0.05/0.12 % Problem : Vampire---4.8_16456 : TPTP v0.0.0. Released v0.0.0. 0.05/0.13 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s 0.13/0.33 % Computer : n009.cluster.edu 0.13/0.33 % Model : x86_64 x86_64 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.33 % Memory : 8042.1875MB 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.33 % CPULimit : 1440 0.13/0.33 % WCLimit : 180 0.13/0.33 % DateTime : Mon Jul 3 12:57:41 EDT 2023 0.13/0.33 % CPUTime : 0.13/0.33 This is a THF_ problem 0.13/0.33 Running vampire_rel_static_ahmed-new-hol_6848 --cores 8 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456 -m 12000 -t 180 0.19/0.36 % (16564)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on Vampire---4 for (1799ds/96Mi) 0.19/0.36 % (16570)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on Vampire---4 for (1799ds/4Mi) 0.19/0.36 % (16569)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 Vampire---4 for (1799ds/74Mi) 0.19/0.36 % (16565)lrs+10_1:2_cnfonf=off:hud=1:inj=on:i=36:si=on:rtra=on_0 on Vampire---4 for (1799ds/36Mi) 0.19/0.36 % (16568)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on Vampire---4 for (1799ds/17Mi) 0.19/0.36 % (16567)lrs+1002_1:1_au=on:s2a=on:s2agt=32:sgt=8:ss=axioms:i=385:si=on:rtra=on_0 on Vampire---4 for (1799ds/385Mi) 0.19/0.36 % (16566)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=34:si=on:rtra=on_0 on Vampire---4 for (1799ds/34Mi) 0.19/0.36 % (16571)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=915:si=on:rtra=on_0 on Vampire---4 for (1799ds/915Mi) 0.19/0.36 % (16570)Instruction limit reached! 0.19/0.36 % (16570)------------------------------ 0.19/0.36 % (16570)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.19/0.36 % (16570)Termination reason: Unknown 0.19/0.36 % (16570)Termination phase: shuffling 0.19/0.36 0.19/0.36 % (16570)Memory used [KB]: 1407 0.19/0.36 % (16570)Time elapsed: 0.003 s 0.19/0.36 % (16570)Instructions burned: 4 (million) 0.19/0.36 % (16570)------------------------------ 0.19/0.36 % (16570)------------------------------ 0.19/0.37 % (16568)Instruction limit reached! 0.19/0.37 % (16568)------------------------------ 0.19/0.37 % (16568)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.19/0.37 % (16568)Termination reason: Unknown 0.19/0.37 % (16568)Termination phase: shuffling 0.19/0.37 0.19/0.37 % (16568)Memory used [KB]: 1663 0.19/0.37 % (16568)Time elapsed: 0.009 s 0.19/0.37 % (16568)Instructions burned: 17 (million) 0.19/0.37 % (16568)------------------------------ 0.19/0.37 % (16568)------------------------------ 0.19/0.37 % (16572)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 Vampire---4 for (1799ds/21Mi) 0.19/0.38 % (16566)Instruction limit reached! 0.19/0.38 % (16566)------------------------------ 0.19/0.38 % (16566)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.19/0.38 % (16566)Termination reason: Unknown 0.19/0.38 % (16566)Termination phase: Property scanning 0.19/0.38 0.19/0.38 % (16566)Memory used [KB]: 1918 0.19/0.38 % (16566)Time elapsed: 0.017 s 0.19/0.38 % (16566)Instructions burned: 35 (million) 0.19/0.38 % (16566)------------------------------ 0.19/0.38 % (16566)------------------------------ 0.19/0.38 % (16565)Instruction limit reached! 0.19/0.38 % (16565)------------------------------ 0.19/0.38 % (16565)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.19/0.38 % (16565)Termination reason: Unknown 0.19/0.38 % (16565)Termination phase: Property scanning 0.19/0.38 0.19/0.38 % (16565)Memory used [KB]: 1918 0.19/0.38 % (16565)Time elapsed: 0.018 s 0.19/0.38 % (16565)Instructions burned: 37 (million) 0.19/0.38 % (16565)------------------------------ 0.19/0.38 % (16565)------------------------------ 0.19/0.38 % (16573)lrs-3_1:1024_cbe=off:chr=on:tnu=1:i=7:si=on:rtra=on_0 on Vampire---4 for (1799ds/7Mi) 0.19/0.38 % (16573)Instruction limit reached! 0.19/0.38 % (16573)------------------------------ 0.19/0.38 % (16573)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.19/0.38 % (16573)Termination reason: Unknown 0.19/0.38 % (16573)Termination phase: shuffling 0.19/0.38 0.19/0.38 % (16573)Memory used [KB]: 1535 0.19/0.38 % (16573)Time elapsed: 0.005 s 0.19/0.38 % (16573)Instructions burned: 8 (million) 0.19/0.38 % (16573)------------------------------ 0.19/0.38 % (16573)------------------------------ 0.19/0.38 % (16572)Instruction limit reached! 0.19/0.38 % (16572)------------------------------ 0.19/0.38 % (16572)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.19/0.38 % (16572)Termination reason: Unknown 0.19/0.38 % (16572)Termination phase: shuffling 0.19/0.38 0.19/0.38 % (16572)Memory used [KB]: 1791 0.19/0.38 % (16572)Time elapsed: 0.011 s 0.19/0.38 % (16572)Instructions burned: 22 (million) 0.19/0.38 % (16572)------------------------------ 0.19/0.38 % (16572)------------------------------ 0.19/0.39 % (16574)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 Vampire---4 for (1799ds/1021Mi) 0.19/0.39 % (16575)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on Vampire---4 for (1799ds/71Mi) 0.19/0.39 % (16569)Instruction limit reached! 0.19/0.39 % (16569)------------------------------ 0.19/0.39 % (16569)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.19/0.39 % (16569)Termination reason: Unknown 0.19/0.39 % (16569)Termination phase: Function definition elimination 0.19/0.39 0.19/0.39 % (16569)Memory used [KB]: 2174 0.19/0.39 % (16569)Time elapsed: 0.033 s 0.19/0.39 % (16569)Instructions burned: 76 (million) 0.19/0.39 % (16569)------------------------------ 0.19/0.39 % (16569)------------------------------ 0.19/0.40 % (16576)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 Vampire---4 for (1799ds/9Mi) 0.19/0.40 % (16577)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=1044:si=on:rtra=on_0 on Vampire---4 for (1799ds/1044Mi) 0.19/0.40 % (16564)Instruction limit reached! 0.19/0.40 % (16564)------------------------------ 0.19/0.40 % (16564)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.19/0.40 % (16564)Termination reason: Unknown 0.19/0.40 % (16564)Termination phase: Saturation 0.19/0.40 0.19/0.40 % (16564)Memory used [KB]: 6780 0.19/0.40 % (16564)Time elapsed: 0.043 s 0.19/0.40 % (16564)Instructions burned: 97 (million) 0.19/0.40 % (16564)------------------------------ 0.19/0.40 % (16564)------------------------------ 0.19/0.40 % (16576)Instruction limit reached! 0.19/0.40 % (16576)------------------------------ 0.19/0.40 % (16576)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.19/0.40 % (16576)Termination reason: Unknown 0.19/0.40 % (16576)Termination phase: shuffling 0.19/0.40 0.19/0.40 % (16576)Memory used [KB]: 1535 0.19/0.40 % (16576)Time elapsed: 0.006 s 0.19/0.40 % (16576)Instructions burned: 10 (million) 0.19/0.40 % (16576)------------------------------ 0.19/0.40 % (16576)------------------------------ 0.19/0.40 % (16578)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=128:si=on:rtra=on_0 on Vampire---4 for (1799ds/128Mi) 0.19/0.41 % (16579)lrs+21_1:1_cond=on:e2e=on:i=61:si=on:rtra=on_0 on Vampire---4 for (1799ds/61Mi) 0.19/0.41 % (16580)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=14:si=on:rtra=on_0 on Vampire---4 for (1799ds/14Mi) 0.19/0.42 % (16575)Instruction limit reached! 0.19/0.42 % (16575)------------------------------ 0.19/0.42 % (16575)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.19/0.42 % (16575)Termination reason: Unknown 0.19/0.42 % (16575)Termination phase: Function definition elimination 0.19/0.42 0.19/0.42 % (16575)Memory used [KB]: 2174 0.19/0.42 % (16575)Time elapsed: 0.032 s 0.19/0.42 % (16575)Instructions burned: 71 (million) 0.19/0.42 % (16575)------------------------------ 0.19/0.42 % (16575)------------------------------ 0.19/0.42 % (16580)Instruction limit reached! 