprodmempair = ! [X0,X1,X2] : ((in @ X1 @ (cartprod @ X0 @ X2)) => (iskpair @ X1)))), 15.72/2.40 inference(rectify,[],[f151])). 15.72/2.40 thf(f151,axiom,( 15.72/2.40 (cartprodmempair = ! [X3,X10,X4] : ((in @ X10 @ (cartprod @ X3 @ X4)) => (iskpair @ X10)))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair)). 15.72/2.40 thf(f788,plain,( 15.72/2.40 (cartprodmempair1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y2)))) & (in @ Y3 @ Y1))))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f562])). 15.72/2.40 thf(f562,plain,( 15.72/2.40 (cartprodmempair1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (cartprod @ Y1 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y2)))) & (in @ Y3 @ Y1))))))))))))), 15.72/2.40 inference(fool_elimination,[],[f561])). 15.72/2.40 thf(f561,plain,( 15.72/2.40 (! [X0,X1,X2] : ((in @ X0 @ (cartprod @ X1 @ X2)) => ? [X3] : ((in @ X3 @ X1) & ? [X4] : (((kpair @ X3 @ X4) = X0) & (in @ X4 @ X2)))) = cartprodmempair1)), 15.72/2.40 inference(rectify,[],[f150])). 15.72/2.40 thf(f150,axiom,( 15.72/2.40 (! [X10,X3,X4] : ((in @ X10 @ (cartprod @ X3 @ X4)) => ? [X1] : ((in @ X1 @ X3) & ? [X2] : (((kpair @ X1 @ X2) = X10) & (in @ X2 @ X4)))) = cartprodmempair1)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair1)). 15.72/2.40 thf(f777,plain,( 15.72/2.40 (cartprodpairin = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y1 @ Y2)))))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f313])). 15.72/2.40 thf(f313,plain,( 15.72/2.40 (cartprodpairin = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y1 @ Y2)))))))))))))), 15.72/2.40 inference(fool_elimination,[],[f312])). 15.72/2.40 thf(f312,plain,( 15.72/2.40 (cartprodpairin = ! [X0,X1,X2] : ((in @ X2 @ X1) => ! [X3] : ((in @ X3 @ X0) => (in @ (kpair @ X2 @ X3) @ (cartprod @ X1 @ X0)))))), 15.72/2.40 inference(rectify,[],[f149])). 15.72/2.40 thf(f149,axiom,( 15.72/2.40 (cartprodpairin = ! [X4,X3,X1] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => (in @ (kpair @ X1 @ X2) @ (cartprod @ X3 @ X4)))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairin)). 15.72/2.40 thf(f749,plain,( 15.72/2.40 (ubforcartprodlem3 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f581])). 15.72/2.40 thf(f581,plain,( 15.72/2.40 (ubforcartprodlem3 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))))), 15.72/2.40 inference(fool_elimination,[],[f580])). 15.72/2.40 thf(f580,plain,( 15.72/2.40 (ubforcartprodlem3 = ! [X0,X1,X2] : ((in @ X1 @ X0) => ! [X3] : ((in @ X3 @ X2) => (in @ (kpair @ X1 @ X3) @ (powerset @ (powerset @ (binunion @ X0 @ X2)))))))), 15.72/2.40 inference(rectify,[],[f148])). 15.72/2.40 thf(f148,axiom,( 15.72/2.40 (ubforcartprodlem3 = ! [X3,X1,X4] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => (in @ (kpair @ X1 @ X2) @ (powerset @ (powerset @ (binunion @ X3 @ X4)))))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem3)). 15.72/2.40 thf(f705,plain,( 15.72/2.40 (ubforcartprodlem2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y1)))))))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f337])). 15.72/2.40 thf(f337,plain,( 15.72/2.40 (ubforcartprodlem2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y1)))))))))))))))), 15.72/2.40 inference(fool_elimination,[],[f336])). 15.72/2.40 thf(f336,plain,( 15.72/2.40 (ubforcartprodlem2 = ! [X0,X1,X2] : ((in @ X0 @ X2) => ! [X3] : ((in @ X3 @ X1) => (in @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X2 @ X1)))))))), 15.72/2.40 inference(rectify,[],[f147])). 15.72/2.40 thf(f147,axiom,( 15.72/2.40 (ubforcartprodlem2 = ! [X1,X4,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)))))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem2)). 15.72/2.40 thf(f707,plain,( 15.72/2.40 (ubforcartprodlem1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y0))))))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f583])). 15.72/2.40 thf(f583,plain,( 15.72/2.40 (ubforcartprodlem1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y1 @ Y0))))))))))))))), 15.72/2.40 inference(fool_elimination,[],[f582])). 15.72/2.40 thf(f582,plain,( 15.72/2.40 (! [X0,X1,X2] : ((in @ X0 @ X1) => ! [X3] : ((in @ X3 @ X2) => (subset @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X1 @ X2))))) = ubforcartprodlem1)), 15.72/2.40 inference(rectify,[],[f146])). 15.72/2.40 thf(f146,axiom,( 15.72/2.40 (! [X1,X3,X4] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => (subset @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X3 @ X4))))) = ubforcartprodlem1)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem1)). 15.72/2.40 thf(f764,plain,( 15.72/2.40 (upairinpowunion = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y0 @ Y2))))))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f227])). 15.72/2.40 thf(f227,plain,( 15.72/2.40 (upairinpowunion = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y0 @ Y2))))))))))))))), 15.72/2.40 inference(fool_elimination,[],[f226])). 15.72/2.40 thf(f226,plain,( 15.72/2.40 (! [X0,X1,X2] : ((in @ X1 @ X2) => ! [X3] : ((in @ X3 @ X0) => (in @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X2 @ X0))))) = upairinpowunion)), 15.72/2.40 inference(rectify,[],[f145])). 15.72/2.40 thf(f145,axiom,( 15.72/2.40 (! [X4,X1,X3] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => (in @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ (powerset @ (binunion @ X3 @ X4))))) = upairinpowunion)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairinpowunion)). 15.72/2.40 thf(f640,plain,( 15.72/2.40 (upairsubunion = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y2)))))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f474])). 15.72/2.40 thf(f474,plain,( 15.72/2.40 (upairsubunion = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y2)))))))))))))), 15.72/2.40 inference(fool_elimination,[],[f473])). 15.72/2.40 thf(f473,plain,( 15.72/2.40 (upairsubunion = ! [X0,X1,X2] : ((in @ X2 @ X1) => ! [X3] : ((in @ X3 @ X0) => (subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X1 @ X0)))))), 15.72/2.40 inference(rectify,[],[f144])). 15.72/2.40 thf(f144,axiom,( 15.72/2.40 (upairsubunion = ! [X4,X3,X1] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => (subset @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ (binunion @ X3 @ X4)))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsubunion)). 15.72/2.40 thf(f769,plain,( 15.72/2.40 (upairset2E = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f413])). 15.72/2.40 thf(f413,plain,( 15.72/2.40 (upairset2E = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))))), 15.72/2.40 inference(fool_elimination,[],[f412])). 15.72/2.40 thf(f412,plain,( 15.72/2.40 (! [X0,X1,X2] : ((in @ X2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) => ((X1 = X2) | (X0 = X2))) = upairset2E)), 15.72/2.40 inference(rectify,[],[f143])). 15.72/2.40 thf(f143,axiom,( 15.72/2.40 (! [X1,X2,X8] : ((in @ X8 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset))) => ((X2 = X8) | (X1 = X8))) = upairset2E)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2E)). 15.72/2.40 thf(f624,plain,( 15.72/2.40 (singletoninpowunion = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y1)))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f403])). 15.72/2.40 thf(f403,plain,( 15.72/2.40 (singletoninpowunion = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y1)))))))))))), 15.72/2.40 inference(fool_elimination,[],[f402])). 15.72/2.40 thf(f402,plain,( 15.72/2.40 (singletoninpowunion = ! [X0,X1,X2] : ((in @ X2 @ X0) => (in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X0 @ X1)))))), 15.72/2.40 inference(rectify,[],[f142])). 15.72/2.40 thf(f142,axiom,( 15.72/2.40 (singletoninpowunion = ! [X3,X4,X1] : ((in @ X1 @ X3) => (in @ (setadjoin @ X1 @ emptyset) @ (powerset @ (binunion @ X3 @ X4)))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowunion)). 15.72/2.40 thf(f685,plain,( 15.72/2.40 (singletoninpowerset = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ Y0))))))))), 15.72/2.40 inference(cnf_transformation,[],[f560])). 15.72/2.40 thf(f560,plain,( 15.72/2.40 (singletoninpowerset = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ Y0))))))))), 15.72/2.40 inference(fool_elimination,[],[f559])). 15.72/2.40 thf(f559,plain,( 15.72/2.40 (singletoninpowerset = ! [X0,X1] : ((in @ X0 @ X1) => (in @ (setadjoin @ X0 @ emptyset) @ (powerset @ X1))))), 15.72/2.40 inference(rectify,[],[f141])). 15.72/2.40 thf(f141,axiom,( 15.72/2.40 (singletoninpowerset = ! [X1,X3] : ((in @ X1 @ X3) => (in @ (setadjoin @ X1 @ emptyset) @ (powerset @ X3))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowerset)). 15.72/2.40 thf(f755,plain,( 15.72/2.40 (singletonsubset = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))))), 15.72/2.40 inference(cnf_transformation,[],[f263])). 15.72/2.40 thf(f263,plain,( 15.72/2.40 (singletonsubset = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))))), 15.72/2.40 inference(fool_elimination,[],[f262])). 15.72/2.40 thf(f262,plain,( 15.72/2.40 (! [X0,X1] : ((in @ X0 @ X1) => (subset @ (setadjoin @ X0 @ emptyset) @ X1)) = singletonsubset)), 15.72/2.40 inference(rectify,[],[f140])). 15.72/2.40 thf(f140,axiom,( 15.72/2.40 (! [X1,X3] : ((in @ X1 @ X3) => (subset @ (setadjoin @ X1 @ emptyset) @ X3)) = singletonsubset)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsubset)). 15.72/2.40 thf(f626,plain,( 15.72/2.40 (kpairp = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y1 @ Y0)))))))), 15.72/2.40 inference(cnf_transformation,[],[f261])). 15.72/2.40 thf(f261,plain,( 15.72/2.40 (kpairp = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y1 @ Y0)))))))), 15.72/2.40 inference(fool_elimination,[],[f260])). 15.72/2.40 thf(f260,plain,( 15.72/2.40 (kpairp = ! [X0,X1] : (iskpair @ (kpair @ X0 @ X1)))), 15.72/2.40 inference(rectify,[],[f139])). 15.72/2.40 thf(f139,axiom,( 15.72/2.40 (kpairp = ! [X1,X2] : (iskpair @ (kpair @ X1 @ X2)))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairp)). 15.72/2.40 thf(f744,plain,( 15.72/2.40 (kpairiskpair = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))))), 15.72/2.40 inference(cnf_transformation,[],[f374])). 15.72/2.40 thf(f374,plain,( 15.72/2.40 (kpairiskpair = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))))), 15.72/2.40 inference(fool_elimination,[],[f373])). 15.72/2.40 thf(f373,plain,( 15.72/2.40 (kpairiskpair = ! [X0,X1] : (iskpair @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset))))), 15.72/2.40 inference(rectify,[],[f138])). 15.72/2.40 thf(f138,axiom,( 15.72/2.40 (kpairiskpair = ! [X2,X1] : (iskpair @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairiskpair)). 15.72/2.40 thf(f645,plain,( 15.72/2.40 (setukpairIR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))))), 15.72/2.40 inference(cnf_transformation,[],[f267])). 15.72/2.40 thf(f267,plain,( 15.72/2.40 (setukpairIR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))))), 15.72/2.40 inference(fool_elimination,[],[f266])). 15.72/2.40 thf(f266,plain,( 15.72/2.40 (setukpairIR = ! [X0,X1] : (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))))), 15.72/2.40 inference(rectify,[],[f137])). 15.72/2.40 thf(f137,axiom,( 15.72/2.40 (setukpairIR = ! [X1,X2] : (in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIR)). 15.72/2.40 thf(f784,plain,( 15.72/2.40 (setukpairIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))))), 15.72/2.40 inference(cnf_transformation,[],[f595])). 15.72/2.40 thf(f595,plain,( 15.72/2.40 (setukpairIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)))))))))), 15.72/2.40 inference(fool_elimination,[],[f594])). 15.72/2.40 thf(f594,plain,( 15.72/2.40 (! [X0,X1] : (in @ X0 @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))) = setukpairIL)), 15.72/2.40 inference(rectify,[],[f136])). 15.72/2.40 thf(f136,axiom,( 15.72/2.40 (! [X1,X2] : (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)))) = setukpairIL)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIL)). 15.72/2.40 thf(f714,plain,( 15.72/2.40 (secondinupair = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))))), 15.72/2.40 inference(cnf_transformation,[],[f470])). 15.72/2.40 thf(f470,plain,( 15.72/2.40 (secondinupair = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))))))))), 15.72/2.40 inference(fool_elimination,[],[f469])). 15.72/2.40 thf(f469,plain,( 15.72/2.40 (! [X0,X1] : (in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))) = secondinupair)), 15.72/2.40 inference(rectify,[],[f135])). 15.72/2.40 thf(f135,axiom,( 15.72/2.40 (! [X2,X1] : (in @ X2 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset))) = secondinupair)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',secondinupair)). 15.72/2.40 thf(f605,plain,( 15.72/2.40 (symdiffIneg2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ Y2)) => ((~ (in @ Y1 @ Y0)) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0))))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f347])). 15.72/2.40 thf(f347,plain,( 15.72/2.40 (symdiffIneg2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ Y2)) => ((~ (in @ Y1 @ Y0)) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0))))))))))))), 15.72/2.40 inference(fool_elimination,[],[f346])). 15.72/2.40 thf(f346,plain,( 15.72/2.40 (! [X0,X1,X2] : (~(in @ X1 @ X0) => (~(in @ X1 @ X2) => ~(in @ X1 @ (symdiff @ X0 @ X2)))) = symdiffIneg2)), 15.72/2.40 inference(rectify,[],[f134])). 15.72/2.40 thf(f134,axiom,( 15.72/2.40 (! [X3,X1,X4] : (~(in @ X1 @ X3) => (~(in @ X1 @ X4) => ~(in @ X1 @ (symdiff @ X3 @ X4)))) = symdiffIneg2)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg2)). 15.72/2.40 thf(f602,plain,( 15.72/2.40 (symdiffIneg1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y1 @ Y0) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0))))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f455])). 15.72/2.40 thf(f455,plain,( 15.72/2.40 (symdiffIneg1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((in @ Y1 @ Y0) => (~ (in @ Y1 @ (symdiff @ Y2 @ Y0))))))))))))), 15.72/2.40 inference(fool_elimination,[],[f454])). 15.72/2.40 thf(f454,plain,( 15.72/2.40 (symdiffIneg1 = ! [X0,X1,X2] : ((in @ X1 @ X0) => ((in @ X1 @ X2) => ~(in @ X1 @ (symdiff @ X0 @ X2)))))), 15.72/2.40 inference(rectify,[],[f133])). 15.72/2.40 thf(f133,axiom,( 15.72/2.40 (symdiffIneg1 = ! [X3,X1,X4] : ((in @ X1 @ X3) => ((in @ X1 @ X4) => ~(in @ X1 @ (symdiff @ X3 @ X4)))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg1)). 15.72/2.40 thf(f762,plain,( 15.72/2.40 (symdiffI2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f327])). 15.72/2.40 thf(f327,plain,( 15.72/2.40 (symdiffI2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))))), 15.72/2.40 inference(fool_elimination,[],[f326])). 