0.19/0.42 % (16580)------------------------------ 0.19/0.42 % (16580)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.19/0.42 % (16580)Termination reason: Unknown 0.19/0.42 % (16580)Termination phase: shuffling 0.19/0.42 0.19/0.42 % (16580)Memory used [KB]: 1663 0.19/0.42 % (16580)Time elapsed: 0.009 s 0.19/0.42 % (16580)Instructions burned: 14 (million) 0.19/0.42 % (16580)------------------------------ 0.19/0.42 % (16580)------------------------------ 0.19/0.43 % (16581)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 Vampire---4 for (1799ds/2Mi) 0.19/0.43 % (16581)Instruction limit reached! 0.19/0.43 % (16581)------------------------------ 0.19/0.43 % (16581)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.19/0.43 % (16581)Termination reason: Unknown 0.19/0.43 % (16581)Termination phase: shuffling 0.19/0.43 0.19/0.43 % (16581)Memory used [KB]: 1407 0.19/0.43 % (16581)Time elapsed: 0.003 s 0.19/0.43 % (16581)Instructions burned: 3 (million) 0.19/0.43 % (16581)------------------------------ 0.19/0.43 % (16581)------------------------------ 0.19/0.44 % (16582)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 Vampire---4 for (1799ds/1041Mi) 0.19/0.44 % (16579)Instruction limit reached! 0.19/0.44 % (16579)------------------------------ 0.19/0.44 % (16579)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.19/0.44 % (16579)Termination reason: Unknown 0.19/0.44 % (16579)Termination phase: Preprocessing 3 0.19/0.44 0.19/0.44 % (16579)Memory used [KB]: 3070 0.19/0.44 % (16579)Time elapsed: 0.031 s 0.19/0.44 % (16579)Instructions burned: 62 (million) 0.19/0.44 % (16579)------------------------------ 0.19/0.44 % (16579)------------------------------ 0.19/0.45 % (16583)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on Vampire---4 for (1799ds/11Mi) 0.19/0.45 % (16583)Instruction limit reached! 0.19/0.45 % (16583)------------------------------ 0.19/0.45 % (16583)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.19/0.45 % (16583)Termination reason: Unknown 0.19/0.45 % (16583)Termination phase: shuffling 0.19/0.45 0.19/0.45 % (16583)Memory used [KB]: 1535 0.19/0.45 % (16583)Time elapsed: 0.007 s 0.19/0.45 % (16583)Instructions burned: 12 (million) 0.19/0.45 % (16583)------------------------------ 0.19/0.45 % (16583)------------------------------ 0.19/0.46 % (16584)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on Vampire---4 for (1798ds/140Mi) 0.19/0.46 % (16578)Instruction limit reached! 0.19/0.46 % (16578)------------------------------ 0.19/0.46 % (16578)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.19/0.46 % (16578)Termination reason: Unknown 0.19/0.46 % (16578)Termination phase: Saturation 0.19/0.46 0.19/0.46 % (16578)Memory used [KB]: 7036 0.19/0.46 % (16578)Time elapsed: 0.056 s 0.19/0.46 % (16578)Instructions burned: 129 (million) 0.19/0.46 % (16578)------------------------------ 0.19/0.46 % (16578)------------------------------ 0.19/0.47 % (16585)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 Vampire---4 for (1798ds/26Mi) 0.19/0.47 % (16586)lrs+1002_1:4_au=on:av=off:bsr=on:cbe=off:nm=2:i=56:si=on:rtra=on_0 on Vampire---4 for (1798ds/56Mi) 0.19/0.48 % (16585)Instruction limit reached! 0.19/0.48 % (16585)------------------------------ 0.19/0.48 % (16585)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.19/0.48 % (16585)Termination reason: Unknown 0.19/0.48 % (16585)Termination phase: shuffling 0.19/0.48 0.19/0.48 % (16585)Memory used [KB]: 1918 0.19/0.48 % (16585)Time elapsed: 0.013 s 0.19/0.48 % (16585)Instructions burned: 26 (million) 0.19/0.48 % (16585)------------------------------ 0.19/0.48 % (16585)------------------------------ 0.19/0.49 % (16587)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on Vampire---4 for (1798ds/275Mi) 0.19/0.50 % (16586)Instruction limit reached! 0.19/0.50 % (16586)------------------------------ 0.19/0.50 % (16586)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.19/0.50 % (16586)Termination reason: Unknown 0.19/0.50 % (16586)Termination phase: Property scanning 0.19/0.50 0.19/0.50 % (16586)Memory used [KB]: 2046 0.19/0.50 % (16586)Time elapsed: 0.026 s 0.19/0.50 % (16586)Instructions burned: 57 (million) 0.19/0.50 % (16586)------------------------------ 0.19/0.50 % (16586)------------------------------ 0.19/0.51 % (16588)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (1798ds/3Mi) 0.19/0.51 % (16588)Instruction limit reached! 0.19/0.51 % (16588)------------------------------ 0.19/0.51 % (16588)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.19/0.51 % (16588)Termination reason: Unknown 0.19/0.51 % (16588)Termination phase: shuffling 0.19/0.51 0.19/0.51 % (16588)Memory used [KB]: 1407 0.19/0.51 % (16588)Time elapsed: 0.003 s 0.19/0.51 % (16588)Instructions burned: 3 (million) 0.19/0.51 % (16588)------------------------------ 0.19/0.51 % (16588)------------------------------ 0.19/0.52 % (16584)Instruction limit reached! 0.19/0.52 % (16584)------------------------------ 0.19/0.52 % (16584)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.19/0.52 % (16584)Termination reason: Unknown 0.19/0.52 % (16584)Termination phase: Saturation 0.19/0.52 0.19/0.52 % (16584)Memory used [KB]: 6908 0.19/0.52 % (16584)Time elapsed: 0.062 s 0.19/0.52 % (16584)Instructions burned: 141 (million) 0.19/0.52 % (16584)------------------------------ 0.19/0.52 % (16584)------------------------------ 0.19/0.52 % (16589)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 Vampire---4 for (1798ds/19Mi) 0.19/0.53 % (16590)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 Vampire---4 for (1798ds/44Mi) 0.19/0.53 % (16589)Instruction limit reached! 0.19/0.53 % (16589)------------------------------ 0.19/0.53 % (16589)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.19/0.53 % (16589)Termination reason: Unknown 0.19/0.53 % (16589)Termination phase: shuffling 0.19/0.53 0.19/0.53 % (16589)Memory used [KB]: 1791 0.19/0.53 % (16589)Time elapsed: 0.010 s 0.19/0.53 % (16589)Instructions burned: 20 (million) 0.19/0.53 % (16589)------------------------------ 0.19/0.53 % (16589)------------------------------ 0.19/0.54 % (16567)Instruction limit reached! 0.19/0.54 % (16567)------------------------------ 0.19/0.54 % (16567)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.19/0.54 % (16567)Termination reason: Unknown 0.19/0.54 % (16567)Termination phase: Saturation 0.19/0.54 0.19/0.54 % (16567)Memory used [KB]: 8315 0.19/0.54 % (16567)Time elapsed: 0.178 s 0.19/0.54 % (16567)Instructions burned: 385 (million) 0.19/0.54 % (16567)------------------------------ 0.19/0.54 % (16567)------------------------------ 0.19/0.55 % (16591)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=191:si=on:rtra=on_0 on Vampire---4 for (1798ds/191Mi) 0.19/0.55 % (16590)Instruction limit reached! 0.19/0.55 % (16590)------------------------------ 0.19/0.55 % (16590)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.19/0.55 % (16590)Termination reason: Unknown 0.19/0.55 % (16590)Termination phase: Property scanning 0.19/0.55 0.19/0.55 % (16590)Memory used [KB]: 2174 0.19/0.55 % (16593)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on Vampire---4 for (1798ds/62Mi) 0.19/0.55 % (16590)Time elapsed: 0.021 s 0.19/0.55 % (16590)Instructions burned: 44 (million) 0.19/0.55 % (16590)------------------------------ 0.19/0.55 % (16590)------------------------------ 1.75/0.56 % (16594)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=105:si=on:rtra=on_0 on Vampire---4 for (1797ds/105Mi) 1.86/0.58 % (16593)Instruction limit reached! 1.86/0.58 % (16593)------------------------------ 1.86/0.58 % (16593)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.86/0.58 % (16593)Termination reason: Unknown 1.86/0.58 % (16593)Termination phase: Property scanning 1.86/0.58 1.86/0.58 % (16593)Memory used [KB]: 2174 1.86/0.58 % (16593)Time elapsed: 0.029 s 1.86/0.58 % (16593)Instructions burned: 64 (million) 1.86/0.58 % (16593)------------------------------ 1.86/0.58 % (16593)------------------------------ 1.86/0.59 % (16595)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on Vampire---4 for (1797ds/3Mi) 1.86/0.59 % (16595)Instruction limit reached! 1.86/0.59 % (16595)------------------------------ 1.86/0.59 % (16595)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.86/0.59 % (16595)Termination reason: Unknown 1.86/0.59 % (16595)Termination phase: shuffling 1.86/0.59 1.86/0.59 % (16595)Memory used [KB]: 1407 1.86/0.59 % (16595)Time elapsed: 0.004 s 1.86/0.59 % (16595)Instructions burned: 4 (million) 1.86/0.59 % (16595)------------------------------ 1.86/0.59 % (16595)------------------------------ 1.86/0.61 % (16596)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 Vampire---4 for (1797ds/238Mi) 1.86/0.61 % (16594)Instruction limit reached! 1.86/0.61 % (16594)------------------------------ 1.86/0.61 % (16594)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.86/0.61 % (16594)Termination reason: Unknown 1.86/0.61 % (16594)Termination phase: Saturation 1.86/0.61 1.86/0.61 % (16594)Memory used [KB]: 6780 1.86/0.61 % (16594)Time elapsed: 0.046 s 1.86/0.61 % (16594)Instructions burned: 106 (million) 1.86/0.61 % (16594)------------------------------ 1.86/0.61 % (16594)------------------------------ 1.86/0.62 % (16597)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 Vampire---4 for (1797ds/3Mi) 1.86/0.62 % (16597)Instruction limit reached! 1.86/0.62 % (16597)------------------------------ 1.86/0.62 % (16597)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.86/0.62 % (16597)Termination reason: Unknown 1.86/0.62 % (16597)Termination phase: shuffling 1.86/0.62 1.86/0.62 % (16597)Memory used [KB]: 1407 1.86/0.62 % (16597)Time elapsed: 0.003 s 1.86/0.62 % (16597)Instructions burned: 3 (million) 1.86/0.62 % (16597)------------------------------ 1.86/0.62 % (16597)------------------------------ 1.86/0.62 % (16587)Instruction limit reached! 1.86/0.62 % (16587)------------------------------ 1.86/0.62 % (16587)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.86/0.62 % (16587)Termination reason: Unknown 1.86/0.62 % (16587)Termination phase: Saturation 1.86/0.62 1.86/0.62 % (16587)Memory used [KB]: 8443 1.86/0.62 % (16587)Time elapsed: 0.134 s 1.86/0.62 % (16587)Instructions burned: 275 (million) 1.86/0.62 % (16587)------------------------------ 1.86/0.62 % (16587)------------------------------ 2.28/0.63 % (16591)Instruction limit reached! 2.28/0.63 % (16591)------------------------------ 2.28/0.63 % (16591)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.28/0.63 % (16591)Termination reason: Unknown 2.28/0.63 % (16591)Termination phase: Saturation 2.28/0.63 2.28/0.63 % (16591)Memory used [KB]: 7547 2.28/0.63 % (16591)Time elapsed: 0.085 s 2.28/0.63 % (16591)Instructions burned: 192 (million) 2.28/0.63 % (16591)------------------------------ 2.28/0.63 % (16591)------------------------------ 2.28/0.64 % (16598)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 Vampire---4 for (1797ds/4Mi) 2.28/0.64 % (16599)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 Vampire---4 for (1797ds/149Mi) 2.28/0.64 % (16598)Instruction limit reached! 2.28/0.64 % (16598)------------------------------ 2.28/0.64 % (16598)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.28/0.64 % (16598)Termination reason: Unknown 2.28/0.64 % (16598)Termination phase: shuffling 2.28/0.64 2.28/0.64 % (16598)Memory used [KB]: 1407 2.28/0.64 % (16598)Time elapsed: 0.003 s 2.28/0.64 % (16598)Instructions burned: 4 (million) 2.28/0.64 % (16598)------------------------------ 2.28/0.64 % (16598)------------------------------ 2.28/0.64 % (16600)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on Vampire---4 for (1797ds/150Mi) 2.28/0.65 % (16601)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 Vampire---4 for (1796ds/199Mi) 2.44/0.70 % (16596)Instruction limit reached! 2.44/0.70 % (16596)------------------------------ 2.44/0.70 % (16596)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.44/0.70 % (16596)Termination reason: Unknown 2.44/0.70 % (16596)Termination phase: Saturation 2.44/0.70 2.44/0.70 % (16596)Memory used [KB]: 6908 2.44/0.70 % (16596)Time elapsed: 0.096 s 2.44/0.70 % (16596)Instructions burned: 240 (million) 2.44/0.70 % (16596)------------------------------ 2.44/0.70 % (16596)------------------------------ 2.44/0.70 % (16599)Instruction limit reached! 2.44/0.70 % (16599)------------------------------ 2.44/0.70 % (16599)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.44/0.70 % (16599)Termination reason: Unknown 2.44/0.70 % (16599)Termination phase: Saturation 2.44/0.70 2.44/0.70 % (16599)Memory used [KB]: 7419 2.44/0.70 % (16599)Time elapsed: 0.091 s 2.44/0.70 % (16599)Instructions burned: 150 (million) 2.44/0.70 % (16599)------------------------------ 2.44/0.70 % (16599)------------------------------ 2.44/0.71 % (16600)Instruction limit reached! 2.44/0.71 % (16600)------------------------------ 2.44/0.71 % (16600)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 2.44/0.71 % (16600)Termination reason: Unknown 2.44/0.71 % (16600)Termination phase: Saturation 2.44/0.71 2.44/0.71 % (16600)Memory used [KB]: 8187 2.44/0.71 % (16600)Time elapsed: 0.095 s 2.44/0.71 % (16600)Instructions burned: 150 (million) 2.44/0.71 % (16600)------------------------------ 2.44/0.71 % (16600)------------------------------ 2.44/0.71 % (16602)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on Vampire---4 for (1796ds/39Mi) 2.44/0.72 % (16603)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=721:si=on:rtra=on_0 on Vampire---4 for (1796ds/721Mi) 3.00/0.73 % (16604)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=3:si=on:rtra=on_0 on Vampire---4 for (1796ds/3Mi) 3.00/0.73 % (16604)Instruction limit reached! 3.00/0.73 % (16604)------------------------------ 3.00/0.73 % (16604)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.00/0.73 % (16604)Termination reason: Unknown 3.00/0.73 % (16604)Termination phase: shuffling 3.00/0.73 3.00/0.73 % (16604)Memory used [KB]: 1407 3.00/0.73 % (16604)Time elapsed: 0.003 s 3.00/0.73 % (16604)Instructions burned: 3 (million) 3.00/0.73 % (16604)------------------------------ 3.00/0.73 % (16604)------------------------------ 3.00/0.73 % (16602)Instruction limit reached! 3.00/0.73 % (16602)------------------------------ 3.00/0.73 % (16602)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.00/0.73 % (16602)Termination reason: Unknown 3.00/0.73 % (16602)Termination phase: Property scanning 3.00/0.73 3.00/0.73 % (16602)Memory used [KB]: 1918 3.00/0.73 % (16602)Time elapsed: 0.019 s 3.00/0.73 % (16602)Instructions burned: 39 (million) 3.00/0.73 % (16602)------------------------------ 3.00/0.73 % (16602)------------------------------ 3.00/0.74 % (16605)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on Vampire---4 for (1796ds/18Mi) 3.00/0.74 % (16601)Instruction limit reached! 