15.72/2.40 thf(f326,plain,( 15.72/2.40 (! [X0,X1,X2] : (~(in @ X2 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ (symdiff @ X0 @ X1)))) = symdiffI2)), 15.72/2.40 inference(rectify,[],[f132])). 15.72/2.40 thf(f132,axiom,( 15.72/2.40 (! [X3,X4,X1] : (~(in @ X1 @ X3) => ((in @ X1 @ X4) => (in @ X1 @ (symdiff @ X3 @ X4)))) = symdiffI2)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI2)). 15.72/2.40 thf(f708,plain,( 15.72/2.40 (symdiffI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f522])). 15.72/2.40 thf(f522,plain,( 15.72/2.40 (symdiffI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (symdiff @ Y2 @ Y1)))))))))))), 15.72/2.40 inference(fool_elimination,[],[f521])). 15.72/2.40 thf(f521,plain,( 15.72/2.40 (! [X0,X1,X2] : ((in @ X2 @ X0) => (~(in @ X2 @ X1) => (in @ X2 @ (symdiff @ X0 @ X1)))) = symdiffI1)), 15.72/2.40 inference(rectify,[],[f131])). 15.72/2.40 thf(f131,axiom,( 15.72/2.40 (! [X3,X4,X1] : ((in @ X1 @ X3) => (~(in @ X1 @ X4) => (in @ X1 @ (symdiff @ X3 @ X4)))) = symdiffI1)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI1)). 15.72/2.40 thf(f756,plain,( 15.72/2.40 (symdiffE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (symdiff @ Y2 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => Y3)) => (((~ (in @ Y1 @ Y2)) => ((in @ Y1 @ Y0) => Y3)) => Y3))))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f225])). 15.72/2.40 thf(f225,plain,( 15.72/2.40 (symdiffE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (symdiff @ Y2 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => Y3)) => (((~ (in @ Y1 @ Y2)) => ((in @ Y1 @ Y0) => Y3)) => Y3))))))))))))), 15.72/2.40 inference(fool_elimination,[],[f224])). 15.72/2.40 thf(f224,plain,( 15.72/2.40 (! [X0,X1,X2] : ((in @ X1 @ (symdiff @ X0 @ X2)) => ! [X3 : $o] : (((in @ X1 @ X0) => (~(in @ X1 @ X2) => X3)) => ((~(in @ X1 @ X0) => ((in @ X1 @ X2) => X3)) => X3))) = symdiffE)), 15.72/2.40 inference(rectify,[],[f130])). 15.72/2.40 thf(f130,axiom,( 15.72/2.40 (! [X3,X1,X4] : ((in @ X1 @ (symdiff @ X3 @ X4)) => ! [X0 : $o] : (((in @ X1 @ X3) => (~(in @ X1 @ X4) => X0)) => ((~(in @ X1 @ X3) => ((in @ X1 @ X4) => X0)) => X0))) = symdiffE)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffE)). 15.72/2.40 thf(f662,plain,( 15.72/2.40 (setminusSubset1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))))), 15.72/2.40 inference(cnf_transformation,[],[f297])). 15.72/2.40 thf(f297,plain,( 15.72/2.40 (setminusSubset1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))))), 15.72/2.40 inference(fool_elimination,[],[f296])). 15.72/2.40 thf(f296,plain,( 15.72/2.40 (setminusSubset1 = ! [X0,X1] : ((emptyset = (setminus @ X0 @ X1)) => (subset @ X0 @ X1)))), 15.72/2.40 inference(rectify,[],[f129])). 15.72/2.40 thf(f129,axiom,( 15.72/2.40 (setminusSubset1 = ! [X3,X4] : ((emptyset = (setminus @ X3 @ X4)) => (subset @ X3 @ X4)))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset1)). 15.72/2.40 thf(f768,plain,( 15.72/2.40 (setminusLsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))))), 15.72/2.40 inference(cnf_transformation,[],[f435])). 15.72/2.40 thf(f435,plain,( 15.72/2.40 (setminusLsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y0 @ Y1) @ Y0))))))), 15.72/2.40 inference(fool_elimination,[],[f434])). 15.72/2.40 thf(f434,plain,( 15.72/2.40 (! [X0,X1] : (subset @ (setminus @ X1 @ X0) @ X1) = setminusLsub)), 15.72/2.40 inference(rectify,[],[f128])). 15.72/2.40 thf(f128,axiom,( 15.72/2.40 (! [X4,X3] : (subset @ (setminus @ X3 @ X4) @ X3) = setminusLsub)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusLsub)). 15.72/2.40 thf(f699,plain,( 15.72/2.40 (setminusIRneg = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (in @ Y2 @ (setminus @ Y1 @ Y0)))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f384])). 15.72/2.40 thf(f384,plain,( 15.72/2.40 (setminusIRneg = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (in @ Y2 @ (setminus @ Y1 @ Y0)))))))))))), 15.72/2.40 inference(fool_elimination,[],[f383])). 15.72/2.40 thf(f383,plain,( 15.72/2.40 (! [X0,X1,X2] : ((in @ X0 @ X2) => ~(in @ X0 @ (setminus @ X1 @ X2))) = setminusIRneg)), 15.72/2.40 inference(rectify,[],[f127])). 15.72/2.40 thf(f127,axiom,( 15.72/2.40 (! [X1,X3,X4] : ((in @ X1 @ X4) => ~(in @ X1 @ (setminus @ X3 @ X4))) = setminusIRneg)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusIRneg)). 15.72/2.40 thf(f669,plain,( 15.72/2.40 (setminusILneg = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (setminus @ Y0 @ Y1)))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f540])). 15.72/2.40 thf(f540,plain,( 15.72/2.40 (setminusILneg = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y0)) => (~ (in @ Y2 @ (setminus @ Y0 @ Y1)))))))))))), 15.72/2.40 inference(fool_elimination,[],[f539])). 15.72/2.40 thf(f539,plain,( 15.72/2.40 (! [X0,X1,X2] : (~(in @ X0 @ X2) => ~(in @ X0 @ (setminus @ X2 @ X1))) = setminusILneg)), 15.72/2.40 inference(rectify,[],[f126])). 15.72/2.40 thf(f126,axiom,( 15.72/2.40 (! [X1,X4,X3] : (~(in @ X1 @ X3) => ~(in @ X1 @ (setminus @ X3 @ X4))) = setminusILneg)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusILneg)). 15.72/2.40 thf(f634,plain,( 15.72/2.40 (setminusELneg = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y0 @ Y1))) => ((~ (in @ Y2 @ Y1)) => (~ (in @ Y2 @ Y0)))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f378])). 15.72/2.40 thf(f378,plain,( 15.72/2.40 (setminusELneg = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y0 @ Y1))) => ((~ (in @ Y2 @ Y1)) => (~ (in @ Y2 @ Y0)))))))))))), 15.72/2.40 inference(fool_elimination,[],[f377])). 15.72/2.40 thf(f377,plain,( 15.72/2.40 (! [X0,X1,X2] : (~(in @ X0 @ (setminus @ X2 @ X1)) => (~(in @ X0 @ X1) => ~(in @ X0 @ X2))) = setminusELneg)), 15.72/2.40 inference(rectify,[],[f125])). 15.72/2.40 thf(f125,axiom,( 15.72/2.40 (! [X1,X4,X3] : (~(in @ X1 @ (setminus @ X3 @ X4)) => (~(in @ X1 @ X4) => ~(in @ X1 @ X3))) = setminusELneg)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusELneg)). 15.72/2.40 thf(f653,plain,( 15.72/2.40 (setminusERneg = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y2 @ Y0))) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f458])). 15.72/2.40 thf(f458,plain,( 15.72/2.40 (setminusERneg = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y1 @ (setminus @ Y2 @ Y0))) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))))), 15.72/2.40 inference(fool_elimination,[],[f457])). 15.72/2.40 thf(f457,plain,( 15.72/2.40 (! [X0,X1,X2] : (~(in @ X1 @ (setminus @ X0 @ X2)) => ((in @ X1 @ X0) => (in @ X1 @ X2))) = setminusERneg)), 15.72/2.40 inference(rectify,[],[f124])). 15.72/2.40 thf(f124,axiom,( 15.72/2.40 (! [X3,X1,X4] : (~(in @ X1 @ (setminus @ X3 @ X4)) => ((in @ X1 @ X3) => (in @ X1 @ X4))) = setminusERneg)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusERneg)). 15.72/2.40 thf(f726,plain,( 15.72/2.40 (setminusSubset2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))))), 15.72/2.40 inference(cnf_transformation,[],[f317])). 15.72/2.40 thf(f317,plain,( 15.72/2.40 (setminusSubset2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))))), 15.72/2.40 inference(fool_elimination,[],[f316])). 15.72/2.40 thf(f316,plain,( 15.72/2.40 (! [X0,X1] : ((subset @ X0 @ X1) => (emptyset = (setminus @ X0 @ X1))) = setminusSubset2)), 15.72/2.40 inference(rectify,[],[f123])). 15.72/2.40 thf(f123,axiom,( 15.72/2.40 (! [X3,X4] : ((subset @ X3 @ X4) => (emptyset = (setminus @ X3 @ X4))) = setminusSubset2)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset2)). 15.72/2.40 thf(f719,plain,( 15.72/2.40 (setminusER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y1 @ Y0)) => (~ (in @ Y2 @ Y0))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f391])). 15.72/2.40 thf(f391,plain,( 15.72/2.40 (setminusER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y1 @ Y0)) => (~ (in @ Y2 @ Y0))))))))))), 15.72/2.40 inference(fool_elimination,[],[f390])). 15.72/2.40 thf(f390,plain,( 15.72/2.40 (! [X0,X1,X2] : ((in @ X0 @ (setminus @ X1 @ X2)) => ~(in @ X0 @ X2)) = setminusER)), 15.72/2.40 inference(rectify,[],[f122])). 15.72/2.40 thf(f122,axiom,( 15.72/2.40 (! [X1,X3,X4] : ((in @ X1 @ (setminus @ X3 @ X4)) => ~(in @ X1 @ X4)) = setminusER)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusER)). 15.72/2.40 thf(f738,plain,( 15.72/2.40 (setminusEL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))))), 15.72/2.40 inference(cnf_transformation,[],[f453])). 15.72/2.40 thf(f453,plain,( 15.72/2.40 (setminusEL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setminus @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))))), 15.72/2.40 inference(fool_elimination,[],[f452])). 15.72/2.40 thf(f452,plain,( 15.72/2.40 (! [X0,X1,X2] : ((in @ X1 @ (setminus @ X0 @ X2)) => (in @ X1 @ X0)) = setminusEL)), 15.72/2.40 inference(rectify,[],[f121])). 15.72/2.40 thf(f121,axiom,( 15.72/2.40 (! [X3,X1,X4] : ((in @ X1 @ (setminus @ X3 @ X4)) => (in @ X1 @ X3)) = setminusEL)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusEL)). 15.72/2.40 thf(f659,plain,( 15.72/2.40 (setminusI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f579])). 15.72/2.40 thf(f579,plain,( 15.72/2.40 (setminusI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((~ (in @ Y0 @ Y1)) => (in @ Y0 @ (setminus @ Y2 @ Y1)))))))))))), 15.72/2.40 inference(fool_elimination,[],[f578])). 15.72/2.40 thf(f578,plain,( 15.72/2.40 (! [X0,X1,X2] : ((in @ X2 @ X0) => (~(in @ X2 @ X1) => (in @ X2 @ (setminus @ X0 @ X1)))) = setminusI)), 15.72/2.40 inference(rectify,[],[f120])). 15.72/2.40 thf(f120,axiom,( 15.72/2.40 (! [X3,X4,X1] : ((in @ X1 @ X3) => (~(in @ X1 @ X4) => (in @ X1 @ (setminus @ X3 @ X4)))) = setminusI)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusI)). 15.72/2.40 thf(f712,plain,( 15.72/2.40 (bs114d = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0)) = (binintersect @ Y2 @ (binunion @ Y1 @ Y0))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f293])). 15.72/2.40 thf(f293,plain,( 15.72/2.40 (bs114d = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y2 @ Y1) @ (binintersect @ Y2 @ Y0)) = (binintersect @ Y2 @ (binunion @ Y1 @ Y0))))))))))), 15.72/2.40 inference(fool_elimination,[],[f292])). 15.72/2.40 thf(f292,plain,( 15.72/2.40 (bs114d = ! [X0,X1,X2] : ((binunion @ (binintersect @ X0 @ X1) @ (binintersect @ X0 @ X2)) = (binintersect @ X0 @ (binunion @ X1 @ X2))))), 15.72/2.40 inference(rectify,[],[f119])). 15.72/2.40 thf(f119,axiom,( 15.72/2.40 (bs114d = ! [X3,X4,X5] : ((binintersect @ X3 @ (binunion @ X4 @ X5)) = (binunion @ (binintersect @ X3 @ X4) @ (binintersect @ X3 @ X5))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',bs114d)). 15.72/2.40 thf(f697,plain,( 15.72/2.40 (binintersectSubset1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))))), 15.72/2.40 inference(cnf_transformation,[],[f351])). 15.72/2.40 thf(f351,plain,( 15.72/2.40 (binintersectSubset1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y1 @ Y0) = Y1) => (subset @ Y1 @ Y0)))))))), 15.72/2.40 inference(fool_elimination,[],[f350])). 15.72/2.40 thf(f350,plain,( 15.72/2.40 (! [X0,X1] : (((binintersect @ X0 @ X1) = X0) => (subset @ X0 @ X1)) = binintersectSubset1)), 15.72/2.40 inference(rectify,[],[f118])). 15.72/2.40 thf(f118,axiom,( 15.72/2.40 (! [X3,X4] : (((binintersect @ X3 @ X4) = X3) => (subset @ X3 @ X4)) = binintersectSubset1)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset1)). 15.72/2.40 thf(f691,plain,( 15.72/2.40 (binintersectSubset4 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))))), 15.72/2.40 inference(cnf_transformation,[],[f571])). 15.72/2.40 thf(f571,plain,( 15.72/2.40 (binintersectSubset4 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((binintersect @ Y1 @ Y0) = Y0)))))))), 15.72/2.40 inference(fool_elimination,[],[f570])). 15.72/2.40 thf(f570,plain,( 15.72/2.40 (! [X0,X1] : ((subset @ X1 @ X0) => ((binintersect @ X0 @ X1) = X1)) = binintersectSubset4)), 15.72/2.40 inference(rectify,[],[f117])). 15.72/2.40 thf(f117,axiom,( 15.72/2.40 (! [X3,X4] : ((subset @ X4 @ X3) => ((binintersect @ X3 @ X4) = X4)) = binintersectSubset4)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset4)). 15.72/2.40 thf(f718,plain,( 15.72/2.40 (binintersectRsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))))), 15.72/2.40 inference(cnf_transformation,[],[f462])). 15.72/2.40 thf(f462,plain,( 15.72/2.40 (binintersectRsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))))), 15.72/2.40 inference(fool_elimination,[],[f461])). 15.72/2.40 thf(f461,plain,( 15.72/2.40 (! [X0,X1] : (subset @ (binintersect @ X1 @ X0) @ X0) = binintersectRsub)), 15.72/2.40 inference(rectify,[],[f116])). 15.72/2.40 thf(f116,axiom,( 15.72/2.40 (! [X4,X3] : (subset @ (binintersect @ X3 @ X4) @ X4) = binintersectRsub)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectRsub)). 15.72/2.40 thf(f656,plain,( 15.72/2.40 (disjointsetsI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))) => (emptyset = (binintersect @ Y1 @ Y0))))))))), 15.72/2.40 inference(cnf_transformation,[],[f556])). 15.72/2.40 thf(f556,plain,( 15.72/2.40 (disjointsetsI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))) => (emptyset = (binintersect @ Y1 @ Y0))))))))), 15.72/2.40 inference(fool_elimination,[],[f555])). 15.72/2.40 thf(f555,plain,( 15.72/2.40 (! [X0,X1] : (~? [X2] : ((in @ X2 @ X1) & (in @ X2 @ X0)) => (emptyset = (binintersect @ X0 @ X1))) = disjointsetsI1)), 15.72/2.40 inference(rectify,[],[f115])). 15.72/2.40 thf(f115,axiom,( 15.72/2.40 (! [X3,X4] : (~? [X1] : ((in @ X1 @ X4) & (in @ X1 @ X3)) => (emptyset = (binintersect @ X3 @ X4))) = disjointsetsI1)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjointsetsI1)). 15.72/2.40 thf(f611,plain,( 15.72/2.40 (binintersectER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1)))))))))), 15.72/2.40 inference(cnf_transformation,[],[f277])). 15.72/2.40 thf(f277,plain,( 15.72/2.40 (binintersectER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1)))))))))), 15.72/2.40 inference(fool_elimination,[],[f276])). 15.72/2.40 thf(f276,plain,( 15.72/2.40 (! [X0,X1,X2] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X1)) = binintersectER)), 15.72/2.40 inference(rectify,[],[f114])). 15.72/2.40 thf(f114,axiom,( 15.72/2.40 (! [X3,X4,X1] : ((in @ X1 @ (binintersect @ X3 @ X4)) => (in @ X1 @ X4)) = binintersectER)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectER)). 15.72/2.40 thf(f651,plain,( 15.72/2.40 (binintersectSubset3 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))))), 15.72/2.40 inference(cnf_transformation,[],[f419])). 15.72/2.40 thf(f419,plain,( 15.72/2.40 (binintersectSubset3 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))))), 15.72/2.40 inference(fool_elimination,[],[f418])). 15.72/2.40 thf(f418,plain,( 15.72/2.40 (! [X0,X1] : (((binintersect @ X1 @ X0) = X0) => (subset @ X0 @ X1)) = binintersectSubset3)), 15.72/2.40 inference(rectify,[],[f113])). 15.72/2.40 thf(f113,axiom,( 15.72/2.40 (! [X4,X3] : (((binintersect @ X3 @ X4) = X4) => (subset @ X4 @ X3)) = binintersectSubset3)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset3)). 15.72/2.40 thf(f599,plain,( 15.72/2.40 (binintersectSubset2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))))), 15.72/2.40 inference(cnf_transformation,[],[f315])). 15.72/2.40 thf(f315,plain,( 15.72/2.40 (binintersectSubset2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))))), 15.72/2.40 inference(fool_elimination,[],[f314])). 15.72/2.40 thf(f314,plain,( 15.72/2.40 (binintersectSubset2 = ! [X0,X1] : ((subset @ X0 @ X1) => ((binintersect @ X0 @ X1) = X0)))), 15.72/2.40 inference(rectify,[],[f112])). 15.72/2.40 thf(f112,axiom,( 15.72/2.40 (binintersectSubset2 = ! [X3,X4] : ((subset @ X3 @ X4) => ((binintersect @ X3 @ X4) = X3)))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset2)). 15.72/2.40 thf(f717,plain,( 15.72/2.40 (binintersectLsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))))), 15.72/2.40 inference(cnf_transformation,[],[f395])). 15.72/2.40 thf(f395,plain,( 15.72/2.40 (binintersectLsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))))), 15.72/2.40 inference(fool_elimination,[],[f394])). 15.72/2.40 thf(f394,plain,( 15.72/2.40 (binintersectLsub = ! [X0,X1] : (subset @ (binintersect @ X0 @ X1) @ X0))), 15.72/2.40 inference(rectify,[],[f111])). 15.72/2.40 thf(f111,axiom,( 15.72/2.40 (binintersectLsub = ! [X3,X4] : (subset @ (binintersect @ X3 @ X4) @ X3))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectLsub)). 15.72/2.40 thf(f623,plain,( 15.72/2.40 (binintersectEL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))))), 15.72/2.40 inference(cnf_transformation,[],[f478])). 15.72/2.40 thf(f478,plain,( 15.72/2.40 (binintersectEL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y1 @ Y2)) => (in @ Y0 @ Y1)))))))))), 15.72/2.40 inference(fool_elimination,[],[f477])). 15.72/2.40 thf(f477,plain,( 15.72/2.40 (binintersectEL = ! [X0,X1,X2] : ((in @ X2 @ (binintersect @ X1 @ X0)) => (in @ X2 @ X1)))), 15.72/2.40 inference(rectify,[],[f110])). 15.72/2.40 thf(f110,axiom,( 15.72/2.40 (binintersectEL = ! [X4,X3,X1] : ((in @ X1 @ (binintersect @ X3 @ X4)) => (in @ X1 @ X3)))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectEL)). 15.72/2.40 thf(f720,plain,( 15.72/2.40 (binintersectSubset5 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((subset @ Y2 @ Y0) => (subset @ Y2 @ (binintersect @ Y1 @ Y0)))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f476])). 15.72/2.40 thf(f476,plain,( 15.72/2.40 (binintersectSubset5 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((subset @ Y2 @ Y0) => (subset @ Y2 @ (binintersect @ Y1 @ Y0)))))))))))), 15.72/2.40 inference(fool_elimination,[],[f475])). 15.72/2.40 thf(f475,plain,( 15.72/2.40 (! [X0,X1,X2] : ((subset @ X0 @ X1) => ((subset @ X0 @ X2) => (subset @ X0 @ (binintersect @ X1 @ X2)))) = binintersectSubset5)), 15.72/2.40 inference(rectify,[],[f109])). 15.72/2.40 thf(f109,axiom,( 15.72/2.40 (! [X5,X3,X4] : ((subset @ X5 @ X3) => ((subset @ X5 @ X4) => (subset @ X5 @ (binintersect @ X3 @ X4)))) = binintersectSubset5)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset5)). 15.72/2.40 thf(f681,plain,( 15.72/2.40 (binintersectI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f494])). 15.72/2.40 thf(f494,plain,( 15.72/2.40 (binintersectI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (in @ Y2 @ (binintersect @ Y0 @ Y1)))))))))))), 15.72/2.40 inference(fool_elimination,[],[f493])). 15.72/2.40 thf(f493,plain,( 15.72/2.40 (binintersectI = ! [X0,X1,X2] : ((in @ X0 @ X2) => ((in @ X0 @ X1) => (in @ X0 @ (binintersect @ X2 @ X1)))))), 15.72/2.40 inference(rectify,[],[f108])). 15.72/2.40 thf(f108,axiom,( 15.72/2.40 (binintersectI = ! [X1,X4,X3] : ((in @ X1 @ X3) => ((in @ X1 @ X4) => (in @ X1 @ (binintersect @ X3 @ X4)))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectI)). 15.72/2.40 thf(f693,plain,( 15.72/2.40 (binunionRsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))))), 15.72/2.40 inference(cnf_transformation,[],[f382])). 15.72/2.40 thf(f382,plain,( 15.72/2.40 (binunionRsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y1 @ Y0)))))))), 15.72/2.40 inference(fool_elimination,[],[f381])). 15.72/2.40 thf(f381,plain,( 15.72/2.40 (! [X0,X1] : (subset @ X1 @ (binunion @ X0 @ X1)) = binunionRsub)), 15.72/2.40 inference(rectify,[],[f107])). 15.72/2.40 thf(f107,axiom,( 15.72/2.40 (! [X3,X4] : (subset @ X4 @ (binunion @ X3 @ X4)) = binunionRsub)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionRsub)). 15.72/2.40 thf(f774,plain,( 15.72/2.40 (binunionLsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1)))))))), 15.72/2.40 inference(cnf_transformation,[],[f534])). 15.72/2.40 thf(f534,plain,( 15.72/2.40 (binunionLsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1)))))))), 15.72/2.40 inference(fool_elimination,[],[f533])). 15.72/2.40 thf(f533,plain,( 15.72/2.40 (binunionLsub = ! [X0,X1] : (subset @ X1 @ (binunion @ X1 @ X0)))), 15.72/2.40 inference(rectify,[],[f106])). 15.72/2.40 thf(f106,axiom,( 15.72/2.40 (binunionLsub = ! [X4,X3] : (subset @ X3 @ (binunion @ X3 @ X4)))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionLsub)). 15.72/2.40 thf(f615,plain,( 15.72/2.40 (binunionE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binunion @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (in @ Y0 @ Y2))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f380])). 15.72/2.40 thf(f380,plain,( 15.72/2.40 (binunionE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binunion @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (in @ Y0 @ Y2))))))))))), 15.72/2.40 inference(fool_elimination,[],[f379])). 15.72/2.40 thf(f379,plain,( 15.72/2.40 (! [X0,X1,X2] : ((in @ X2 @ (binunion @ X0 @ X1)) => ((in @ X2 @ X0) | (in @ X2 @ X1))) = binunionE)), 15.72/2.40 inference(rectify,[],[f105])). 15.72/2.40 thf(f105,axiom,( 15.72/2.40 (! [X3,X4,X1] : ((in @ X1 @ (binunion @ X3 @ X4)) => ((in @ X1 @ X3) | (in @ X1 @ X4))) = binunionE)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionE)). 15.72/2.40 thf(f650,plain,( 15.72/2.40 (binunionEcases = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: ((in @ Y0 @ (binunion @ Y1 @ Y2)) => (((in @ Y0 @ Y1) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f496])). 15.72/2.40 thf(f496,plain,( 15.72/2.40 (binunionEcases = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: ((in @ Y0 @ (binunion @ Y1 @ Y2)) => (((in @ Y0 @ Y1) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))))), 15.72/2.40 inference(fool_elimination,[],[f495])). 15.72/2.40 thf(f495,plain,( 15.72/2.40 (binunionEcases = ! [X0 : $o,X1,X2,X3] : ((in @ X3 @ (binunion @ X2 @ X1)) => (((in @ X3 @ X2) => X0) => (((in @ X3 @ X1) => X0) => X0))))), 15.72/2.40 inference(rectify,[],[f104])). 15.72/2.40 thf(f104,axiom,( 15.72/2.40 (binunionEcases = ! [X0 : $o,X4,X3,X1] : ((in @ X1 @ (binunion @ X3 @ X4)) => (((in @ X1 @ X3) => X0) => (((in @ X1 @ X4) => X0) => X0))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionEcases)). 15.72/2.40 thf(f776,plain,( 15.72/2.40 (binunionIR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f472])). 15.72/2.40 thf(f472,plain,( 15.72/2.40 (binunionIR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))))), 15.72/2.40 inference(fool_elimination,[],[f471])). 15.72/2.40 thf(f471,plain,( 15.72/2.40 (binunionIR = ! [X0,X1,X2] : ((in @ X2 @ X1) => (in @ X2 @ (binunion @ X0 @ X1))))), 15.72/2.40 inference(rectify,[],[f103])). 15.72/2.40 thf(f103,axiom,( 15.72/2.40 (binunionIR = ! [X3,X4,X1] : ((in @ X1 @ X4) => (in @ X1 @ (binunion @ X3 @ X4))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIR)). 15.72/2.40 thf(f683,plain,( 15.72/2.40 (upairset2IR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))), 15.72/2.40 inference(cnf_transformation,[],[f593])). 15.72/2.40 thf(f593,plain,( 15.72/2.40 (upairset2IR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))), 15.72/2.40 inference(fool_elimination,[],[f592])). 15.72/2.40 thf(f592,plain,( 15.72/2.40 (upairset2IR = ! [X0,X1] : (in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))))), 15.72/2.40 inference(rectify,[],[f102])). 15.72/2.40 thf(f102,axiom,( 15.72/2.40 (upairset2IR = ! [X1,X2] : (in @ X2 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2IR)). 15.72/2.40 thf(f637,plain,( 15.72/2.40 (binunionIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ (binunion @ Y0 @ Y1))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f321])). 15.72/2.40 thf(f321,plain,( 15.72/2.40 (binunionIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ (binunion @ Y0 @ Y1))))))))))), 15.72/2.40 inference(fool_elimination,[],[f320])). 15.72/2.40 thf(f320,plain,( 15.72/2.40 (! [X0,X1,X2] : ((in @ X0 @ X2) => (in @ X0 @ (binunion @ X2 @ X1))) = binunionIL)), 15.72/2.40 inference(rectify,[],[f101])). 15.72/2.40 thf(f101,axiom,( 15.72/2.40 (! [X1,X4,X3] : ((in @ X1 @ X3) => (in @ X1 @ (binunion @ X3 @ X4))) = binunionIL)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIL)). 15.72/2.40 thf(f682,plain,( 15.72/2.40 (sepSubset = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ (^[Y2 : $i]: (Y0 @ Y2))) @ Y1))))))), 15.72/2.40 inference(cnf_transformation,[],[f393])). 15.72/2.40 thf(f393,plain,( 15.72/2.40 (sepSubset = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (subset @ (dsetconstr @ Y1 @ (^[Y2 : $i]: (Y0 @ Y2))) @ Y1))))))), 15.72/2.40 inference(fool_elimination,[],[f392])). 15.72/2.40 thf(f392,plain,( 15.72/2.40 (sepSubset = ! [X0,X1 : $i > $o] : (subset @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))) @ X0))), 15.72/2.40 inference(rectify,[],[f100])). 15.72/2.40 thf(f100,axiom,( 15.72/2.40 (sepSubset = ! [X3,X0 : $i > $o] : (subset @ (dsetconstr @ X3 @ (^[X1 : $i] : (X0 @ X1))) @ X3))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepSubset)). 15.72/2.40 thf(f706,plain,( 15.72/2.40 (sepInPowerset = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) @ (powerset @ Y0)))))))), 15.72/2.40 inference(cnf_transformation,[],[f329])). 15.72/2.40 thf(f329,plain,( 15.72/2.40 (sepInPowerset = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) @ (powerset @ Y0)))))))), 15.72/2.40 inference(fool_elimination,[],[f328])). 15.72/2.40 thf(f328,plain,( 15.72/2.40 (sepInPowerset = ! [X0 : $i > $o,X1] : (in @ (dsetconstr @ X1 @ (^[X2 : $i] : (X0 @ X2))) @ (powerset @ X1)))), 15.72/2.40 inference(rectify,[],[f99])). 15.72/2.40 thf(f99,axiom,( 15.72/2.40 (sepInPowerset = ! [X0 : $i > $o,X3] : (in @ (dsetconstr @ X3 @ (^[X1 : $i] : (X0 @ X1))) @ (powerset @ X3)))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepInPowerset)). 15.72/2.40 thf(f732,plain,( 15.72/2.40 (powersetsubset = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (subset @ (powerset @ Y1) @ (powerset @ Y0))))))))), 15.72/2.40 inference(cnf_transformation,[],[f577])). 15.72/2.40 thf(f577,plain,( 15.72/2.40 (powersetsubset = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (subset @ (powerset @ Y1) @ (powerset @ Y0))))))))), 15.72/2.40 inference(fool_elimination,[],[f576])). 15.72/2.40 thf(f576,plain,( 15.72/2.40 (powersetsubset = ! [X0,X1] : ((subset @ X0 @ X1) => (subset @ (powerset @ X0) @ (powerset @ X1))))), 15.72/2.40 inference(rectify,[],[f98])). 15.72/2.40 thf(f98,axiom,( 15.72/2.40 (powersetsubset = ! [X3,X4] : ((subset @ X3 @ X4) => (subset @ (powerset @ X3) @ (powerset @ X4))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetsubset)). 15.72/2.40 thf(f742,plain,( 15.72/2.40 (inPowerset = (!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))))), 15.72/2.40 inference(cnf_transformation,[],[f558])). 15.72/2.40 thf(f558,plain,( 15.72/2.40 (inPowerset = (!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))))), 15.72/2.40 inference(fool_elimination,[],[f557])). 15.72/2.40 thf(f557,plain,( 15.72/2.40 (! [X0] : (in @ X0 @ (powerset @ X0)) = inPowerset)), 15.72/2.40 inference(rectify,[],[f97])). 15.72/2.40 thf(f97,axiom,( 15.72/2.40 (! [X3] : (in @ X3 @ (powerset @ X3)) = inPowerset)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',inPowerset)). 15.72/2.40 thf(f684,plain,( 15.72/2.40 (powersetE1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))))), 15.72/2.40 inference(cnf_transformation,[],[f245])). 15.72/2.40 thf(f245,plain,( 15.72/2.40 (powersetE1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (subset @ Y1 @ Y0)))))))), 15.72/2.40 inference(fool_elimination,[],[f244])). 15.72/2.40 thf(f244,plain,( 15.72/2.40 (powersetE1 = ! [X0,X1] : ((in @ X0 @ (powerset @ X1)) => (subset @ X0 @ X1)))), 15.72/2.40 inference(rectify,[],[f96])). 15.72/2.40 thf(f96,axiom,( 15.72/2.40 (powersetE1 = ! [X4,X3] : ((in @ X4 @ (powerset @ X3)) => (subset @ X4 @ X3)))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1)). 15.72/2.40 thf(f675,plain,( 15.72/2.40 (powersetI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))))), 15.72/2.40 inference(cnf_transformation,[],[f203])). 15.72/2.40 thf(f203,plain,( 15.72/2.40 (powersetI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))))), 15.72/2.40 inference(fool_elimination,[],[f202])). 15.72/2.40 thf(f202,plain,( 15.72/2.40 (powersetI1 = ! [X0,X1] : ((subset @ X1 @ X0) => (in @ X1 @ (powerset @ X0))))), 15.72/2.40 inference(rectify,[],[f95])). 15.72/2.40 thf(f95,axiom,( 15.72/2.40 (powersetI1 = ! [X3,X4] : ((subset @ X4 @ X3) => (in @ X4 @ (powerset @ X3))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI1)). 15.72/2.40 thf(f739,plain,( 15.72/2.40 (subsetemptysetimpeq = (!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))))), 15.72/2.40 inference(cnf_transformation,[],[f303])). 15.72/2.40 thf(f303,plain,( 15.72/2.40 (subsetemptysetimpeq = (!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))))), 15.72/2.40 inference(fool_elimination,[],[f302])). 15.72/2.40 thf(f302,plain,( 15.72/2.40 (subsetemptysetimpeq = ! [X0] : ((subset @ X0 @ emptyset) => (emptyset = X0)))), 15.72/2.40 inference(rectify,[],[f94])). 15.72/2.40 thf(f94,axiom,( 15.72/2.40 (subsetemptysetimpeq = ! [X3] : ((subset @ X3 @ emptyset) => (emptyset = X3)))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetemptysetimpeq)). 15.72/2.40 thf(f713,plain,( 15.72/2.40 (setextsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (Y1 = Y0))))))))), 15.72/2.40 inference(cnf_transformation,[],[f223])). 15.72/2.40 thf(f223,plain,( 15.72/2.40 (setextsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y0) => (Y1 = Y0))))))))), 15.72/2.40 inference(fool_elimination,[],[f222])). 