3.00/0.74 % (16601)------------------------------ 3.00/0.74 % (16601)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.00/0.74 % (16601)Termination reason: Unknown 3.00/0.74 % (16601)Termination phase: Saturation 3.00/0.74 3.00/0.74 % (16601)Memory used [KB]: 7164 3.00/0.74 % (16601)Time elapsed: 0.094 s 3.00/0.74 % (16601)Instructions burned: 199 (million) 3.00/0.74 % (16601)------------------------------ 3.00/0.74 % (16601)------------------------------ 3.00/0.74 % (16606)lrs+10_1:1_au=on:c=on:sac=on:slsq=on:slsqc=2:i=218:si=on:rtra=on_0 on Vampire---4 for (1795ds/218Mi) 3.00/0.75 % (16605)Instruction limit reached! 3.00/0.75 % (16605)------------------------------ 3.00/0.75 % (16605)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.00/0.75 % (16605)Termination reason: Unknown 3.00/0.75 % (16605)Termination phase: shuffling 3.00/0.75 3.00/0.75 % (16605)Memory used [KB]: 1791 3.00/0.75 % (16605)Time elapsed: 0.010 s 3.00/0.75 % (16605)Instructions burned: 19 (million) 3.00/0.75 % (16605)------------------------------ 3.00/0.75 % (16605)------------------------------ 3.00/0.76 % (16607)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 Vampire---4 for (1795ds/448Mi) 3.00/0.76 % (16608)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 Vampire---4 for (1795ds/6Mi) 3.00/0.76 % (16608)Instruction limit reached! 3.00/0.76 % (16608)------------------------------ 3.00/0.76 % (16608)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.00/0.76 % (16608)Termination reason: Unknown 3.00/0.76 % (16608)Termination phase: shuffling 3.00/0.76 3.00/0.76 % (16608)Memory used [KB]: 1407 3.00/0.77 % (16608)Time elapsed: 0.005 s 3.00/0.77 % (16608)Instructions burned: 7 (million) 3.00/0.77 % (16608)------------------------------ 3.00/0.77 % (16608)------------------------------ 3.36/0.78 % (16609)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=9:si=on:rtra=on_0 on Vampire---4 for (1795ds/9Mi) 3.36/0.78 % (16609)Instruction limit reached! 3.36/0.78 % (16609)------------------------------ 3.36/0.78 % (16609)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.36/0.78 % (16609)Termination reason: Unknown 3.36/0.78 % (16609)Termination phase: shuffling 3.36/0.78 3.36/0.78 % (16609)Memory used [KB]: 1535 3.36/0.78 % (16609)Time elapsed: 0.006 s 3.36/0.78 % (16609)Instructions burned: 9 (million) 3.36/0.78 % (16609)------------------------------ 3.36/0.78 % (16609)------------------------------ 3.36/0.80 % (16610)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on Vampire---4 for (1795ds/16Mi) 3.36/0.80 % (16571)Instruction limit reached! 3.36/0.80 % (16571)------------------------------ 3.36/0.80 % (16571)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.36/0.80 % (16571)Termination reason: Unknown 3.36/0.80 % (16571)Termination phase: Saturation 3.36/0.80 3.36/0.80 % (16571)Memory used [KB]: 9594 3.36/0.80 % (16571)Time elapsed: 0.444 s 3.36/0.80 % (16571)Instructions burned: 915 (million) 3.36/0.80 % (16571)------------------------------ 3.36/0.80 % (16571)------------------------------ 3.36/0.80 % (16610)Instruction limit reached! 3.36/0.80 % (16610)------------------------------ 3.36/0.80 % (16610)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.36/0.80 % (16610)Termination reason: Unknown 3.36/0.80 % (16610)Termination phase: shuffling 3.36/0.80 3.36/0.80 % (16610)Memory used [KB]: 1663 3.36/0.80 % (16610)Time elapsed: 0.009 s 3.36/0.80 % (16610)Instructions burned: 16 (million) 3.36/0.80 % (16610)------------------------------ 3.36/0.80 % (16610)------------------------------ 3.36/0.81 % (16582)Instruction limit reached! 3.36/0.81 % (16582)------------------------------ 3.36/0.81 % (16582)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.36/0.81 % (16582)Termination reason: Unknown 3.36/0.81 % (16582)Termination phase: Saturation 3.36/0.81 3.36/0.81 % (16582)Memory used [KB]: 11257 3.36/0.81 % (16582)Time elapsed: 0.376 s 3.36/0.81 % (16582)Instructions burned: 1042 (million) 3.36/0.81 % (16582)------------------------------ 3.36/0.81 % (16582)------------------------------ 3.36/0.82 % (16611)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 Vampire---4 for (1795ds/40Mi) 3.36/0.82 % (16612)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (1795ds/2Mi) 3.36/0.82 % (16612)Instruction limit reached! 3.36/0.82 % (16612)------------------------------ 3.36/0.82 % (16612)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.36/0.82 % (16612)Termination reason: Unknown 3.36/0.82 % (16612)Termination phase: shuffling 3.36/0.82 3.36/0.82 % (16612)Memory used [KB]: 1407 3.36/0.82 % (16612)Time elapsed: 0.003 s 3.36/0.82 % (16612)Instructions burned: 3 (million) 3.36/0.82 % (16612)------------------------------ 3.36/0.82 % (16612)------------------------------ 3.36/0.82 % (16613)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 Vampire---4 for (1795ds/98Mi) 3.36/0.83 % (16614)lrs+1004_1:1_chr=on:prag=on:i=8:si=on:rtra=on_0 on Vampire---4 for (1795ds/8Mi) 3.36/0.83 % (16611)Instruction limit reached! 3.36/0.83 % (16611)------------------------------ 3.36/0.83 % (16611)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.36/0.83 % (16611)Termination reason: Unknown 3.36/0.83 % (16611)Termination phase: Property scanning 3.36/0.83 3.36/0.83 % (16611)Memory used [KB]: 1918 3.36/0.83 % (16611)Time elapsed: 0.019 s 3.36/0.83 % (16611)Instructions burned: 40 (million) 3.36/0.83 % (16611)------------------------------ 3.36/0.83 % (16611)------------------------------ 3.36/0.83 % (16614)Instruction limit reached! 3.36/0.83 % (16614)------------------------------ 3.36/0.83 % (16614)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.36/0.83 % (16614)Termination reason: Unknown 3.36/0.83 % (16614)Termination phase: shuffling 3.36/0.83 3.36/0.83 % (16614)Memory used [KB]: 1535 3.36/0.83 % (16614)Time elapsed: 0.005 s 3.36/0.83 % (16614)Instructions burned: 8 (million) 3.36/0.83 % (16614)------------------------------ 3.36/0.83 % (16614)------------------------------ 3.70/0.84 % (16606)Instruction limit reached! 3.70/0.84 % (16606)------------------------------ 3.70/0.84 % (16606)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.70/0.84 % (16606)Termination reason: Unknown 3.70/0.84 % (16606)Termination phase: Saturation 3.70/0.84 3.70/0.84 % (16606)Memory used [KB]: 7803 3.70/0.84 % (16606)Time elapsed: 0.097 s 3.70/0.84 % (16606)Instructions burned: 218 (million) 3.70/0.84 % (16606)------------------------------ 3.70/0.84 % (16606)------------------------------ 3.70/0.85 % (16615)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 Vampire---4 for (1795ds/86Mi) 3.70/0.85 % (16616)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 Vampire---4 for (1795ds/3Mi) 3.70/0.85 % (16616)Instruction limit reached! 3.70/0.85 % (16616)------------------------------ 3.70/0.85 % (16616)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.70/0.85 % (16616)Termination reason: Unknown 3.70/0.85 % (16616)Termination phase: shuffling 3.70/0.85 3.70/0.85 % (16616)Memory used [KB]: 1407 3.70/0.85 % (16616)Time elapsed: 0.003 s 3.70/0.85 % (16616)Instructions burned: 3 (million) 3.70/0.85 % (16616)------------------------------ 3.70/0.85 % (16616)------------------------------ 3.70/0.85 % (16617)lrs+1010_1:1024_au=on:hud=10:ntd=on:ss=included:i=294:si=on:rtra=on_0 on Vampire---4 for (1794ds/294Mi) 3.70/0.86 % (16618)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 Vampire---4 for (1794ds/274Mi) 3.70/0.86 % (16613)Instruction limit reached! 