15.72/2.40 thf(f222,plain,( 15.72/2.40 (setextsub = ! [X0,X1] : ((subset @ X1 @ X0) => ((subset @ X0 @ X1) => (X0 = X1))))), 15.72/2.40 inference(rectify,[],[f93])). 15.72/2.40 thf(f93,axiom,( 15.72/2.40 (setextsub = ! [X4,X3] : ((subset @ X3 @ X4) => ((subset @ X4 @ X3) => (X3 = X4))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextsub)). 15.72/2.40 thf(f734,plain,( 15.72/2.40 (subset2powerset = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))))), 15.72/2.40 inference(cnf_transformation,[],[f490])). 15.72/2.40 thf(f490,plain,( 15.72/2.40 (subset2powerset = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))))), 15.72/2.40 inference(fool_elimination,[],[f489])). 15.72/2.40 thf(f489,plain,( 15.72/2.40 (! [X0,X1] : ((subset @ X1 @ X0) => (in @ X1 @ (powerset @ X0))) = subset2powerset)), 15.72/2.40 inference(rectify,[],[f92])). 15.72/2.40 thf(f92,axiom,( 15.72/2.40 (! [X4,X3] : ((subset @ X3 @ X4) => (in @ X3 @ (powerset @ X4))) = subset2powerset)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2powerset)). 15.72/2.40 thf(f694,plain,( 15.72/2.40 (setadjoinSub2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f427])). 15.72/2.40 thf(f427,plain,( 15.72/2.40 (setadjoinSub2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))))), 15.72/2.40 inference(fool_elimination,[],[f426])). 15.72/2.40 thf(f426,plain,( 15.72/2.40 (setadjoinSub2 = ! [X0,X1,X2] : ((subset @ X1 @ X0) => (subset @ X1 @ (setadjoin @ X2 @ X0))))), 15.72/2.40 inference(rectify,[],[f91])). 15.72/2.40 thf(f91,axiom,( 15.72/2.40 (setadjoinSub2 = ! [X4,X3,X1] : ((subset @ X3 @ X4) => (subset @ X3 @ (setadjoin @ X1 @ X4))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub2)). 15.72/2.40 thf(f716,plain,( 15.72/2.40 (setadjoinSub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (setadjoin @ Y1 @ Y0)))))))), 15.72/2.40 inference(cnf_transformation,[],[f486])). 15.72/2.40 thf(f486,plain,( 15.72/2.40 (setadjoinSub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (setadjoin @ Y1 @ Y0)))))))), 15.72/2.40 inference(fool_elimination,[],[f485])). 15.72/2.40 thf(f485,plain,( 15.72/2.40 (! [X0,X1] : (subset @ X1 @ (setadjoin @ X0 @ X1)) = setadjoinSub)), 15.72/2.40 inference(rectify,[],[f90])). 15.72/2.40 thf(f90,axiom,( 15.72/2.40 (! [X1,X3] : (subset @ X3 @ (setadjoin @ X1 @ X3)) = setadjoinSub)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub)). 15.72/2.40 thf(f603,plain,( 15.72/2.40 (subsetTrans = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y2) => (subset @ Y0 @ Y2))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f492])). 15.72/2.40 thf(f492,plain,( 15.72/2.40 (subsetTrans = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((subset @ Y1 @ Y2) => (subset @ Y0 @ Y2))))))))))), 15.72/2.40 inference(fool_elimination,[],[f491])). 15.72/2.40 thf(f491,plain,( 15.72/2.40 (! [X0,X1,X2] : ((subset @ X2 @ X1) => ((subset @ X1 @ X0) => (subset @ X2 @ X0))) = subsetTrans)), 15.72/2.40 inference(rectify,[],[f89])). 15.72/2.40 thf(f89,axiom,( 15.72/2.40 (! [X5,X4,X3] : ((subset @ X3 @ X4) => ((subset @ X4 @ X5) => (subset @ X3 @ X5))) = subsetTrans)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTrans)). 15.72/2.40 thf(f668,plain,( 15.72/2.40 (subsetRefl = (!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))))), 15.72/2.40 inference(cnf_transformation,[],[f247])). 15.72/2.40 thf(f247,plain,( 15.72/2.40 (subsetRefl = (!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))))), 15.72/2.40 inference(fool_elimination,[],[f246])). 15.72/2.40 thf(f246,plain,( 15.72/2.40 (subsetRefl = ! [X0] : (subset @ X0 @ X0))), 15.72/2.40 inference(rectify,[],[f88])). 15.72/2.40 thf(f88,axiom,( 15.72/2.40 (subsetRefl = ! [X3] : (subset @ X3 @ X3))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetRefl)). 15.72/2.40 thf(f748,plain,( 15.72/2.40 (notequalI2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = Y0)))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f249])). 15.72/2.40 thf(f249,plain,( 15.72/2.40 (notequalI2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = Y0)))))))))))), 15.72/2.40 inference(fool_elimination,[],[f248])). 15.72/2.40 thf(f248,plain,( 15.72/2.40 (! [X0,X1,X2] : ((in @ X1 @ X0) => (~(in @ X1 @ X2) => (X0 != X2))) = notequalI2)), 15.72/2.40 inference(rectify,[],[f87])). 15.72/2.40 thf(f87,axiom,( 15.72/2.40 (! [X3,X1,X4] : ((in @ X1 @ X3) => (~(in @ X1 @ X4) => (X3 != X4))) = notequalI2)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI2)). 15.72/2.40 thf(f664,plain,( 15.72/2.40 (notequalI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))))), 15.72/2.40 inference(cnf_transformation,[],[f484])). 15.72/2.40 thf(f484,plain,( 15.72/2.40 (notequalI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y1 @ Y0)) => (~ (Y1 = Y0))))))))), 15.72/2.40 inference(fool_elimination,[],[f483])). 15.72/2.40 thf(f483,plain,( 15.72/2.40 (notequalI1 = ! [X0,X1] : (~(subset @ X0 @ X1) => (X0 != X1)))), 15.72/2.40 inference(rectify,[],[f86])). 15.72/2.40 thf(f86,axiom,( 15.72/2.40 (notequalI1 = ! [X3,X4] : (~(subset @ X3 @ X4) => (X3 != X4)))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI1)). 15.72/2.40 thf(f737,plain,( 15.72/2.40 (notsubsetI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (subset @ Y2 @ Y0)))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f480])). 15.72/2.40 thf(f480,plain,( 15.72/2.40 (notsubsetI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (subset @ Y2 @ Y0)))))))))))), 15.72/2.40 inference(fool_elimination,[],[f479])). 15.72/2.40 thf(f479,plain,( 15.72/2.40 (! [X0,X1,X2] : ((in @ X1 @ X0) => (~(in @ X1 @ X2) => ~(subset @ X0 @ X2))) = notsubsetI)), 15.72/2.40 inference(rectify,[],[f85])). 15.72/2.40 thf(f85,axiom,( 15.72/2.40 (! [X3,X1,X4] : ((in @ X1 @ X3) => (~(in @ X1 @ X4) => ~(subset @ X3 @ X4))) = notsubsetI)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',notsubsetI)). 15.72/2.40 thf(f671,plain,( 15.72/2.40 (subsetE2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f243])). 15.72/2.40 thf(f243,plain,( 15.72/2.40 (subsetE2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y1) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))))), 15.72/2.40 inference(fool_elimination,[],[f242])). 15.72/2.40 thf(f242,plain,( 15.72/2.40 (subsetE2 = ! [X0,X1,X2] : ((subset @ X0 @ X1) => (~(in @ X2 @ X1) => ~(in @ X2 @ X0))))), 15.72/2.40 inference(rectify,[],[f84])). 15.72/2.40 thf(f84,axiom,( 15.72/2.40 (subsetE2 = ! [X3,X4,X1] : ((subset @ X3 @ X4) => (~(in @ X1 @ X4) => ~(in @ X1 @ X3))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE2)). 15.72/2.40 thf(f702,plain,( 15.72/2.40 (subsetE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f217])). 15.72/2.40 thf(f217,plain,( 15.72/2.40 (subsetE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2))))))))))), 15.72/2.40 inference(fool_elimination,[],[f216])). 15.72/2.40 thf(f216,plain,( 15.72/2.40 (subsetE = ! [X0,X1,X2] : ((subset @ X1 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ X0))))), 15.72/2.40 inference(rectify,[],[f83])). 15.72/2.40 thf(f83,axiom,( 15.72/2.40 (subsetE = ! [X4,X3,X1] : ((subset @ X3 @ X4) => ((in @ X1 @ X3) => (in @ X1 @ X4))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE)). 15.72/2.40 thf(f655,plain,( 15.72/2.40 (emptysetsubset = (!! @ $i @ (^[Y0 : $i]: (subset @ emptyset @ Y0))))), 15.72/2.40 inference(cnf_transformation,[],[f376])). 15.72/2.40 thf(f376,plain,( 15.72/2.40 (emptysetsubset = (!! @ $i @ (^[Y0 : $i]: (subset @ emptyset @ Y0))))), 15.72/2.40 inference(fool_elimination,[],[f375])). 15.72/2.40 thf(f375,plain,( 15.72/2.40 (! [X0] : (subset @ emptyset @ X0) = emptysetsubset)), 15.72/2.40 inference(rectify,[],[f82])). 15.72/2.40 thf(f82,axiom,( 15.72/2.40 (! [X3] : (subset @ emptyset @ X3) = emptysetsubset)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetsubset)). 15.72/2.40 thf(f607,plain,( 15.72/2.40 (subsetI2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))))), 15.72/2.40 inference(cnf_transformation,[],[f301])). 15.72/2.40 thf(f301,plain,( 15.72/2.40 (subsetI2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))))), 15.72/2.40 inference(fool_elimination,[],[f300])). 15.72/2.40 thf(f300,plain,( 15.72/2.40 (! [X0,X1] : (! [X2] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI2)), 15.72/2.40 inference(rectify,[],[f81])). 15.72/2.40 thf(f81,axiom,( 15.72/2.40 (! [X3,X4] : (! [X1] : ((in @ X1 @ X3) => (in @ X1 @ X4)) => (subset @ X3 @ X4)) = subsetI2)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2)). 15.72/2.40 thf(f747,plain,( 15.72/2.40 (eqimpsubset1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))))), 15.72/2.40 inference(cnf_transformation,[],[f508])). 15.72/2.40 thf(f508,plain,( 15.72/2.40 (eqimpsubset1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))))), 15.72/2.40 inference(fool_elimination,[],[f507])). 15.72/2.40 thf(f507,plain,( 15.72/2.40 (! [X0,X1] : ((X0 = X1) => (subset @ X1 @ X0)) = eqimpsubset1)), 15.72/2.40 inference(rectify,[],[f80])). 15.72/2.40 thf(f80,axiom,( 15.72/2.40 (! [X4,X3] : ((X3 = X4) => (subset @ X3 @ X4)) = eqimpsubset1)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset1)). 15.72/2.40 thf(f629,plain,( 15.72/2.40 (eqimpsubset2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))))), 15.72/2.40 inference(cnf_transformation,[],[f335])). 15.72/2.40 thf(f335,plain,( 15.72/2.40 (eqimpsubset2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y1 @ Y0)))))))), 15.72/2.40 inference(fool_elimination,[],[f334])). 15.72/2.40 thf(f334,plain,( 15.72/2.40 (eqimpsubset2 = ! [X0,X1] : ((X0 = X1) => (subset @ X0 @ X1)))), 15.72/2.40 inference(rectify,[],[f79])). 15.72/2.40 thf(f79,axiom,( 15.72/2.40 (eqimpsubset2 = ! [X4,X3] : ((X3 = X4) => (subset @ X4 @ X3)))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset2)). 15.72/2.40 thf(f724,plain,( 15.72/2.40 (subsetI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))))), 15.72/2.40 inference(cnf_transformation,[],[f366])). 15.72/2.40 thf(f366,plain,( 15.72/2.40 (subsetI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))))), 15.72/2.40 inference(fool_elimination,[],[f365])). 15.72/2.40 thf(f365,plain,( 15.72/2.40 (! [X0,X1] : (! [X2] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)) = subsetI1)), 15.72/2.40 inference(rectify,[],[f78])). 15.72/2.40 thf(f78,axiom,( 15.72/2.40 (! [X4,X3] : (! [X1] : ((in @ X1 @ X3) => (in @ X1 @ X4)) => (subset @ X3 @ X4)) = subsetI1)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI1)). 15.72/2.40 thf(f754,plain,( 15.72/2.40 (dsetconstr__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ (^[Y4 : $i]: (Y3 @ Y4))) = (dsetconstr @ Y0 @ (^[Y4 : $i]: (Y2 @ Y4)))))))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f257])). 15.72/2.40 thf(f257,plain,( 15.72/2.40 (dsetconstr__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y4) = (Y2 @ Y5))))))))) => ((dsetconstr @ Y1 @ (^[Y4 : $i]: (Y3 @ Y4))) = (dsetconstr @ Y0 @ (^[Y4 : $i]: (Y2 @ Y4)))))))))))))))), 15.72/2.40 inference(fool_elimination,[],[f256])). 15.72/2.40 thf(f256,plain,( 15.72/2.40 (dsetconstr__Cong = ! [X0,X1] : ((X0 = X1) => ! [X2 : $i > $o,X3 : $i > $o] : (! [X4] : ((in @ X4 @ X0) => ! [X5] : ((in @ X5 @ X1) => ((X4 = X5) => ((X2 @ X4) <=> (X3 @ X5))))) => ((dsetconstr @ X0 @ (^[X6 : $i] : (X2 @ X6))) = (dsetconstr @ X1 @ (^[X7 : $i] : (X3 @ X7)))))))), 15.72/2.40 inference(rectify,[],[f77])). 15.72/2.40 thf(f77,axiom,( 15.72/2.40 (dsetconstr__Cong = ! [X3,X4] : ((X3 = X4) => ! [X0 : $i > $o,X9 : $i > $o] : (! [X1] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => ((X1 = X2) => ((X0 @ X1) <=> (X9 @ X2))))) => ((dsetconstr @ X3 @ (^[X1 : $i] : (X0 @ X1))) = (dsetconstr @ X4 @ (^[X1 : $i] : (X9 @ X1)))))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstr__Cong)). 15.72/2.40 thf(f810,plain,( 15.72/2.40 (descr__Cong = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => (((^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) => (Y3 = Y4)))) & (Y2 @ Y3))))) @ (^[Y2 : $i]: (Y1 @ Y2))) => (((^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) => (Y3 = Y4)))) & (Y2 @ Y3))))) @ (^[Y2 : $i]: (Y0 @ Y2))) => ((descr @ (^[Y2 : $i]: (Y0 @ Y2))) = (descr @ (^[Y2 : $i]: (Y1 @ Y2))))))))))))), 15.72/2.40 inference(definition_unfolding,[],[f676,f647,f647])). 15.72/2.40 thf(f647,plain,( 15.72/2.40 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))), 15.72/2.40 inference(cnf_transformation,[],[f425])). 15.72/2.40 thf(f425,plain,( 15.72/2.40 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))), 15.72/2.40 inference(fool_elimination,[],[f424])). 15.72/2.40 thf(f424,plain,( 15.72/2.40 ((^[X0 : $i > $o] : (? [X1] : ((X0 @ X1) & ! [X2] : ((X0 @ X2) => (X1 = X2))))) = exu)), 15.72/2.40 inference(rectify,[],[f1])). 15.72/2.40 thf(f1,axiom,( 15.72/2.40 ((^[X0 : $i > $o] : (? [X1] : ((X0 @ X1) & ! [X2] : ((X0 @ X2) => (X1 = X2))))) = exu)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu)). 15.72/2.40 thf(f676,plain,( 15.72/2.40 (descr__Cong = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((exu @ (^[Y2 : $i]: (Y1 @ Y2))) => ((exu @ (^[Y2 : $i]: (Y0 @ Y2))) => ((descr @ (^[Y2 : $i]: (Y0 @ Y2))) = (descr @ (^[Y2 : $i]: (Y1 @ Y2))))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f387])). 15.72/2.40 thf(f387,plain,( 15.72/2.40 (descr__Cong = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((exu @ (^[Y2 : $i]: (Y1 @ Y2))) => ((exu @ (^[Y2 : $i]: (Y0 @ Y2))) => ((descr @ (^[Y2 : $i]: (Y0 @ Y2))) = (descr @ (^[Y2 : $i]: (Y1 @ Y2))))))))))))), 15.72/2.40 inference(fool_elimination,[],[f386])). 15.72/2.40 thf(f386,plain,( 15.72/2.40 (! [X0 : $i > $o,X1 : $i > $o] : (! [X2,X3] : ((X2 = X3) => ((X1 @ X2) <=> (X0 @ X3))) => ((exu @ (^[X4 : $i] : (X0 @ X4))) => ((exu @ (^[X5 : $i] : (X1 @ X5))) => ((descr @ (^[X6 : $i] : (X1 @ X6))) = (descr @ (^[X7 : $i] : (X0 @ X7))))))) = descr__Cong)), 15.72/2.40 inference(rectify,[],[f76])). 15.72/2.40 thf(f76,axiom,( 15.72/2.40 (! [X0 : $i > $o,X9 : $i > $o] : (! [X2,X1] : ((X1 = X2) => ((X9 @ X2) <=> (X0 @ X1))) => ((exu @ (^[X1 : $i] : (X0 @ X1))) => ((exu @ (^[X1 : $i] : (X9 @ X1))) => ((descr @ (^[X1 : $i] : (X9 @ X1))) = (descr @ (^[X1 : $i] : (X0 @ X1))))))) = descr__Cong)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',descr__Cong)). 15.72/2.40 thf(f809,plain,( 15.72/2.40 (exuEu = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2))))) @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))))), 15.72/2.40 inference(definition_unfolding,[],[f679,f647])). 15.72/2.40 thf(f679,plain,( 15.72/2.40 (exuEu = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f343])). 15.72/2.40 thf(f343,plain,( 15.72/2.40 (exuEu = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))))), 15.72/2.40 inference(fool_elimination,[],[f342])). 15.72/2.40 thf(f342,plain,( 15.72/2.40 (! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ! [X2,X3] : ((X0 @ X2) => ((X0 @ X3) => (X2 = X3)))) = exuEu)), 15.72/2.40 inference(rectify,[],[f75])). 15.72/2.40 thf(f75,axiom,( 15.72/2.40 (! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ! [X1,X2] : ((X0 @ X1) => ((X0 @ X2) => (X1 = X2)))) = exuEu)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuEu)). 15.72/2.40 thf(f787,plain,( 15.72/2.40 (omega__Cong = (omega = omega))), 15.72/2.40 inference(cnf_transformation,[],[f385])). 15.72/2.40 thf(f385,plain,( 15.72/2.40 (omega__Cong = (omega = omega))), 15.72/2.40 inference(fool_elimination,[],[f74])). 15.72/2.40 thf(f74,axiom,( 15.72/2.40 (omega__Cong = (omega = omega))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega__Cong)). 15.72/2.40 thf(f657,plain,( 15.72/2.40 (setunion__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))))), 15.72/2.40 inference(cnf_transformation,[],[f573])). 15.72/2.40 thf(f573,plain,( 15.72/2.40 (setunion__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y1) = (setunion @ Y0))))))))), 15.72/2.40 inference(fool_elimination,[],[f572])). 15.72/2.40 thf(f572,plain,( 15.72/2.40 (! [X0,X1] : ((X0 = X1) => ((setunion @ X0) = (setunion @ X1))) = setunion__Cong)), 15.72/2.40 inference(rectify,[],[f73])). 15.72/2.40 thf(f73,axiom,( 15.72/2.40 (! [X3,X4] : ((X3 = X4) => ((setunion @ X3) = (setunion @ X4))) = setunion__Cong)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunion__Cong)). 15.72/2.40 thf(f771,plain,( 15.72/2.40 (powerset__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))))), 15.72/2.40 inference(cnf_transformation,[],[f355])). 15.72/2.40 thf(f355,plain,( 15.72/2.40 (powerset__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))))), 15.72/2.40 inference(fool_elimination,[],[f354])). 15.72/2.40 thf(f354,plain,( 15.72/2.40 (! [X0,X1] : ((X0 = X1) => ((powerset @ X1) = (powerset @ X0))) = powerset__Cong)), 15.72/2.40 inference(rectify,[],[f72])). 15.72/2.40 thf(f72,axiom,( 15.72/2.40 (! [X3,X4] : ((X3 = X4) => ((powerset @ X3) = (powerset @ X4))) = powerset__Cong)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset__Cong)). 15.72/2.40 thf(f667,plain,( 15.72/2.40 (setadjoin__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f512])). 15.72/2.40 thf(f512,plain,( 15.72/2.40 (setadjoin__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))))), 15.72/2.40 inference(fool_elimination,[],[f511])). 15.72/2.40 thf(f511,plain,( 15.72/2.40 (! [X0,X1] : ((X0 = X1) => ! [X2,X3] : ((X2 = X3) => ((setadjoin @ X1 @ X2) = (setadjoin @ X0 @ X3)))) = setadjoin__Cong)), 15.72/2.40 inference(rectify,[],[f71])). 15.72/2.40 thf(f71,axiom,( 15.72/2.40 (! [X1,X2] : ((X1 = X2) => ! [X10,X8] : ((X8 = X10) => ((setadjoin @ X1 @ X8) = (setadjoin @ X2 @ X10)))) = setadjoin__Cong)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoin__Cong)). 15.72/2.40 thf(f643,plain,( 15.72/2.40 (emptyset__Cong = (emptyset = emptyset))), 15.72/2.40 inference(cnf_transformation,[],[f456])). 15.72/2.40 thf(f456,plain,( 15.72/2.40 (emptyset__Cong = (emptyset = emptyset))), 15.72/2.40 inference(fool_elimination,[],[f70])). 15.72/2.40 thf(f70,axiom,( 15.72/2.40 ((emptyset = emptyset) = emptyset__Cong)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyset__Cong)). 15.72/2.40 thf(f808,plain,( 15.72/2.40 (exu__Cong = (!! @ ($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]: ((!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) => (Y3 = Y4)))) & (Y2 @ Y3))))) @ (^[Y2 : $i]: (Y0 @ Y2))) = ((^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) => (Y3 = Y4)))) & (Y2 @ Y3))))) @ (^[Y2 : $i]: (Y1 @ Y2))))))))))), 15.72/2.40 inference(definition_unfolding,[],[f731,f647,f647])). 15.72/2.40 thf(f731,plain,( 15.72/2.40 (exu__Cong = (!! @ ($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 : $i]: (Y1 @ Y2))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f445])). 15.72/2.40 thf(f445,plain,( 15.72/2.40 (exu__Cong = (!! @ ($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))))))))))), 15.72/2.40 inference(fool_elimination,[],[f444])). 15.72/2.40 thf(f444,plain,( 15.72/2.40 (! [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)), 15.72/2.40 inference(rectify,[],[f69])). 15.72/2.40 thf(f69,axiom,( 15.72/2.40 (! [X0 : $i > $o,X9 : $i > $o] : (! [X2,X1] : ((X1 = X2) => ((X9 @ X2) <=> (X0 @ X1))) => ((exu @ (^[X1 : $i] : (X9 @ X1))) <=> (exu @ (^[X1 : $i] : (X0 @ X1))))) = exu__Cong)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu__Cong)). 15.72/2.40 thf(f807,plain,( 15.72/2.40 (exuE3u = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2))))) @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))))), 15.72/2.40 inference(definition_unfolding,[],[f649,f647])). 15.72/2.40 thf(f649,plain,( 15.72/2.40 (exuE3u = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f569])). 15.72/2.40 thf(f569,plain,( 15.72/2.40 (exuE3u = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))))), 15.72/2.40 inference(fool_elimination,[],[f568])). 15.72/2.40 thf(f568,plain,( 15.72/2.40 (! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ! [X2,X3] : ((X0 @ X2) => ((X0 @ X3) => (X2 = X3)))) = exuE3u)), 15.72/2.40 inference(rectify,[],[f68])). 15.72/2.40 thf(f68,axiom,( 15.72/2.40 (! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ! [X1,X2] : ((X0 @ X1) => ((X0 @ X2) => (X1 = X2)))) = exuE3u)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3u)). 15.72/2.40 thf(f753,plain,( 15.72/2.40 (in__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f488])). 15.72/2.40 thf(f488,plain,( 15.72/2.40 (in__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))))), 15.72/2.40 inference(fool_elimination,[],[f487])). 15.72/2.40 thf(f487,plain,( 15.72/2.40 (in__Cong = ! [X0,X1] : ((X0 = X1) => ! [X2,X3] : ((X2 = X3) => ((in @ X2 @ X1) <=> (in @ X3 @ X0)))))), 15.72/2.40 inference(rectify,[],[f67])). 15.72/2.40 thf(f67,axiom,( 15.72/2.40 (in__Cong = ! [X4,X3] : ((X3 = X4) => ! [X1,X2] : ((X1 = X2) => ((in @ X1 @ X3) <=> (in @ X2 @ X4)))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',in__Cong)). 15.72/2.40 thf(f743,plain,( 15.72/2.40 (inCongP = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1)))))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f575])). 15.72/2.40 thf(f575,plain,( 15.72/2.40 (inCongP = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) => (in @ Y2 @ Y1)))))))))))))), 15.72/2.40 inference(fool_elimination,[],[f574])). 15.72/2.40 thf(f574,plain,( 15.72/2.40 (! [X0,X1] : ((X0 = X1) => ! [X2,X3] : ((X2 = X3) => ((in @ X2 @ X1) => (in @ X3 @ X0)))) = inCongP)), 15.72/2.40 inference(rectify,[],[f66])). 15.72/2.40 thf(f66,axiom,( 15.72/2.40 (! [X4,X3] : ((X3 = X4) => ! [X1,X2] : ((X1 = X2) => ((in @ X1 @ X3) => (in @ X2 @ X4)))) = inCongP)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',inCongP)). 15.72/2.40 thf(f806,plain,( 15.72/2.40 (exuI2 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2))))) @ (^[Y1 : $i]: (Y0 @ Y1)))))))), 15.72/2.40 inference(definition_unfolding,[],[f759,f647])). 15.72/2.40 thf(f759,plain,( 15.72/2.40 (exuI2 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1)))))))), 15.72/2.40 inference(cnf_transformation,[],[f285])). 15.72/2.40 thf(f285,plain,( 15.72/2.40 (exuI2 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1)))))))), 15.72/2.40 inference(fool_elimination,[],[f284])). 15.72/2.40 thf(f284,plain,( 15.72/2.40 (! [X0 : $i > $o] : (? [X1] : ! [X2] : ((X0 @ X2) <=> (X1 = X2)) => (exu @ (^[X3 : $i] : (X0 @ X3)))) = exuI2)), 15.72/2.40 inference(rectify,[],[f65])). 15.72/2.40 thf(f65,axiom,( 15.72/2.40 (! [X0 : $i > $o] : (? [X1] : ! [X2] : ((X0 @ X2) <=> (X1 = X2)) => (exu @ (^[X1 : $i] : (X0 @ X1)))) = exuI2)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI2)). 15.72/2.40 thf(f805,plain,( 15.72/2.40 (exuI3 = (!! @ ($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]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2))))) @ (^[Y1 : $i]: (Y0 @ Y1))))))))), 15.72/2.40 inference(definition_unfolding,[],[f672,f647])). 15.72/2.40 thf(f672,plain,( 15.72/2.40 (exuI3 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1))))))))), 15.72/2.40 inference(cnf_transformation,[],[f362])). 15.72/2.40 thf(f362,plain,( 15.72/2.40 (exuI3 = (!! @ ($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))))))))), 15.72/2.40 inference(fool_elimination,[],[f361])). 15.72/2.40 thf(f361,plain,( 15.72/2.40 (! [X0 : $i > $o] : (? [X1] : (X0 @ X1) => (! [X2,X3] : ((X0 @ X3) => ((X0 @ X2) => (X2 = X3))) => (exu @ (^[X4 : $i] : (X0 @ X4))))) = exuI3)), 15.72/2.40 inference(rectify,[],[f64])). 15.72/2.40 thf(f64,axiom,( 15.72/2.40 (! [X0 : $i > $o] : (? [X1] : (X0 @ X1) => (! [X2,X1] : ((X0 @ X1) => ((X0 @ X2) => (X1 = X2))) => (exu @ (^[X1 : $i] : (X0 @ X1))))) = exuI3)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI3)). 15.72/2.40 thf(f804,plain,( 15.72/2.40 (exuI1 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2))))) @ (^[Y1 : $i]: (Y0 @ Y1)))))))), 15.72/2.40 inference(definition_unfolding,[],[f758,f647])). 15.72/2.40 thf(f758,plain,( 15.72/2.40 (exuI1 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1)))))))), 15.72/2.40 inference(cnf_transformation,[],[f538])). 15.72/2.40 thf(f538,plain,( 15.72/2.40 (exuI1 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1)))))))), 15.72/2.40 inference(fool_elimination,[],[f537])). 15.72/2.40 thf(f537,plain,( 15.72/2.40 (exuI1 = ! [X0 : $i > $o] : (? [X1] : (! [X2] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)) => (exu @ (^[X3 : $i] : (X0 @ X3)))))), 15.72/2.40 inference(rectify,[],[f63])). 15.72/2.40 thf(f63,axiom,( 15.72/2.40 (exuI1 = ! [X0 : $i > $o] : (? [X1] : (! [X2] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)) => (exu @ (^[X1 : $i] : (X0 @ X1)))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI1)). 15.72/2.40 thf(f663,plain,( 15.72/2.40 (notdallE = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f349])). 15.72/2.40 thf(f349,plain,( 15.72/2.40 (notdallE = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))))), 15.72/2.40 inference(fool_elimination,[],[f348])). 15.72/2.40 thf(f348,plain,( 15.72/2.40 (! [X0,X1 : $i > $o] : (~! [X2] : ((in @ X2 @ X0) => (X1 @ X2)) => ? [X3] : (~(X1 @ X3) & (in @ X3 @ X0))) = notdallE)), 15.72/2.40 inference(rectify,[],[f62])). 15.72/2.40 thf(f62,axiom,( 15.72/2.40 (! [X3,X0 : $i > $o] : (~! [X1] : ((in @ X1 @ X3) => (X0 @ X1)) => ? [X1] : (~(X0 @ X1) & (in @ X1 @ X3))) = notdallE)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdallE)). 15.72/2.40 thf(f711,plain,( 15.72/2.40 (notdexE = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f331])). 15.72/2.40 thf(f331,plain,( 15.72/2.40 (notdexE = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))))), 15.72/2.40 inference(fool_elimination,[],[f330])). 15.72/2.40 thf(f330,plain,( 15.72/2.40 (! [X0 : $i > $o,X1] : (~? [X2] : ((in @ X2 @ X1) & (X0 @ X2)) => ! [X3] : ((in @ X3 @ X1) => ~(X0 @ X3))) = notdexE)), 15.72/2.40 inference(rectify,[],[f61])). 15.72/2.40 thf(f61,axiom,( 15.72/2.40 (! [X0 : $i > $o,X3] : (~? [X1] : ((in @ X1 @ X3) & (X0 @ X1)) => ! [X1] : ((in @ X1 @ X3) => ~(X0 @ X1))) = notdexE)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdexE)). 15.72/2.40 thf(f791,plain,( 15.72/2.40 (prop2set2propI = (!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))))), 15.72/2.40 inference(cnf_transformation,[],[f447])). 15.72/2.40 thf(f447,plain,( 15.72/2.40 (prop2set2propI = (!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))))), 15.72/2.40 inference(fool_elimination,[],[f446])). 15.72/2.40 thf(f446,plain,( 15.72/2.40 (prop2set2propI = ! [X0 : $o] : (X0 => (set2prop @ (prop2set @ X0))))), 15.72/2.40 inference(rectify,[],[f60])). 15.72/2.40 thf(f60,axiom,( 15.72/2.40 (prop2set2propI = ! [X0 : $o] : (X0 => (set2prop @ (prop2set @ X0))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2set2propI)). 15.72/2.40 thf(f687,plain,( 15.72/2.40 (prop2setI = (!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))))), 15.72/2.40 inference(cnf_transformation,[],[f360])). 15.72/2.40 thf(f360,plain,( 15.72/2.40 (prop2setI = (!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))))), 15.72/2.40 inference(fool_elimination,[],[f359])). 15.72/2.40 thf(f359,plain,( 15.72/2.40 (prop2setI = ! [X0 : $o] : (X0 => (in @ emptyset @ (prop2set @ X0))))), 15.72/2.40 inference(rectify,[],[f59])). 15.72/2.40 thf(f59,axiom,( 15.72/2.40 (prop2setI = ! [X0 : $o] : (X0 => (in @ emptyset @ (prop2set @ X0))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setI)). 15.72/2.40 thf(f751,plain,( 15.72/2.40 (quantDeMorgan4 = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f532])). 15.72/2.40 thf(f532,plain,( 15.72/2.40 (quantDeMorgan4 = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (~ (Y1 @ Y2))))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))))), 15.72/2.40 inference(fool_elimination,[],[f531])). 15.72/2.40 thf(f531,plain,( 15.72/2.40 (quantDeMorgan4 = ! [X0 : $i > $o,X1] : (? [X2] : (~(X0 @ X2) & (in @ X2 @ X1)) => ~! [X3] : ((in @ X3 @ X1) => (X0 @ X3))))), 15.72/2.40 inference(rectify,[],[f58])). 15.72/2.40 thf(f58,axiom,( 15.72/2.40 (quantDeMorgan4 = ! [X0 : $i > $o,X3] : (? [X1] : (~(X0 @ X1) & (in @ X1 @ X3)) => ~! [X1] : ((in @ X1 @ X3) => (X0 @ X1))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan4)). 15.72/2.40 thf(f631,plain,( 15.72/2.40 (quantDeMorgan3 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f309])). 15.72/2.40 thf(f309,plain,( 15.72/2.40 (quantDeMorgan3 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))))), 15.72/2.40 inference(fool_elimination,[],[f308])). 15.72/2.40 thf(f308,plain,( 15.72/2.40 (quantDeMorgan3 = ! [X0,X1 : $i > $o] : (~? [X2] : ((X1 @ X2) & (in @ X2 @ X0)) => ! [X3] : ((in @ X3 @ X0) => ~(X1 @ X3))))), 15.72/2.40 inference(rectify,[],[f57])). 15.72/2.40 thf(f57,axiom,( 15.72/2.40 (quantDeMorgan3 = ! [X3,X0 : $i > $o] : (~? [X1] : ((X0 @ X1) & (in @ X1 @ X3)) => ! [X1] : ((in @ X1 @ X3) => ~(X0 @ X1))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan3)). 15.72/2.40 thf(f736,plain,( 15.72/2.40 (quantDeMorgan2 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f433])). 15.72/2.40 thf(f433,plain,( 15.72/2.40 (quantDeMorgan2 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))))))))))), 15.72/2.40 inference(fool_elimination,[],[f432])). 15.72/2.40 thf(f432,plain,( 15.72/2.40 (! [X0,X1 : $i > $o] : (! [X2] : ((in @ X2 @ X0) => ~(X1 @ X2)) => ~? [X3] : ((X1 @ X3) & (in @ X3 @ X0))) = quantDeMorgan2)), 15.72/2.40 inference(rectify,[],[f56])). 15.72/2.40 thf(f56,axiom,( 15.72/2.40 (! [X3,X0 : $i > $o] : (! [X1] : ((in @ X1 @ X3) => ~(X0 @ X1)) => ~? [X1] : ((X0 @ X1) & (in @ X1 @ X3))) = quantDeMorgan2)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan2)). 