3.70/0.86 % (16613)------------------------------ 3.70/0.86 % (16613)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.70/0.86 % (16613)Termination reason: Unknown 3.70/0.86 % (16613)Termination phase: Property scanning 3.70/0.86 3.70/0.86 % (16613)Memory used [KB]: 2174 3.70/0.86 % (16613)Time elapsed: 0.042 s 3.70/0.86 % (16613)Instructions burned: 98 (million) 3.70/0.86 % (16613)------------------------------ 3.70/0.86 % (16613)------------------------------ 3.93/0.88 % (16619)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on Vampire---4 for (1794ds/47Mi) 3.93/0.88 % (16615)Instruction limit reached! 3.93/0.88 % (16615)------------------------------ 3.93/0.88 % (16615)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.93/0.88 % (16615)Termination reason: Unknown 3.93/0.88 % (16615)Termination phase: Property scanning 3.93/0.88 3.93/0.88 % (16615)Memory used [KB]: 2174 3.93/0.88 % (16615)Time elapsed: 0.038 s 3.93/0.88 % (16615)Instructions burned: 87 (million) 3.93/0.88 % (16615)------------------------------ 3.93/0.88 % (16615)------------------------------ 3.93/0.90 % (16620)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 Vampire---4 for (1794ds/37Mi) 3.93/0.90 % (16619)Instruction limit reached! 3.93/0.90 % (16619)------------------------------ 3.93/0.90 % (16619)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.93/0.90 % (16619)Termination reason: Unknown 3.93/0.90 % (16619)Termination phase: Property scanning 3.93/0.90 3.93/0.90 % (16619)Memory used [KB]: 1918 3.93/0.90 % (16619)Time elapsed: 0.022 s 3.93/0.90 % (16619)Instructions burned: 47 (million) 3.93/0.90 % (16619)------------------------------ 3.93/0.90 % (16619)------------------------------ 3.93/0.90 % (16574)Instruction limit reached! 3.93/0.90 % (16574)------------------------------ 3.93/0.90 % (16574)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.93/0.90 % (16574)Termination reason: Unknown 3.93/0.90 % (16574)Termination phase: Saturation 3.93/0.90 3.93/0.90 % (16574)Memory used [KB]: 10746 3.93/0.90 % (16574)Time elapsed: 0.524 s 3.93/0.90 % (16574)Instructions burned: 1021 (million) 3.93/0.90 % (16574)------------------------------ 3.93/0.90 % (16574)------------------------------ 3.93/0.91 % (16621)lrs+1002_1:16_av=off:e2e=on:fe=axiom:prag=on:sos=on:ss=axioms:i=3:si=on:rtra=on_0 on Vampire---4 for (1794ds/3Mi) 3.93/0.91 % (16621)Instruction limit reached! 3.93/0.91 % (16621)------------------------------ 3.93/0.91 % (16621)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.93/0.91 % (16621)Termination reason: Unknown 3.93/0.91 % (16621)Termination phase: shuffling 3.93/0.91 3.93/0.91 % (16621)Memory used [KB]: 1407 3.93/0.91 % (16621)Time elapsed: 0.003 s 3.93/0.91 % (16621)Instructions burned: 3 (million) 3.93/0.91 % (16621)------------------------------ 3.93/0.91 % (16621)------------------------------ 3.93/0.91 % (16620)Instruction limit reached! 3.93/0.91 % (16620)------------------------------ 3.93/0.91 % (16620)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.93/0.91 % (16620)Termination reason: Unknown 3.93/0.91 % (16620)Termination phase: Property scanning 3.93/0.91 3.93/0.91 % (16620)Memory used [KB]: 2046 3.93/0.91 % (16620)Time elapsed: 0.018 s 3.93/0.91 % (16620)Instructions burned: 37 (million) 3.93/0.91 % (16620)------------------------------ 3.93/0.91 % (16620)------------------------------ 3.93/0.92 % (16577)Instruction limit reached! 3.93/0.92 % (16577)------------------------------ 3.93/0.92 % (16577)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.93/0.92 % (16577)Termination reason: Unknown 3.93/0.92 % (16577)Termination phase: Saturation 3.93/0.92 3.93/0.92 % (16577)Memory used [KB]: 8827 3.93/0.92 % (16577)Time elapsed: 0.520 s 3.93/0.92 % (16577)Instructions burned: 1044 (million) 3.93/0.92 % (16577)------------------------------ 3.93/0.92 % (16577)------------------------------ 3.93/0.92 % (16622)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 Vampire---4 for (1794ds/19Mi) 3.93/0.92 % (16607)Instruction limit reached! 3.93/0.92 % (16607)------------------------------ 3.93/0.92 % (16607)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 3.93/0.92 % (16607)Termination reason: Unknown 3.93/0.92 % (16607)Termination phase: Saturation 3.93/0.92 3.93/0.92 % (16607)Memory used [KB]: 6908 3.93/0.92 % (16607)Time elapsed: 0.163 s 3.93/0.92 % (16607)Instructions burned: 451 (million) 3.93/0.92 % (16607)------------------------------ 3.93/0.92 % (16607)------------------------------ 4.35/0.93 % (16623)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 Vampire---4 for (1794ds/5Mi) 4.35/0.93 % (16622)Instruction limit reached! 4.35/0.93 % (16622)------------------------------ 4.35/0.93 % (16622)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 4.35/0.93 % (16622)Termination reason: Unknown 4.35/0.93 % (16622)Termination phase: Property scanning 4.35/0.93 4.35/0.93 % (16622)Memory used [KB]: 1663 4.35/0.93 % (16622)Time elapsed: 0.011 s 4.35/0.93 % (16622)Instructions burned: 19 (million) 4.35/0.93 % (16622)------------------------------ 4.35/0.93 % (16622)------------------------------ 4.35/0.93 % (16624)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 Vampire---4 for (1794ds/44Mi) 4.35/0.93 % (16623)Instruction limit reached! 4.35/0.93 % (16623)------------------------------ 4.35/0.93 % (16623)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 4.35/0.93 % (16623)Termination reason: Unknown 4.35/0.93 % (16623)Termination phase: shuffling 4.35/0.93 4.35/0.93 % (16623)Memory used [KB]: 1407 4.35/0.93 % (16623)Time elapsed: 0.004 s 4.35/0.93 % (16623)Instructions burned: 5 (million) 4.35/0.93 % (16623)------------------------------ 4.35/0.93 % (16623)------------------------------ 4.35/0.93 % (16625)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 Vampire---4 for (1794ds/450Mi) 4.35/0.93 % (16626)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=102:si=on:rtra=on_0 on Vampire---4 for (1794ds/102Mi) 4.35/0.94 % (16627)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on Vampire---4 for (1794ds/134Mi) 4.35/0.94 % (16628)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 Vampire---4 for (1794ds/204Mi) 4.35/0.95 % (16624)Instruction limit reached! 4.35/0.95 % (16624)------------------------------ 4.35/0.95 % (16624)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 4.35/0.95 % (16624)Termination reason: Unknown 4.35/0.95 % (16624)Termination phase: Property scanning 4.35/0.95 4.35/0.95 % (16624)Memory used [KB]: 2174 4.35/0.95 % (16624)Time elapsed: 0.021 s 4.35/0.95 % (16624)Instructions burned: 46 (million) 4.35/0.95 % (16624)------------------------------ 4.35/0.95 % (16624)------------------------------ 4.42/0.96 % (16629)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 Vampire---4 for (1793ds/154Mi) 4.42/0.98 % (16626)Instruction limit reached! 4.42/0.98 % (16626)------------------------------ 4.42/0.98 % (16626)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 4.42/0.98 % (16626)Termination reason: Unknown 4.42/0.98 % (16626)Termination phase: Property scanning 4.42/0.98 4.42/0.98 % (16626)Memory used [KB]: 3454 4.42/0.98 % (16626)Time elapsed: 0.048 s 4.42/0.98 % (16626)Instructions burned: 103 (million) 4.42/0.98 % (16626)------------------------------ 4.42/0.98 % (16626)------------------------------ 4.42/0.98 % (16618)Instruction limit reached! 