15.72/2.40 thf(f780,plain,( 15.72/2.40 (quantDeMorgan1 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f528])). 15.72/2.40 thf(f528,plain,( 15.72/2.40 (quantDeMorgan1 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))))), 15.72/2.40 inference(fool_elimination,[],[f527])). 15.72/2.40 thf(f527,plain,( 15.72/2.40 (quantDeMorgan1 = ! [X0,X1 : $i > $o] : (~! [X2] : ((in @ X2 @ X0) => (X1 @ X2)) => ? [X3] : (~(X1 @ X3) & (in @ X3 @ X0))))), 15.72/2.40 inference(rectify,[],[f55])). 15.72/2.40 thf(f55,axiom,( 15.72/2.40 (quantDeMorgan1 = ! [X3,X0 : $i > $o] : (~! [X1] : ((in @ X1 @ X3) => (X0 @ X1)) => ? [X1] : (~(X0 @ X1) & (in @ X1 @ X3))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan1)). 15.72/2.40 thf(f735,plain,( 15.72/2.40 (vacuousDall = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))))), 15.72/2.40 inference(cnf_transformation,[],[f283])). 15.72/2.40 thf(f283,plain,( 15.72/2.40 (vacuousDall = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ emptyset) => (Y0 @ Y1)))))))), 15.72/2.40 inference(fool_elimination,[],[f282])). 15.72/2.40 thf(f282,plain,( 15.72/2.40 (! [X0,X1 : $i > $o] : ((in @ X0 @ emptyset) => (X1 @ X0)) = vacuousDall)), 15.72/2.40 inference(rectify,[],[f54])). 15.72/2.40 thf(f54,axiom,( 15.72/2.40 (! [X1,X0 : $i > $o] : ((in @ X1 @ emptyset) => (X0 @ X1)) = vacuousDall)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall)). 15.72/2.40 thf(f621,plain,( 15.72/2.40 (emptyE1 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => ((emptyset = (dsetconstr @ Y1 @ (^[Y2 : $i]: (Y0 @ Y2)))) => $false)))))))), 15.72/2.40 inference(cnf_transformation,[],[f368])). 15.72/2.40 thf(f368,plain,( 15.72/2.40 (emptyE1 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => ((emptyset = (dsetconstr @ Y1 @ (^[Y2 : $i]: (Y0 @ Y2)))) => $false)))))))), 15.72/2.40 inference(fool_elimination,[],[f367])). 15.72/2.40 thf(f367,plain,( 15.72/2.40 (! [X0,X1 : $i > $o] : (? [X2] : ((X1 @ X2) & (in @ X2 @ X0)) => ((emptyset = (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => $false)) = emptyE1)), 15.72/2.40 inference(rectify,[],[f53])). 15.72/2.40 thf(f53,axiom,( 15.72/2.40 (! [X3,X0 : $i > $o] : (? [X1] : ((X0 @ X1) & (in @ X1 @ X3)) => ((emptyset = (dsetconstr @ X3 @ (^[X1 : $i] : (X0 @ X1)))) => $false)) = emptyE1)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyE1)). 15.72/2.40 thf(f733,plain,( 15.72/2.40 (upairsetIR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))), 15.72/2.40 inference(cnf_transformation,[],[f443])). 15.72/2.40 thf(f443,plain,( 15.72/2.40 (upairsetIR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))), 15.72/2.40 inference(fool_elimination,[],[f442])). 15.72/2.40 thf(f442,plain,( 15.72/2.40 (upairsetIR = ! [X0,X1] : (in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))))), 15.72/2.40 inference(rectify,[],[f52])). 15.72/2.40 thf(f52,axiom,( 15.72/2.40 (upairsetIR = ! [X1,X2] : (in @ X2 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIR)). 15.72/2.40 thf(f674,plain,( 15.72/2.40 (upairsetIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))), 15.72/2.40 inference(cnf_transformation,[],[f269])). 15.72/2.40 thf(f269,plain,( 15.72/2.40 (upairsetIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))), 15.72/2.40 inference(fool_elimination,[],[f268])). 15.72/2.40 thf(f268,plain,( 15.72/2.40 (upairsetIL = ! [X0,X1] : (in @ X0 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))))), 15.72/2.40 inference(rectify,[],[f51])). 15.72/2.40 thf(f51,axiom,( 15.72/2.40 (upairsetIL = ! [X1,X2] : (in @ X1 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIL)). 15.72/2.40 thf(f612,plain,( 15.72/2.40 (upairsetE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f273])). 15.72/2.40 thf(f273,plain,( 15.72/2.40 (upairsetE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y1))))))))))), 15.72/2.40 inference(fool_elimination,[],[f272])). 15.72/2.40 thf(f272,plain,( 15.72/2.40 (! [X0,X1,X2] : ((in @ X1 @ (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset))) => ((X0 = X1) | (X1 = X2))) = upairsetE)), 15.72/2.40 inference(rectify,[],[f50])). 15.72/2.40 thf(f50,axiom,( 15.72/2.40 (! [X2,X8,X1] : ((in @ X8 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset))) => ((X2 = X8) | (X1 = X8))) = upairsetE)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetE)). 15.72/2.40 thf(f790,plain,( 15.72/2.40 (singletonsswitch = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))), 15.72/2.40 inference(cnf_transformation,[],[f325])). 15.72/2.40 thf(f325,plain,( 15.72/2.40 (singletonsswitch = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))), 15.72/2.40 inference(fool_elimination,[],[f324])). 15.72/2.40 thf(f324,plain,( 15.72/2.40 (singletonsswitch = ! [X0,X1] : ((in @ X1 @ (setadjoin @ X0 @ emptyset)) => (in @ X0 @ (setadjoin @ X1 @ emptyset))))), 15.72/2.40 inference(rectify,[],[f49])). 15.72/2.40 thf(f49,axiom,( 15.72/2.40 (singletonsswitch = ! [X2,X1] : ((in @ X1 @ (setadjoin @ X2 @ emptyset)) => (in @ X2 @ (setadjoin @ X1 @ emptyset))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsswitch)). 15.72/2.40 thf(f660,plain,( 15.72/2.40 (eqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))), 15.72/2.40 inference(cnf_transformation,[],[f291])). 15.72/2.40 thf(f291,plain,( 15.72/2.40 (eqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))), 15.72/2.40 inference(fool_elimination,[],[f290])). 15.72/2.40 thf(f290,plain,( 15.72/2.40 (! [X0,X1] : ((X0 = X1) => (in @ X0 @ (setadjoin @ X1 @ emptyset))) = eqinunit)), 15.72/2.40 inference(rectify,[],[f48])). 15.72/2.40 thf(f48,axiom,( 15.72/2.40 (! [X1,X2] : ((X1 = X2) => (in @ X1 @ (setadjoin @ X2 @ emptyset))) = eqinunit)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit)). 15.72/2.40 thf(f673,plain,( 15.72/2.40 (notinsingleton = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))))), 15.72/2.40 inference(cnf_transformation,[],[f233])). 15.72/2.40 thf(f233,plain,( 15.72/2.40 (notinsingleton = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))))), 15.72/2.40 inference(fool_elimination,[],[f232])). 15.72/2.40 thf(f232,plain,( 15.72/2.40 (notinsingleton = ! [X0,X1] : ((X0 != X1) => ~(in @ X1 @ (setadjoin @ X0 @ emptyset))))), 15.72/2.40 inference(rectify,[],[f47])). 15.72/2.40 thf(f47,axiom,( 15.72/2.40 (notinsingleton = ! [X1,X2] : ((X1 != X2) => ~(in @ X2 @ (setadjoin @ X1 @ emptyset))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinsingleton)). 15.72/2.40 thf(f785,plain,( 15.72/2.40 (uniqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))))), 15.72/2.40 inference(cnf_transformation,[],[f311])). 15.72/2.40 thf(f311,plain,( 15.72/2.40 (uniqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))))), 15.72/2.40 inference(fool_elimination,[],[f310])). 15.72/2.40 thf(f310,plain,( 15.72/2.40 (uniqinunit = ! [X0,X1] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)))), 15.72/2.40 inference(rectify,[],[f46])). 15.72/2.40 thf(f46,axiom,( 15.72/2.40 (uniqinunit = ! [X1,X2] : ((in @ X1 @ (setadjoin @ X2 @ emptyset)) => (X1 = X2)))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit)). 15.72/2.40 thf(f803,plain,( 15.72/2.40 (nonemptyImpWitness = (!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (~ (emptyset = Y1))) @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))))), 15.72/2.40 inference(definition_unfolding,[],[f628,f606])). 15.72/2.40 thf(f606,plain,( 15.72/2.40 (nonempty = (^[Y0 : $i]: (~ (emptyset = Y0))))), 15.72/2.40 inference(cnf_transformation,[],[f399])). 15.72/2.40 thf(f399,plain,( 15.72/2.40 (nonempty = (^[Y0 : $i]: (~ (emptyset = Y0))))), 15.72/2.40 inference(fool_elimination,[],[f398])). 15.72/2.40 thf(f398,plain,( 15.72/2.40 ((^[X0 : $i] : ((emptyset != X0))) = nonempty)), 15.72/2.40 inference(rectify,[],[f27])). 15.72/2.40 thf(f27,axiom,( 15.72/2.40 ((^[X1 : $i] : ((emptyset != X1))) = nonempty)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty)). 15.72/2.40 thf(f628,plain,( 15.72/2.40 (nonemptyImpWitness = (!! @ $i @ (^[Y0 : $i]: ((nonempty @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))))), 15.72/2.40 inference(cnf_transformation,[],[f295])). 15.72/2.40 thf(f295,plain,( 15.72/2.40 (nonemptyImpWitness = (!! @ $i @ (^[Y0 : $i]: ((nonempty @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))))), 15.72/2.40 inference(fool_elimination,[],[f294])). 15.72/2.40 thf(f294,plain,( 15.72/2.40 (! [X0] : ((nonempty @ X0) => ? [X1] : ($true & (in @ X1 @ X0))) = nonemptyImpWitness)), 15.72/2.40 inference(rectify,[],[f45])). 15.72/2.40 thf(f45,axiom,( 15.72/2.40 (! [X3] : ((nonempty @ X3) => ? [X1] : ($true & (in @ X1 @ X3))) = nonemptyImpWitness)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyImpWitness)). 15.72/2.40 thf(f802,plain,( 15.72/2.40 (exuE2 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2))))) @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))))), 15.72/2.40 inference(definition_unfolding,[],[f761,f647])). 15.72/2.40 thf(f761,plain,( 15.72/2.40 (exuE2 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f275])). 15.72/2.40 thf(f275,plain,( 15.72/2.40 (exuE2 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2))))))))))), 15.72/2.40 inference(fool_elimination,[],[f274])). 15.72/2.40 thf(f274,plain,( 15.72/2.40 (exuE2 = ! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ? [X2] : ! [X3] : ((X0 @ X3) <=> (X2 = X3))))), 15.72/2.40 inference(rectify,[],[f44])). 15.72/2.40 thf(f44,axiom,( 15.72/2.40 (exuE2 = ! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ? [X1] : ! [X2] : ((X0 @ X2) <=> (X1 = X2))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE2)). 15.72/2.40 thf(f633,plain,( 15.72/2.40 (subPowSU = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))))), 15.72/2.40 inference(cnf_transformation,[],[f364])). 15.72/2.40 thf(f364,plain,( 15.72/2.40 (subPowSU = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (powerset @ (setunion @ Y1)))))))))), 15.72/2.40 inference(fool_elimination,[],[f363])). 15.72/2.40 thf(f363,plain,( 15.72/2.40 (subPowSU = ! [X0,X1] : ((in @ X1 @ X0) => (in @ X1 @ (powerset @ (setunion @ X0)))))), 15.72/2.40 inference(rectify,[],[f43])). 15.72/2.40 thf(f43,axiom,( 15.72/2.40 (subPowSU = ! [X3,X1] : ((in @ X1 @ X3) => (in @ X1 @ (powerset @ (setunion @ X3)))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subPowSU)). 15.72/2.40 thf(f723,plain,( 15.72/2.40 (setunionE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))))), 15.72/2.40 inference(cnf_transformation,[],[f500])). 15.72/2.40 thf(f500,plain,( 15.72/2.40 (setunionE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))))), 15.72/2.40 inference(fool_elimination,[],[f499])). 15.72/2.40 thf(f499,plain,( 15.72/2.40 (setunionE = ! [X0,X1] : ((in @ X1 @ (setunion @ X0)) => ! [X2 : $o] : (! [X3] : ((in @ X1 @ X3) => ((in @ X3 @ X0) => X2)) => X2)))), 15.72/2.40 inference(rectify,[],[f42])). 15.72/2.40 thf(f42,axiom,( 15.72/2.40 (setunionE = ! [X3,X1] : ((in @ X1 @ (setunion @ X3)) => ! [X0 : $o] : (! [X4] : ((in @ X1 @ X4) => ((in @ X4 @ X3) => X0)) => X0)))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE)). 15.72/2.40 thf(f622,plain,( 15.72/2.40 (setunionI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f279])). 15.72/2.40 thf(f279,plain,( 15.72/2.40 (setunionI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((in @ Y1 @ Y0) => (in @ Y2 @ (setunion @ Y0)))))))))))), 15.72/2.40 inference(fool_elimination,[],[f278])). 15.72/2.40 thf(f278,plain,( 15.72/2.40 (setunionI = ! [X0,X1,X2] : ((in @ X0 @ X1) => ((in @ X1 @ X2) => (in @ X0 @ (setunion @ X2)))))), 15.72/2.40 inference(rectify,[],[f41])). 15.72/2.40 thf(f41,axiom,( 15.72/2.40 (setunionI = ! [X1,X4,X3] : ((in @ X1 @ X4) => ((in @ X4 @ X3) => (in @ X1 @ (setunion @ X3)))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionI)). 15.72/2.40 thf(f630,plain,( 15.72/2.40 (powersetE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f482])). 15.72/2.40 thf(f482,plain,( 15.72/2.40 (powersetE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))))), 15.72/2.40 inference(fool_elimination,[],[f481])). 15.72/2.40 thf(f481,plain,( 15.72/2.40 (! [X0,X1,X2] : ((in @ X0 @ (powerset @ X1)) => ((in @ X2 @ X0) => (in @ X2 @ X1))) = powersetE)), 15.72/2.40 inference(rectify,[],[f40])). 15.72/2.40 thf(f40,axiom,( 15.72/2.40 (! [X4,X3,X1] : ((in @ X4 @ (powerset @ X3)) => ((in @ X1 @ X4) => (in @ X1 @ X3))) = powersetE)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE)). 15.72/2.40 thf(f627,plain,( 15.72/2.40 (emptyInPowerset = (!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))))), 15.72/2.40 inference(cnf_transformation,[],[f205])). 15.72/2.40 thf(f205,plain,( 15.72/2.40 (emptyInPowerset = (!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))))), 15.72/2.40 inference(fool_elimination,[],[f204])). 15.72/2.40 thf(f204,plain,( 15.72/2.40 (emptyInPowerset = ! [X0] : (in @ emptyset @ (powerset @ X0)))), 15.72/2.40 inference(rectify,[],[f39])). 15.72/2.40 thf(f39,axiom,( 15.72/2.40 (emptyInPowerset = ! [X3] : (in @ emptyset @ (powerset @ X3)))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyInPowerset)). 15.72/2.40 thf(f793,plain,( 15.72/2.40 (emptyinPowerset = (!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))))), 15.72/2.40 inference(cnf_transformation,[],[f323])). 15.72/2.40 thf(f323,plain,( 15.72/2.40 (emptyinPowerset = (!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))))), 15.72/2.40 inference(fool_elimination,[],[f322])). 15.72/2.40 thf(f322,plain,( 15.72/2.40 (emptyinPowerset = ! [X0] : (in @ emptyset @ (powerset @ X0)))), 15.72/2.40 inference(rectify,[],[f38])). 15.72/2.40 thf(f38,axiom,( 15.72/2.40 (emptyinPowerset = ! [X3] : (in @ emptyset @ (powerset @ X3)))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinPowerset)). 15.72/2.40 thf(f792,plain,( 15.72/2.40 (powersetI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))))), 15.72/2.40 inference(cnf_transformation,[],[f566])). 15.72/2.40 thf(f566,plain,( 15.72/2.40 (powersetI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (in @ Y1 @ (powerset @ Y0))))))))), 15.72/2.40 inference(fool_elimination,[],[f565])). 15.72/2.40 thf(f565,plain,( 15.72/2.40 (powersetI = ! [X0,X1] : (! [X2] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (in @ X0 @ (powerset @ X1))))), 15.72/2.40 inference(rectify,[],[f37])). 15.72/2.40 thf(f37,axiom,( 15.72/2.40 (powersetI = ! [X4,X3] : (! [X1] : ((in @ X1 @ X4) => (in @ X1 @ X3)) => (in @ X4 @ (powerset @ X3))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI)). 15.72/2.40 thf(f596,plain,( 15.72/2.40 (setoftrueEq = (!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))))), 15.72/2.40 inference(cnf_transformation,[],[f372])). 