4.42/0.98 % (16618)------------------------------ 4.42/0.98 % (16618)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 4.42/0.98 % (16618)Termination reason: Unknown 4.42/0.98 % (16618)Termination phase: Saturation 4.42/0.98 4.42/0.98 % (16618)Memory used [KB]: 7547 4.42/0.98 % (16618)Time elapsed: 0.124 s 4.42/0.98 % (16618)Instructions burned: 275 (million) 4.42/0.98 % (16618)------------------------------ 4.42/0.98 % (16618)------------------------------ 4.42/0.99 % (16617)Instruction limit reached! 4.42/0.99 % (16617)------------------------------ 4.42/0.99 % (16617)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 4.42/0.99 % (16617)Termination reason: Unknown 4.42/0.99 % (16617)Termination phase: Saturation 4.42/0.99 4.42/0.99 % (16617)Memory used [KB]: 8059 4.42/0.99 % (16617)Time elapsed: 0.136 s 4.42/0.99 % (16617)Instructions burned: 295 (million) 4.42/0.99 % (16617)------------------------------ 4.42/0.99 % (16617)------------------------------ 4.42/0.99 % (16630)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 Vampire---4 for (1793ds/424Mi) 4.42/1.00 % (16627)Instruction limit reached! 4.42/1.00 % (16627)------------------------------ 4.42/1.00 % (16627)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 4.42/1.00 % (16627)Termination reason: Unknown 4.42/1.00 % (16627)Termination phase: Saturation 4.42/1.00 4.42/1.00 % (16627)Memory used [KB]: 7036 4.42/1.00 % (16627)Time elapsed: 0.058 s 4.42/1.00 % (16627)Instructions burned: 135 (million) 4.42/1.00 % (16627)------------------------------ 4.42/1.00 % (16627)------------------------------ 4.42/1.00 % (16631)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 Vampire---4 for (1793ds/41Mi) 4.42/1.00 % (16632)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 Vampire---4 for (1793ds/231Mi) 4.42/1.01 % (16633)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 Vampire---4 for (1793ds/70Mi) 4.42/1.02 % (16631)Instruction limit reached! 4.42/1.02 % (16631)------------------------------ 4.42/1.02 % (16631)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 4.42/1.02 % (16631)Termination reason: Unknown 4.42/1.02 % (16631)Termination phase: Property scanning 4.42/1.02 4.42/1.02 % (16631)Memory used [KB]: 2174 4.42/1.02 % (16631)Time elapsed: 0.020 s 4.42/1.02 % (16631)Instructions burned: 42 (million) 4.42/1.02 % (16631)------------------------------ 4.42/1.02 % (16631)------------------------------ 4.42/1.02 % (16629)Instruction limit reached! 4.42/1.02 % (16629)------------------------------ 4.42/1.02 % (16629)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 4.42/1.02 % (16629)Termination reason: Unknown 4.42/1.02 % (16629)Termination phase: Saturation 4.42/1.02 4.42/1.02 % (16629)Memory used [KB]: 6908 4.42/1.02 % (16629)Time elapsed: 0.064 s 4.42/1.02 % (16629)Instructions burned: 154 (million) 4.42/1.02 % (16629)------------------------------ 4.42/1.02 % (16629)------------------------------ 4.94/1.03 % (16628)Instruction limit reached! 4.94/1.03 % (16628)------------------------------ 4.94/1.03 % (16628)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 4.94/1.03 % (16628)Termination reason: Unknown 4.94/1.03 % (16628)Termination phase: Saturation 4.94/1.03 4.94/1.03 % (16628)Memory used [KB]: 7547 4.94/1.03 % (16628)Time elapsed: 0.089 s 4.94/1.03 % (16628)Instructions burned: 204 (million) 4.94/1.03 % (16628)------------------------------ 4.94/1.03 % (16628)------------------------------ 4.94/1.03 % (16634)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 Vampire---4 for (1793ds/297Mi) 4.94/1.03 % (16635)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 Vampire---4 for (1793ds/182Mi) 4.94/1.04 % (16633)Instruction limit reached! 4.94/1.04 % (16633)------------------------------ 4.94/1.04 % (16633)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 4.94/1.04 % (16633)Termination reason: Unknown 4.94/1.04 % (16633)Termination phase: Function definition elimination 4.94/1.04 4.94/1.04 % (16633)Memory used [KB]: 2174 4.94/1.04 % (16633)Time elapsed: 0.032 s 4.94/1.04 % (16633)Instructions burned: 72 (million) 4.94/1.04 % (16633)------------------------------ 4.94/1.04 % (16633)------------------------------ 4.94/1.04 % (16636)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 Vampire---4 for (1793ds/130Mi) 4.94/1.05 % (16637)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 Vampire---4 for (1793ds/570Mi) 4.94/1.07 % (16603)Instruction limit reached! 4.94/1.07 % (16603)------------------------------ 4.94/1.07 % (16603)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 4.94/1.07 % (16603)Termination reason: Unknown 4.94/1.07 % (16603)Termination phase: Saturation 4.94/1.07 4.94/1.07 % (16603)Memory used [KB]: 9850 4.94/1.07 % (16603)Time elapsed: 0.355 s 4.94/1.07 % (16603)Instructions burned: 721 (million) 4.94/1.07 % (16603)------------------------------ 4.94/1.07 % (16603)------------------------------ 5.94/1.08 % (16638)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 Vampire---4 for (1792ds/297Mi) 5.94/1.10 % (16625)Instruction limit reached! 5.94/1.10 % (16625)------------------------------ 5.94/1.10 % (16625)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 5.94/1.10 % (16625)Termination reason: Unknown 5.94/1.10 % (16625)Termination phase: Saturation 5.94/1.10 5.94/1.10 % (16625)Memory used [KB]: 7931 5.94/1.10 % (16625)Time elapsed: 0.169 s 5.94/1.10 % (16625)Instructions burned: 450 (million) 5.94/1.10 % (16625)------------------------------ 5.94/1.10 % (16625)------------------------------ 5.94/1.10 % (16636)Instruction limit reached! 5.94/1.10 % (16636)------------------------------ 5.94/1.10 % (16636)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 5.94/1.10 % (16636)Termination reason: Unknown 5.94/1.10 % (16636)Termination phase: Saturation 5.94/1.10 5.94/1.10 % (16636)Memory used [KB]: 7036 5.94/1.10 % (16636)Time elapsed: 0.057 s 5.94/1.10 % (16636)Instructions burned: 130 (million) 5.94/1.10 % (16636)------------------------------ 5.94/1.10 % (16636)------------------------------ 5.94/1.11 % (16632)Instruction limit reached! 5.94/1.11 % (16632)------------------------------ 5.94/1.11 % (16632)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 5.94/1.11 % (16632)Termination reason: Unknown 5.94/1.11 % (16632)Termination phase: Saturation 5.94/1.11 5.94/1.11 % (16632)Memory used [KB]: 12281 5.94/1.11 % (16632)Time elapsed: 0.107 s 5.94/1.11 % (16632)Instructions burned: 231 (million) 5.94/1.11 % (16632)------------------------------ 5.94/1.11 % (16632)------------------------------ 5.94/1.11 % (16639)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=190:si=on:rtra=on_0 on Vampire---4 for (1792ds/190Mi) 5.94/1.11 % (16640)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on Vampire---4 for (1792ds/96Mi) 5.94/1.11 % (16635)Instruction limit reached! 5.94/1.11 % (16635)------------------------------ 5.94/1.11 % (16635)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 5.94/1.11 % (16635)Termination reason: Unknown 5.94/1.11 % (16635)Termination phase: Saturation 5.94/1.11 5.94/1.11 % (16635)Memory used [KB]: 7547 5.94/1.11 % (16635)Time elapsed: 0.081 s 5.94/1.11 % (16635)Instructions burned: 183 (million) 5.94/1.11 % (16635)------------------------------ 5.94/1.11 % (16635)------------------------------ 5.94/1.12 % (16641)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 Vampire---4 for (1792ds/182Mi) 5.94/1.13 % (16642)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on Vampire---4 for (1792ds/368Mi) 5.94/1.15 % (16640)Instruction limit reached! 