15.72/2.40 thf(f372,plain,( 15.72/2.40 (setoftrueEq = (!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))))), 15.72/2.40 inference(fool_elimination,[],[f371])). 15.72/2.40 thf(f371,plain,( 15.72/2.40 (setoftrueEq = ! [X0] : (X0 = (dsetconstr @ X0 @ (^[X1 : $i] : ($true)))))), 15.72/2.40 inference(rectify,[],[f36])). 15.72/2.40 thf(f36,axiom,( 15.72/2.40 (setoftrueEq = ! [X3] : (X3 = (dsetconstr @ X3 @ (^[X1 : $i] : ($true)))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setoftrueEq)). 15.72/2.40 thf(f617,plain,( 15.72/2.40 (setadjoinOr = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f209])). 15.72/2.40 thf(f209,plain,( 15.72/2.40 (setadjoinOr = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ Y1)) => ((in @ Y0 @ Y1) | (Y2 = Y0))))))))))), 15.72/2.40 inference(fool_elimination,[],[f208])). 15.72/2.40 thf(f208,plain,( 15.72/2.40 (! [X0,X1,X2] : ((in @ X2 @ (setadjoin @ X0 @ X1)) => ((X0 = X2) | (in @ X2 @ X1))) = setadjoinOr)), 15.72/2.40 inference(rectify,[],[f35])). 15.72/2.40 thf(f35,axiom,( 15.72/2.40 (! [X1,X3,X2] : ((in @ X2 @ (setadjoin @ X1 @ X3)) => ((X1 = X2) | (in @ X2 @ X3))) = setadjoinOr)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinOr)). 15.72/2.40 thf(f703,plain,( 15.72/2.40 (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))))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f542])). 15.72/2.40 thf(f542,plain,( 15.72/2.40 (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))))))))))))), 15.72/2.40 inference(fool_elimination,[],[f541])). 15.72/2.40 thf(f541,plain,( 15.72/2.40 (setadjoinE = ! [X0,X1,X2] : ((in @ X2 @ (setadjoin @ X1 @ X0)) => ! [X3 : $o] : (((X1 = X2) => X3) => (((in @ X2 @ X0) => X3) => X3))))), 15.72/2.40 inference(rectify,[],[f34])). 15.72/2.40 thf(f34,axiom,( 15.72/2.40 (setadjoinE = ! [X3,X1,X2] : ((in @ X2 @ (setadjoin @ X1 @ X3)) => ! [X0 : $o] : (((X1 = X2) => X0) => (((in @ X2 @ X3) => X0) => X0))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinE)). 15.72/2.40 thf(f692,plain,( 15.72/2.40 (setadjoinIR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f520])). 15.72/2.40 thf(f520,plain,( 15.72/2.40 (setadjoinIR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (setadjoin @ Y1 @ Y2))))))))))), 15.72/2.40 inference(fool_elimination,[],[f519])). 15.72/2.40 thf(f519,plain,( 15.72/2.40 (setadjoinIR = ! [X0,X1,X2] : ((in @ X2 @ X0) => (in @ X2 @ (setadjoin @ X1 @ X0))))), 15.72/2.40 inference(rectify,[],[f33])). 15.72/2.40 thf(f33,axiom,( 15.72/2.40 (setadjoinIR = ! [X3,X1,X2] : ((in @ X2 @ X3) => (in @ X2 @ (setadjoin @ X1 @ X3))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIR)). 15.72/2.40 thf(f636,plain,( 15.72/2.40 (emptyinunitempty = (in @ emptyset @ (setadjoin @ emptyset @ emptyset)))), 15.72/2.40 inference(cnf_transformation,[],[f567])). 15.72/2.40 thf(f567,plain,( 15.72/2.40 (emptyinunitempty = (in @ emptyset @ (setadjoin @ emptyset @ emptyset)))), 15.72/2.40 inference(fool_elimination,[],[f32])). 15.72/2.40 thf(f32,axiom,( 15.72/2.40 (emptyinunitempty = (in @ emptyset @ (setadjoin @ emptyset @ emptyset)))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinunitempty)). 15.72/2.40 thf(f775,plain,( 15.72/2.40 (setadjoinIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))))), 15.72/2.40 inference(cnf_transformation,[],[f589])). 15.72/2.40 thf(f589,plain,( 15.72/2.40 (setadjoinIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y0 @ Y1)))))))), 15.72/2.40 inference(fool_elimination,[],[f588])). 15.72/2.40 thf(f588,plain,( 15.72/2.40 (setadjoinIL = ! [X0,X1] : (in @ X1 @ (setadjoin @ X1 @ X0)))), 15.72/2.40 inference(rectify,[],[f31])). 15.72/2.40 thf(f31,axiom,( 15.72/2.40 (setadjoinIL = ! [X2,X1] : (in @ X1 @ (setadjoin @ X1 @ X2)))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL)). 15.72/2.40 thf(f801,plain,( 15.72/2.40 (nonemptyI1 = (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => ((^[Y1 : $i]: (~ (emptyset = Y1))) @ Y0)))))), 15.72/2.40 inference(definition_unfolding,[],[f604,f606])). 15.72/2.40 thf(f604,plain,( 15.72/2.40 (nonemptyI1 = (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (nonempty @ Y0)))))), 15.72/2.40 inference(cnf_transformation,[],[f530])). 15.72/2.40 thf(f530,plain,( 15.72/2.40 (nonemptyI1 = (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (nonempty @ Y0)))))), 15.72/2.40 inference(fool_elimination,[],[f529])). 15.72/2.40 thf(f529,plain,( 15.72/2.40 (! [X0] : (? [X1] : (in @ X1 @ X0) => (nonempty @ X0)) = nonemptyI1)), 15.72/2.40 inference(rectify,[],[f30])). 15.72/2.40 thf(f30,axiom,( 15.72/2.40 (! [X3] : (? [X1] : (in @ X1 @ X3) => (nonempty @ X3)) = nonemptyI1)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI1)). 15.72/2.40 thf(f800,plain,( 15.72/2.40 (nonemptyI = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => ((^[Y3 : $i]: (~ (emptyset = Y3))) @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))), 15.72/2.40 inference(definition_unfolding,[],[f614,f606])). 15.72/2.40 thf(f614,plain,( 15.72/2.40 (nonemptyI = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (nonempty @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f251])). 15.72/2.40 thf(f251,plain,( 15.72/2.40 (nonemptyI = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (nonempty @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))), 15.72/2.40 inference(fool_elimination,[],[f250])). 15.72/2.40 thf(f250,plain,( 15.72/2.40 (nonemptyI = ! [X0,X1,X2 : $i > $o] : ((in @ X0 @ X1) => ((X2 @ X0) => (nonempty @ (dsetconstr @ X1 @ (^[X3 : $i] : (X2 @ X3)))))))), 15.72/2.40 inference(rectify,[],[f29])). 15.72/2.40 thf(f29,axiom,( 15.72/2.40 (nonemptyI = ! [X1,X3,X0 : $i > $o] : ((in @ X1 @ X3) => ((X0 @ X1) => (nonempty @ (dsetconstr @ X3 @ (^[X2 : $i] : (X0 @ X2)))))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI)). 15.72/2.40 thf(f799,plain,( 15.72/2.40 (nonemptyE1 = (!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (~ (emptyset = Y1))) @ Y0) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))))), 15.72/2.40 inference(definition_unfolding,[],[f666,f606])). 15.72/2.40 thf(f666,plain,( 15.72/2.40 (nonemptyE1 = (!! @ $i @ (^[Y0 : $i]: ((nonempty @ Y0) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))))), 15.72/2.40 inference(cnf_transformation,[],[f506])). 15.72/2.40 thf(f506,plain,( 15.72/2.40 (nonemptyE1 = (!! @ $i @ (^[Y0 : $i]: ((nonempty @ Y0) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))))), 15.72/2.40 inference(fool_elimination,[],[f505])). 15.72/2.40 thf(f505,plain,( 15.72/2.40 (! [X0] : ((nonempty @ X0) => ? [X1] : (in @ X1 @ X0)) = nonemptyE1)), 15.72/2.40 inference(rectify,[],[f28])). 15.72/2.40 thf(f28,axiom,( 15.72/2.40 (! [X3] : ((nonempty @ X3) => ? [X1] : (in @ X1 @ X3)) = nonemptyE1)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1)). 15.72/2.40 thf(f752,plain,( 15.72/2.40 (setbeta = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f353])). 15.72/2.40 thf(f353,plain,( 15.72/2.40 (setbeta = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) = (in @ Y2 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))), 15.72/2.40 inference(fool_elimination,[],[f352])). 15.72/2.40 thf(f352,plain,( 15.72/2.40 (setbeta = ! [X0,X1,X2 : $i > $o] : ((in @ X0 @ X1) => ((X2 @ X0) <=> (in @ X0 @ (dsetconstr @ X1 @ (^[X3 : $i] : (X2 @ X3)))))))), 15.72/2.40 inference(rectify,[],[f26])). 15.72/2.40 thf(f26,axiom,( 15.72/2.40 (setbeta = ! [X1,X3,X0 : $i > $o] : ((in @ X1 @ X3) => ((X0 @ X1) <=> (in @ X1 @ (dsetconstr @ X3 @ (^[X2 : $i] : (X0 @ X2)))))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setbeta)). 15.72/2.40 thf(f690,plain,( 15.72/2.40 (noeltsimpempty = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))))), 15.72/2.40 inference(cnf_transformation,[],[f548])). 15.72/2.40 thf(f548,plain,( 15.72/2.40 (noeltsimpempty = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))))), 15.72/2.40 inference(fool_elimination,[],[f547])). 15.72/2.40 thf(f547,plain,( 15.72/2.40 (! [X0] : (! [X1] : ~(in @ X1 @ X0) => (emptyset = X0)) = noeltsimpempty)), 15.72/2.40 inference(rectify,[],[f25])). 15.72/2.40 thf(f25,axiom,( 15.72/2.40 (! [X3] : (! [X1] : ~(in @ X1 @ X3) => (emptyset = X3)) = noeltsimpempty)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty)). 15.72/2.40 thf(f728,plain,( 15.72/2.40 (emptyI = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))))), 15.72/2.40 inference(cnf_transformation,[],[f526])). 15.72/2.40 thf(f526,plain,( 15.72/2.40 (emptyI = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))))), 15.72/2.40 inference(fool_elimination,[],[f525])). 15.72/2.40 thf(f525,plain,( 15.72/2.40 (emptyI = ! [X0] : (! [X1] : ~(in @ X1 @ X0) => (emptyset = X0)))), 15.72/2.40 inference(rectify,[],[f24])). 15.72/2.40 thf(f24,axiom,( 15.72/2.40 (emptyI = ! [X3] : (! [X1] : ~(in @ X1 @ X3) => (emptyset = X3)))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyI)). 15.72/2.40 thf(f695,plain,( 15.72/2.40 (setext = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))))), 15.72/2.40 inference(cnf_transformation,[],[f215])). 15.72/2.40 thf(f215,plain,( 15.72/2.40 (setext = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (Y1 = Y0))))))))), 15.72/2.40 inference(fool_elimination,[],[f214])). 15.72/2.40 thf(f214,plain,( 15.72/2.40 (! [X0,X1] : (! [X2] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (! [X3] : ((in @ X3 @ X1) => (in @ X3 @ X0)) => (X0 = X1))) = setext)), 15.72/2.40 inference(rectify,[],[f23])). 15.72/2.40 thf(f23,axiom,( 15.72/2.40 (! [X3,X4] : (! [X1] : ((in @ X1 @ X3) => (in @ X1 @ X4)) => (! [X1] : ((in @ X1 @ X4) => (in @ X1 @ X3)) => (X3 = X4))) = setext)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setext)). 15.72/2.40 thf(f798,plain,( 15.72/2.40 (exuE3e = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2))))) @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))), 15.72/2.40 inference(definition_unfolding,[],[f704,f647])). 15.72/2.40 thf(f704,plain,( 15.72/2.40 (exuE3e = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))), 15.72/2.40 inference(cnf_transformation,[],[f466])). 15.72/2.40 thf(f466,plain,( 15.72/2.40 (exuE3e = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))), 15.72/2.40 inference(fool_elimination,[],[f465])). 15.72/2.40 thf(f465,plain,( 15.72/2.40 (! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ? [X2] : (X0 @ X2)) = exuE3e)), 15.72/2.40 inference(rectify,[],[f22])). 15.72/2.40 thf(f22,axiom,( 15.72/2.40 (! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ? [X1] : (X0 @ X1)) = exuE3e)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3e)). 15.72/2.40 thf(f688,plain,( 15.72/2.40 (notinemptyset = (!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))))), 15.72/2.40 inference(cnf_transformation,[],[f449])). 15.72/2.40 thf(f449,plain,( 15.72/2.40 (notinemptyset = (!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))))), 15.72/2.40 inference(fool_elimination,[],[f448])). 15.72/2.40 thf(f448,plain,( 15.72/2.40 (! [X0] : ~(in @ X0 @ emptyset) = notinemptyset)), 15.72/2.40 inference(rectify,[],[f21])). 15.72/2.40 thf(f21,axiom,( 15.72/2.40 (! [X1] : ~(in @ X1 @ emptyset) = notinemptyset)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinemptyset)). 15.72/2.40 thf(f778,plain,( 15.72/2.40 (emptysetimpfalse = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))))), 15.72/2.40 inference(cnf_transformation,[],[f460])). 15.72/2.40 thf(f460,plain,( 15.72/2.40 (emptysetimpfalse = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))))), 15.72/2.40 inference(fool_elimination,[],[f459])). 15.72/2.40 thf(f459,plain,( 15.72/2.40 (emptysetimpfalse = ! [X0] : ((in @ X0 @ emptyset) => $false))), 15.72/2.40 inference(rectify,[],[f20])). 15.72/2.40 thf(f20,axiom,( 15.72/2.40 (emptysetimpfalse = ! [X1] : ((in @ X1 @ emptyset) => $false))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse)). 15.72/2.40 thf(f709,plain,( 15.72/2.40 (emptysetE = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))))), 15.72/2.40 inference(cnf_transformation,[],[f219])). 15.72/2.40 thf(f219,plain,( 15.72/2.40 (emptysetE = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))))), 15.72/2.40 inference(fool_elimination,[],[f218])). 15.72/2.40 thf(f218,plain,( 15.72/2.40 (! [X0] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1) = emptysetE)), 15.72/2.40 inference(rectify,[],[f19])). 15.72/2.40 thf(f19,axiom,( 15.72/2.40 (! [X1] : ((in @ X1 @ emptyset) => ! [X0 : $o] : X0) = emptysetE)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE)). 15.72/2.40 thf(f721,plain,( 15.72/2.40 (prop2setE = (!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))))), 15.72/2.40 inference(cnf_transformation,[],[f213])). 15.72/2.40 thf(f213,plain,( 15.72/2.40 (prop2setE = (!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))))), 15.72/2.40 inference(fool_elimination,[],[f212])). 15.72/2.40 thf(f212,plain,( 15.72/2.40 (prop2setE = ! [X0 : $o,X1] : ((in @ X1 @ (prop2set @ X0)) => X0))), 15.72/2.40 inference(rectify,[],[f18])). 15.72/2.40 thf(f18,axiom,( 15.72/2.40 (prop2setE = ! [X0 : $o,X1] : ((in @ X1 @ (prop2set @ X0)) => X0))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setE)). 15.72/2.40 thf(f797,plain,( 15.72/2.40 (exuE1 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2))))) @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))))), 15.72/2.40 inference(definition_unfolding,[],[f740,f647])). 15.72/2.40 thf(f740,plain,( 15.72/2.40 (exuE1 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))))), 15.72/2.40 inference(cnf_transformation,[],[f241])). 15.72/2.40 thf(f241,plain,( 15.72/2.40 (exuE1 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))))), 15.72/2.40 inference(fool_elimination,[],[f240])). 15.72/2.40 thf(f240,plain,( 15.72/2.40 (! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ? [X2] : ((X0 @ X2) & ! [X3] : ((X0 @ X3) => (X2 = X3)))) = exuE1)), 15.72/2.40 inference(rectify,[],[f17])). 15.72/2.40 thf(f17,axiom,( 15.72/2.40 (! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ? [X1] : ((X0 @ X1) & ! [X2] : ((X0 @ X2) => (X1 = X2)))) = exuE1)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE1)). 15.72/2.40 thf(f786,plain,( 15.72/2.40 (dsetconstrER = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))) => (Y0 @ Y2)))))))))), 15.72/2.40 inference(cnf_transformation,[],[f464])). 15.72/2.40 thf(f464,plain,( 15.72/2.40 (dsetconstrER = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))) => (Y0 @ Y2)))))))))), 15.72/2.40 inference(fool_elimination,[],[f463])). 15.72/2.40 thf(f463,plain,( 15.72/2.40 (dsetconstrER = ! [X0,X1,X2 : $i > $o] : ((in @ X0 @ (dsetconstr @ X1 @ (^[X3 : $i] : (X2 @ X3)))) => (X2 @ X0)))), 15.72/2.40 inference(rectify,[],[f16])). 