5.94/1.15 % (16640)------------------------------ 5.94/1.15 % (16640)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 5.94/1.15 % (16640)Termination reason: Unknown 5.94/1.15 % (16640)Termination phase: Property scanning 5.94/1.15 5.94/1.15 % (16640)Memory used [KB]: 2302 5.94/1.15 % (16640)Time elapsed: 0.041 s 5.94/1.15 % (16640)Instructions burned: 96 (million) 5.94/1.15 % (16640)------------------------------ 5.94/1.15 % (16640)------------------------------ 6.35/1.16 % (16634)Instruction limit reached! 6.35/1.16 % (16634)------------------------------ 6.35/1.16 % (16634)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 6.35/1.16 % (16634)Termination reason: Unknown 6.35/1.16 % (16634)Termination phase: Saturation 6.35/1.16 6.35/1.16 % (16634)Memory used [KB]: 8059 6.35/1.16 % (16634)Time elapsed: 0.135 s 6.35/1.16 % (16634)Instructions burned: 297 (million) 6.35/1.16 % (16634)------------------------------ 6.35/1.16 % (16634)------------------------------ 6.35/1.16 % (16643)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 Vampire---4 for (1791ds/390Mi) 6.35/1.18 % (16644)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on Vampire---4 for (1791ds/192Mi) 6.40/1.20 % (16639)Instruction limit reached! 6.40/1.20 % (16639)------------------------------ 6.40/1.20 % (16639)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 6.40/1.20 % (16639)Termination reason: Unknown 6.40/1.20 % (16639)Termination phase: Saturation 6.40/1.20 6.40/1.20 % (16639)Memory used [KB]: 8187 6.40/1.20 % (16639)Time elapsed: 0.088 s 6.40/1.20 % (16639)Instructions burned: 190 (million) 6.40/1.20 % (16639)------------------------------ 6.40/1.20 % (16639)------------------------------ 6.40/1.20 % (16638)Instruction limit reached! 6.40/1.20 % (16638)------------------------------ 6.40/1.20 % (16638)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 6.40/1.20 % (16638)Termination reason: Unknown 6.40/1.20 % (16638)Termination phase: Saturation 6.40/1.20 6.40/1.20 % (16638)Memory used [KB]: 8443 6.40/1.20 % (16638)Time elapsed: 0.114 s 6.40/1.20 % (16638)Instructions burned: 297 (million) 6.40/1.20 % (16638)------------------------------ 6.40/1.20 % (16638)------------------------------ 6.40/1.21 % (16641)Instruction limit reached! 6.40/1.21 % (16641)------------------------------ 6.40/1.21 % (16641)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 6.40/1.21 % (16641)Termination reason: Unknown 6.40/1.21 % (16641)Termination phase: Saturation 6.40/1.21 6.40/1.21 % (16641)Memory used [KB]: 10362 6.40/1.21 % (16641)Time elapsed: 0.088 s 6.40/1.21 % (16641)Instructions burned: 182 (million) 6.40/1.21 % (16641)------------------------------ 6.40/1.21 % (16641)------------------------------ 6.40/1.21 % (16630)Instruction limit reached! 6.40/1.21 % (16630)------------------------------ 6.40/1.21 % (16630)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 6.40/1.21 % (16630)Termination reason: Unknown 6.40/1.21 % (16630)Termination phase: Saturation 6.40/1.21 6.40/1.21 % (16630)Memory used [KB]: 9466 6.40/1.21 % (16630)Time elapsed: 0.221 s 6.40/1.21 % (16630)Instructions burned: 425 (million) 6.40/1.21 % (16630)------------------------------ 6.40/1.21 % (16630)------------------------------ 6.40/1.21 % (16645)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=279:si=on:rtra=on_0 on Vampire---4 for (1791ds/279Mi) 6.40/1.21 % (16646)lrs+1010_1:1024_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:ixr=off:i=25:si=on:rtra=on_0 on Vampire---4 for (1791ds/25Mi) 6.40/1.22 % (16647)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 Vampire---4 for (1791ds/940Mi) 6.40/1.22 % (16646)Instruction limit reached! 6.40/1.22 % (16646)------------------------------ 6.40/1.22 % (16646)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 6.40/1.22 % (16646)Termination reason: Unknown 6.40/1.22 % (16646)Termination phase: shuffling 6.40/1.22 6.40/1.22 % (16646)Memory used [KB]: 1918 6.40/1.22 % (16646)Time elapsed: 0.013 s 6.40/1.22 % (16646)Instructions burned: 26 (million) 6.40/1.22 % (16646)------------------------------ 6.40/1.22 % (16646)------------------------------ 6.40/1.22 % (16648)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 Vampire---4 for (1791ds/422Mi) 6.84/1.24 % (16649)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 Vampire---4 for (1791ds/103Mi) 6.86/1.26 % (16644)Instruction limit reached! 6.86/1.26 % (16644)------------------------------ 6.86/1.26 % (16644)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 6.86/1.26 % (16644)Termination reason: Unknown 6.86/1.26 % (16644)Termination phase: Saturation 6.86/1.26 6.86/1.26 % (16644)Memory used [KB]: 7547 6.86/1.26 % (16644)Time elapsed: 0.086 s 6.86/1.26 % (16644)Instructions burned: 193 (million) 6.86/1.26 % (16644)------------------------------ 6.86/1.26 % (16644)------------------------------ 6.86/1.27 % (16637)Instruction limit reached! 6.86/1.27 % (16637)------------------------------ 6.86/1.27 % (16637)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 6.86/1.27 % (16637)Termination reason: Unknown 6.86/1.27 % (16637)Termination phase: Saturation 6.86/1.27 6.86/1.27 % (16637)Memory used [KB]: 11129 6.86/1.27 % (16637)Time elapsed: 0.237 s 6.86/1.27 % (16637)Instructions burned: 572 (million) 6.86/1.27 % (16637)------------------------------ 6.86/1.27 % (16637)------------------------------ 6.86/1.27 % (16650)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 Vampire---4 for (1790ds/182Mi) 6.86/1.28 % (16649)Instruction limit reached! 6.86/1.28 % (16649)------------------------------ 6.86/1.28 % (16649)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 6.86/1.28 % (16649)Termination reason: Unknown 6.86/1.28 % (16649)Termination phase: Saturation 6.86/1.28 6.86/1.28 % (16649)Memory used [KB]: 6780 6.86/1.28 % (16649)Time elapsed: 0.045 s 6.86/1.28 % (16649)Instructions burned: 104 (million) 6.86/1.28 % (16649)------------------------------ 6.86/1.28 % (16649)------------------------------ 6.86/1.28 % (16642)Instruction limit reached! 6.86/1.28 % (16642)------------------------------ 6.86/1.28 % (16642)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 6.86/1.28 % (16642)Termination reason: Unknown 6.86/1.28 % (16642)Termination phase: Saturation 6.86/1.28 6.86/1.28 % (16642)Memory used [KB]: 7931 6.86/1.28 % (16642)Time elapsed: 0.158 s 6.86/1.28 % (16642)Instructions burned: 369 (million) 6.86/1.28 % (16642)------------------------------ 6.86/1.28 % (16642)------------------------------ 6.86/1.29 % (16651)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 Vampire---4 for (1790ds/230Mi) 6.86/1.29 % (16652)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on Vampire---4 for (1790ds/83Mi) 6.86/1.30 % (16653)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 Vampire---4 for (1790ds/202Mi) 7.23/1.32 % (16645)Instruction limit reached! 7.23/1.32 % (16645)------------------------------ 7.23/1.32 % (16645)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 7.23/1.32 % (16645)Termination reason: Unknown 7.23/1.32 % (16645)Termination phase: Saturation 7.23/1.32 7.23/1.32 % (16645)Memory used [KB]: 6908 7.23/1.32 % (16645)Time elapsed: 0.110 s 7.23/1.32 % (16645)Instructions burned: 279 (million) 7.23/1.32 % (16645)------------------------------ 7.23/1.32 % (16645)------------------------------ 7.23/1.33 % (16652)Instruction limit reached! 