15.72/2.40 thf(f16,axiom,( 15.72/2.40 (dsetconstrER = ! [X1,X3,X0 : $i > $o] : ((in @ X1 @ (dsetconstr @ X3 @ (^[X2 : $i] : (X0 @ X2)))) => (X0 @ X1)))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER)). 15.72/2.40 thf(f598,plain,( 15.72/2.40 (dsetconstrEL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (in @ Y1 @ Y0)))))))))), 15.72/2.40 inference(cnf_transformation,[],[f441])). 15.72/2.40 thf(f441,plain,( 15.72/2.40 (dsetconstrEL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (in @ Y1 @ Y0)))))))))), 15.72/2.40 inference(fool_elimination,[],[f440])). 15.72/2.40 thf(f440,plain,( 15.72/2.40 (dsetconstrEL = ! [X0 : $i > $o,X1,X2] : ((in @ X1 @ (dsetconstr @ X2 @ (^[X3 : $i] : (X0 @ X3)))) => (in @ X1 @ X2)))), 15.72/2.40 inference(rectify,[],[f15])). 15.72/2.40 thf(f15,axiom,( 15.72/2.40 (dsetconstrEL = ! [X0 : $i > $o,X1,X3] : ((in @ X1 @ (dsetconstr @ X3 @ (^[X2 : $i] : (X0 @ X2)))) => (in @ X1 @ X3)))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL)). 15.72/2.40 thf(f600,plain,( 15.72/2.40 (dsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3)))))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f409])). 15.72/2.40 thf(f409,plain,( 15.72/2.40 (dsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3)))))))))))))), 15.72/2.40 inference(fool_elimination,[],[f408])). 15.72/2.40 thf(f408,plain,( 15.72/2.40 (dsetconstrI = ! [X0,X1 : $i > $o,X2] : ((in @ X2 @ X0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))))))), 15.72/2.40 inference(rectify,[],[f14])). 15.72/2.40 thf(f14,axiom,( 15.72/2.40 (dsetconstrI = ! [X3,X0 : $i > $o,X1] : ((in @ X1 @ X3) => ((X0 @ X1) => (in @ X1 @ (dsetconstr @ X3 @ (^[X2 : $i] : (X0 @ X2)))))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI)). 15.72/2.40 thf(f796,plain,( 15.72/2.40 (descrp = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))) & (Y1 @ Y2))))) @ (^[Y1 : $i]: (Y0 @ Y1))) => (Y0 @ (descr @ (^[Y1 : $i]: (Y0 @ Y1))))))))), 15.72/2.40 inference(definition_unfolding,[],[f782,f647])). 15.72/2.40 thf(f782,plain,( 15.72/2.40 (descrp = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (Y0 @ (descr @ (^[Y1 : $i]: (Y0 @ Y1))))))))), 15.72/2.40 inference(cnf_transformation,[],[f265])). 15.72/2.40 thf(f265,plain,( 15.72/2.40 (descrp = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (Y0 @ (descr @ (^[Y1 : $i]: (Y0 @ Y1))))))))), 15.72/2.40 inference(fool_elimination,[],[f264])). 15.72/2.40 thf(f264,plain,( 15.72/2.40 (! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => (X0 @ (descr @ (^[X2 : $i] : (X0 @ X2))))) = descrp)), 15.72/2.40 inference(rectify,[],[f13])). 15.72/2.40 thf(f13,axiom,( 15.72/2.40 (! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => (X0 @ (descr @ (^[X1 : $i] : (X0 @ X1))))) = descrp)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',descrp)). 15.72/2.40 thf(f632,plain,( 15.72/2.40 (wellorderingAx = (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $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]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f370])). 15.72/2.40 thf(f370,plain,( 15.72/2.40 (wellorderingAx = (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $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]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y1) & (in @ Y3 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))))))) & (!! @ $i @ (^[Y2 : $i]: (((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0)))) & (?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2)))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y4)))) | (in @ Y3 @ Y5)))))) & (in @ Y3 @ Y2)) & (in @ Y4 @ Y1)))))))))))))))), 15.72/2.40 inference(fool_elimination,[],[f369])). 15.72/2.40 thf(f369,plain,( 15.72/2.40 (wellorderingAx = ! [X0] : ? [X1] : (! [X2] : ((? [X3] : (in @ X3 @ X2) & ! [X4] : ((in @ X4 @ X2) => (in @ X4 @ X0))) => ? [X5,X6] : ((in @ X5 @ X1) & (in @ X6 @ X2) & ! [X7] : ((in @ X7 @ X1) => ((in @ X6 @ X7) | ! [X8] : ((in @ X8 @ X7) => (in @ X8 @ X5)))) & ~? [X9] : ((in @ X9 @ X2) & (in @ X9 @ X5)))) & ! [X10] : ((in @ X10 @ X1) => ! [X11] : ((in @ X11 @ X10) => (in @ X11 @ X0))) & ! [X12,X13] : (((in @ X12 @ X1) & (in @ X13 @ X1)) => (! [X14] : ((in @ X14 @ X12) => (in @ X14 @ X13)) | ! [X15] : ((in @ X15 @ X13) => (in @ X15 @ X12)))) & ! [X16,X17] : (((in @ X17 @ X0) & (in @ X16 @ X0)) => (! [X18] : ((in @ X18 @ X1) => ((in @ X16 @ X18) <=> (in @ X17 @ X18))) => (X16 = X17)))))), 15.72/2.40 inference(rectify,[],[f12])). 15.72/2.40 thf(f12,axiom,( 15.72/2.40 (wellorderingAx = ! [X3] : ? [X4] : (! [X5] : ((? [X1] : (in @ X1 @ X5) & ! [X1] : ((in @ X1 @ X5) => (in @ X1 @ X3))) => ? [X6,X1] : ((in @ X6 @ X4) & (in @ X1 @ X5) & ! [X7] : ((in @ X7 @ X4) => ((in @ X1 @ X7) | ! [X2] : ((in @ X2 @ X7) => (in @ X2 @ X6)))) & ~? [X2] : ((in @ X2 @ X5) & (in @ X2 @ X6)))) & ! [X5] : ((in @ X5 @ X4) => ! [X1] : ((in @ X1 @ X5) => (in @ X1 @ X3))) & ! [X6,X5] : (((in @ X6 @ X4) & (in @ X5 @ X4)) => (! [X1] : ((in @ X1 @ X6) => (in @ X1 @ X5)) | ! [X1] : ((in @ X1 @ X5) => (in @ X1 @ X6)))) & ! [X2,X1] : (((in @ X1 @ X3) & (in @ X2 @ X3)) => (! [X5] : ((in @ X5 @ X4) => ((in @ X2 @ X5) <=> (in @ X1 @ X5))) => (X1 = X2)))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderingAx)). 15.72/2.40 thf(f781,plain,( 15.72/2.40 (foundationAx = (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))))), 15.72/2.40 inference(cnf_transformation,[],[f255])). 15.72/2.40 thf(f255,plain,( 15.72/2.40 (foundationAx = (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) & (in @ Y1 @ Y0))))))))), 15.72/2.40 inference(fool_elimination,[],[f254])). 15.72/2.40 thf(f254,plain,( 15.72/2.40 (foundationAx = ! [X0] : (? [X1] : (in @ X1 @ X0) => ? [X2] : ((in @ X2 @ X0) & ~? [X3] : ((in @ X3 @ X2) & (in @ X3 @ X0)))))), 15.72/2.40 inference(rectify,[],[f11])). 15.72/2.40 thf(f11,axiom,( 15.72/2.40 (foundationAx = ! [X3] : (? [X1] : (in @ X1 @ X3) => ? [X4] : ((in @ X4 @ X3) & ~? [X1] : ((in @ X1 @ X4) & (in @ X1 @ X3)))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',foundationAx)). 15.72/2.40 thf(f795,plain,( 15.72/2.40 (replAx = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((^[Y3 : $i > $o]: (?? @ $i @ (^[Y4 : $i]: ((!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5) => (Y4 = Y5)))) & (Y3 @ Y4))))) @ (^[Y3 : $i]: (Y1 @ Y2 @ Y3)))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & (Y1 @ Y4 @ Y3)))))))))))))))), 15.72/2.40 inference(definition_unfolding,[],[f665,f647])). 15.72/2.40 thf(f665,plain,( 15.72/2.40 (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)))))))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f518])). 15.72/2.40 thf(f518,plain,( 15.72/2.40 (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)))))))))))))))), 15.72/2.40 inference(fool_elimination,[],[f517])). 15.72/2.40 thf(f517,plain,( 15.72/2.40 (! [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)))) = replAx)), 15.72/2.40 inference(rectify,[],[f10])). 15.72/2.40 thf(f10,axiom,( 15.72/2.40 (! [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)))) = replAx)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',replAx)). 15.72/2.40 thf(f678,plain,( 15.72/2.40 (omegaIndAx = (!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))))), 15.72/2.40 inference(cnf_transformation,[],[f451])). 15.72/2.40 thf(f451,plain,( 15.72/2.40 (omegaIndAx = (!! @ $i @ (^[Y0 : $i]: (((in @ emptyset @ Y0) & (!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ omega) & (in @ Y1 @ Y0)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))))), 15.72/2.40 inference(fool_elimination,[],[f450])). 15.72/2.40 thf(f450,plain,( 15.72/2.40 (! [X0] : ((! [X1] : (((in @ X1 @ X0) & (in @ X1 @ omega)) => (in @ (setadjoin @ X1 @ X1) @ X0)) & (in @ emptyset @ X0)) => ! [X2] : ((in @ X2 @ omega) => (in @ X2 @ X0))) = omegaIndAx)), 15.72/2.40 inference(rectify,[],[f9])). 15.72/2.40 thf(f9,axiom,( 15.72/2.40 (! [X3] : ((! [X1] : (((in @ X1 @ X3) & (in @ X1 @ omega)) => (in @ (setadjoin @ X1 @ X1) @ X3)) & (in @ emptyset @ X3)) => ! [X1] : ((in @ X1 @ omega) => (in @ X1 @ X3))) = omegaIndAx)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaIndAx)). 15.72/2.40 thf(f616,plain,( 15.72/2.40 (omegaSAx = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))))), 15.72/2.40 inference(cnf_transformation,[],[f305])). 15.72/2.40 thf(f305,plain,( 15.72/2.40 (omegaSAx = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))))), 15.72/2.40 inference(fool_elimination,[],[f304])). 15.72/2.40 thf(f304,plain,( 15.72/2.40 (! [X0] : ((in @ X0 @ omega) => (in @ (setadjoin @ X0 @ X0) @ omega)) = omegaSAx)), 15.72/2.40 inference(rectify,[],[f8])). 15.72/2.40 thf(f8,axiom,( 15.72/2.40 (! [X1] : ((in @ X1 @ omega) => (in @ (setadjoin @ X1 @ X1) @ omega)) = omegaSAx)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx)). 15.72/2.40 thf(f613,plain,( 15.72/2.40 (omega0Ax = (in @ emptyset @ omega))), 15.72/2.40 inference(cnf_transformation,[],[f356])). 15.72/2.40 thf(f356,plain,( 15.72/2.40 (omega0Ax = (in @ emptyset @ omega))), 15.72/2.40 inference(fool_elimination,[],[f7])). 15.72/2.40 thf(f7,axiom,( 15.72/2.40 (omega0Ax = (in @ emptyset @ omega))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega0Ax)). 15.72/2.40 thf(f727,plain,( 15.72/2.40 (setunionAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f411])). 15.72/2.40 thf(f411,plain,( 15.72/2.40 (setunionAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1))))))))))), 15.72/2.40 inference(fool_elimination,[],[f410])). 15.72/2.40 thf(f410,plain,( 15.72/2.40 (setunionAx = ! [X0,X1] : ((in @ X1 @ (setunion @ X0)) <=> ? [X2] : ((in @ X2 @ X0) & (in @ X1 @ X2))))), 15.72/2.40 inference(rectify,[],[f6])). 15.72/2.40 thf(f6,axiom,( 15.72/2.40 (setunionAx = ! [X3,X1] : ((in @ X1 @ (setunion @ X3)) <=> ? [X4] : ((in @ X4 @ X3) & (in @ X1 @ X4))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionAx)). 15.72/2.40 thf(f644,plain,( 15.72/2.40 (powersetAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))))), 15.72/2.40 inference(cnf_transformation,[],[f229])). 15.72/2.40 thf(f229,plain,( 15.72/2.40 (powersetAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))))), 15.72/2.40 inference(fool_elimination,[],[f228])). 15.72/2.40 thf(f228,plain,( 15.72/2.40 (powersetAx = ! [X0,X1] : (! [X2] : ((in @ X2 @ X0) => (in @ X2 @ X1)) <=> (in @ X0 @ (powerset @ X1))))), 15.72/2.40 inference(rectify,[],[f5])). 15.72/2.40 thf(f5,axiom,( 15.72/2.40 (powersetAx = ! [X4,X3] : (! [X1] : ((in @ X1 @ X4) => (in @ X1 @ X3)) <=> (in @ X4 @ (powerset @ X3))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetAx)). 15.72/2.40 thf(f730,plain,( 15.72/2.40 (setadjoinAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))))), 15.72/2.40 inference(cnf_transformation,[],[f281])). 15.72/2.40 thf(f281,plain,( 15.72/2.40 (setadjoinAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((in @ Y2 @ Y0) | (Y2 = Y1)) = (in @ Y2 @ (setadjoin @ Y1 @ Y0))))))))))), 15.72/2.40 inference(fool_elimination,[],[f280])). 15.72/2.40 thf(f280,plain,( 15.72/2.40 (! [X0,X1,X2] : (((X0 = X1) | (in @ X0 @ X2)) <=> (in @ X0 @ (setadjoin @ X1 @ X2))) = setadjoinAx)), 15.72/2.40 inference(rectify,[],[f4])). 15.72/2.40 thf(f4,axiom,( 15.72/2.40 (! [X2,X1,X3] : (((X1 = X2) | (in @ X2 @ X3)) <=> (in @ X2 @ (setadjoin @ X1 @ X3))) = setadjoinAx)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinAx)). 15.72/2.40 thf(f757,plain,( 15.72/2.40 (emptysetAx = (!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))))), 15.72/2.40 inference(cnf_transformation,[],[f587])). 15.72/2.40 thf(f587,plain,( 15.72/2.40 (emptysetAx = (!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))))), 15.72/2.40 inference(fool_elimination,[],[f586])). 15.72/2.40 thf(f586,plain,( 15.72/2.40 (emptysetAx = ! [X0] : ~(in @ X0 @ emptyset))), 15.72/2.40 inference(rectify,[],[f3])). 15.72/2.40 thf(f3,axiom,( 15.72/2.40 (emptysetAx = ! [X1] : ~(in @ X1 @ emptyset))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx)). 15.72/2.40 thf(f766,plain,( 15.72/2.40 (setextAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))))), 15.72/2.40 inference(cnf_transformation,[],[f437])). 15.72/2.40 thf(f437,plain,( 15.72/2.40 (setextAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) = (in @ Y2 @ Y0)))) => (Y1 = Y0)))))))), 15.72/2.40 inference(fool_elimination,[],[f436])). 15.72/2.40 thf(f436,plain,( 15.72/2.40 (! [X0,X1] : (! [X2] : ((in @ X2 @ X0) <=> (in @ X2 @ X1)) => (X0 = X1)) = setextAx)), 15.72/2.40 inference(rectify,[],[f2])). 15.72/2.40 thf(f2,axiom,( 15.72/2.40 (! [X4,X3] : (! [X1] : ((in @ X1 @ X4) <=> (in @ X1 @ X3)) => (X3 = X4)) = setextAx)), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextAx)). 15.72/2.40 thf(f642,plain,( 15.72/2.40 ((~ (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 @ Y2 @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (ap @ Y2 @ Y1 @ Y0 @ Y3) @ Y1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.40 inference(cnf_transformation,[],[f544])). 15.72/2.40 thf(f544,plain,( 15.72/2.40 ((~ (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 @ Y2 @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (ap @ Y2 @ Y1 @ Y0 @ Y3) @ Y1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 15.72/2.40 inference(fool_elimination,[],[f543])). 15.72/2.40 thf(f543,plain,( 15.72/2.40 ~(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 @ X0 @ X1 @ X2) => ! [X3] : ((in @ X3 @ X0) => (in @ (ap @ X0 @ X1 @ X2 @ X3) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 15.72/2.40 inference(rectify,[],[f200])). 15.72/2.40 thf(f200,negated_conjecture,( 15.72/2.40 ~(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 => ! [X3,X4,X13] : ((func @ X3 @ X4 @ X13) => ! [X1] : ((in @ X1 @ X3) => (in @ (ap @ X3 @ X4 @ X13 @ X1) @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 15.72/2.40 inference(negated_conjecture,[],[f199])). 15.72/2.40 thf(f199,conjecture,( 15.72/2.40 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 => ! [X3,X4,X13] : ((func @ X3 @ X4 @ X13) => ! [X1] : ((in @ X1 @ X3) => (in @ (ap @ X3 @ X4 @ X13 @ X1) @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 15.72/2.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',app)). 15.72/2.40 % SZS output end Proof for theBenchmark 15.72/2.40 % (2177)------------------------------ 15.72/2.40 % (2177)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 15.72/2.40 % (2177)Termination reason: Refutation 15.72/2.40 15.72/2.40 % (2177)Memory used [KB]: 200337 15.72/2.40 % (2177)Time elapsed: 0.694 s 15.72/2.40 % (2177)Instructions burned: 775 (million) 15.72/2.40 % (2177)------------------------------ 15.72/2.40 % (2177)------------------------------ 15.72/2.40 % (1971)Success in time 2.039 s 15.72/2.40 % Vampire---4.8 exiting 15.72/2.40 EOF