7.23/1.33 % (16652)------------------------------ 7.23/1.33 % (16652)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 7.23/1.33 % (16652)Termination reason: Unknown 7.23/1.33 % (16652)Termination phase: Function definition elimination 7.23/1.33 7.23/1.33 % (16652)Memory used [KB]: 2046 7.23/1.33 % (16652)Time elapsed: 0.037 s 7.23/1.33 % (16652)Instructions burned: 85 (million) 7.23/1.33 % (16652)------------------------------ 7.23/1.33 % (16652)------------------------------ 7.23/1.33 % (16654)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 Vampire---4 for (1790ds/148Mi) 7.23/1.34 % (16655)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on Vampire---4 for (1790ds/104Mi) 7.23/1.34 % (16643)Instruction limit reached! 7.23/1.34 % (16643)------------------------------ 7.23/1.34 % (16643)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 7.23/1.34 % (16643)Termination reason: Unknown 7.23/1.34 % (16643)Termination phase: Saturation 7.23/1.34 7.23/1.34 % (16643)Memory used [KB]: 8315 7.23/1.34 % (16643)Time elapsed: 0.183 s 7.23/1.34 % (16643)Instructions burned: 391 (million) 7.23/1.34 % (16643)------------------------------ 7.23/1.34 % (16643)------------------------------ 7.23/1.35 % (16650)Instruction limit reached! 7.23/1.35 % (16650)------------------------------ 7.23/1.35 % (16650)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 7.23/1.35 % (16650)Termination reason: Unknown 7.23/1.35 % (16650)Termination phase: Saturation 7.23/1.35 7.23/1.35 % (16650)Memory used [KB]: 6908 7.23/1.35 % (16650)Time elapsed: 0.075 s 7.23/1.35 % (16650)Instructions burned: 183 (million) 7.23/1.35 % (16650)------------------------------ 7.23/1.35 % (16650)------------------------------ 7.23/1.36 % (16656)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on Vampire---4 for (1789ds/6Mi) 7.23/1.36 % (16656)Instruction limit reached! 7.23/1.36 % (16656)------------------------------ 7.23/1.36 % (16656)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 7.23/1.36 % (16656)Termination reason: Unknown 7.23/1.36 % (16656)Termination phase: shuffling 7.23/1.36 7.23/1.36 % (16656)Memory used [KB]: 1407 7.23/1.36 % (16656)Time elapsed: 0.004 s 7.23/1.36 % (16656)Instructions burned: 6 (million) 7.23/1.36 % (16656)------------------------------ 7.23/1.36 % (16656)------------------------------ 7.23/1.36 % (16657)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 Vampire---4 for (1789ds/1200Mi) 7.71/1.37 % (16658)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 Vampire---4 for (1789ds/90Mi) 7.71/1.38 % (16653)Instruction limit reached! 7.71/1.38 % (16653)------------------------------ 7.71/1.38 % (16653)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 7.71/1.38 % (16653)Termination reason: Unknown 7.71/1.38 % (16653)Termination phase: Saturation 7.71/1.38 7.71/1.38 % (16653)Memory used [KB]: 6908 7.71/1.38 % (16653)Time elapsed: 0.082 s 7.71/1.38 % (16653)Instructions burned: 203 (million) 7.71/1.38 % (16653)------------------------------ 7.71/1.38 % (16653)------------------------------ 7.71/1.38 % (16655)Instruction limit reached! 7.71/1.38 % (16655)------------------------------ 7.71/1.38 % (16655)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 7.71/1.38 % (16655)Termination reason: Unknown 7.71/1.38 % (16655)Termination phase: Saturation 7.71/1.38 7.71/1.38 % (16655)Memory used [KB]: 6908 7.71/1.38 % (16655)Time elapsed: 0.046 s 7.71/1.38 % (16655)Instructions burned: 104 (million) 7.71/1.38 % (16655)------------------------------ 7.71/1.38 % (16655)------------------------------ 7.71/1.39 % (16651)Instruction limit reached! 7.71/1.39 % (16651)------------------------------ 7.71/1.39 % (16651)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 7.71/1.39 % (16651)Termination reason: Unknown 7.71/1.39 % (16651)Termination phase: Saturation 7.71/1.39 7.71/1.39 % (16651)Memory used [KB]: 3326 7.71/1.39 % (16651)Time elapsed: 0.101 s 7.71/1.39 % (16651)Instructions burned: 230 (million) 7.71/1.39 % (16651)------------------------------ 7.71/1.39 % (16651)------------------------------ 7.71/1.39 % (16659)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 Vampire---4 for (1789ds/164Mi) 7.71/1.39 % (16654)Instruction limit reached! 7.71/1.39 % (16654)------------------------------ 7.71/1.39 % (16654)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 7.71/1.39 % (16654)Termination reason: Unknown 7.71/1.39 % (16654)Termination phase: Saturation 7.71/1.39 7.71/1.39 % (16654)Memory used [KB]: 6908 7.71/1.39 % (16654)Time elapsed: 0.061 s 7.71/1.39 % (16654)Instructions burned: 150 (million) 7.71/1.39 % (16654)------------------------------ 7.71/1.39 % (16654)------------------------------ 7.71/1.40 % (16660)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 Vampire---4 for (1789ds/392Mi) 7.71/1.40 % (16661)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on Vampire---4 for (1789ds/279Mi) 7.71/1.40 % (16662)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 Vampire---4 for (1789ds/59Mi) 7.71/1.41 % (16658)Instruction limit reached! 7.71/1.41 % (16658)------------------------------ 7.71/1.41 % (16658)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 7.71/1.41 % (16658)Termination reason: Unknown 7.71/1.41 % (16658)Termination phase: Twee Goal Transformation 7.71/1.41 7.71/1.41 % (16658)Memory used [KB]: 2558 7.71/1.41 % (16658)Time elapsed: 0.040 s 7.71/1.41 % (16658)Instructions burned: 90 (million) 7.71/1.41 % (16658)------------------------------ 7.71/1.41 % (16658)------------------------------ 7.71/1.43 % (16663)lrs+10_1:1_au=on:sd=1:sgt=32:sos=on:ss=axioms:i=141:si=on:rtra=on_0 on Vampire---4 for (1789ds/141Mi) 7.71/1.43 % (16662)Instruction limit reached! 7.71/1.43 % (16662)------------------------------ 7.71/1.43 % (16662)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 7.71/1.43 % (16662)Termination reason: Unknown 7.71/1.43 % (16662)Termination phase: Property scanning 7.71/1.43 7.71/1.43 % (16662)Memory used [KB]: 2174 7.71/1.43 % (16662)Time elapsed: 0.027 s 7.71/1.43 % (16662)Instructions burned: 60 (million) 7.71/1.43 % (16662)------------------------------ 7.71/1.43 % (16662)------------------------------ 7.71/1.44 % (16664)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=389:si=on:rtra=on_0 on Vampire---4 for (1789ds/389Mi) 7.71/1.44 % (16648)Instruction limit reached! 7.71/1.44 % (16648)------------------------------ 7.71/1.44 % (16648)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 7.71/1.45 % (16648)Termination reason: Unknown 7.71/1.45 % (16648)Termination phase: Saturation 7.71/1.45 7.71/1.45 % (16648)Memory used [KB]: 10106 7.71/1.45 % (16648)Time elapsed: 0.223 s 7.71/1.45 % (16648)Instructions burned: 423 (million) 7.71/1.45 % (16648)------------------------------ 7.71/1.45 % (16648)------------------------------ 8.36/1.46 % (16665)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on Vampire---4 for (1788ds/593Mi) 8.36/1.46 % (16659)Instruction limit reached! 8.36/1.46 % (16659)------------------------------ 8.36/1.46 % (16659)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 8.36/1.46 % (16659)Termination reason: Unknown 8.36/1.46 % (16659)Termination phase: Saturation 8.36/1.46 8.36/1.46 % (16659)Memory used [KB]: 2430 8.36/1.46 % (16659)Time elapsed: 0.072 s 8.36/1.46 % (16659)Instructions burned: 165 (million) 8.36/1.46 % (16659)------------------------------ 8.36/1.46 % (16659)------------------------------ 8.36/1.47 % (16666)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 Vampire---4 for (1788ds/4759Mi) 8.44/1.49 % (16663)Instruction limit reached! 8.44/1.49 % (16663)------------------------------ 8.44/1.49 % (16663)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 8.44/1.49 % (16663)Termination reason: Unknown 8.44/1.49 % (16663)Termination phase: Saturation 8.44/1.49 8.44/1.49 % (16663)Memory used [KB]: 7036 8.44/1.49 % (16663)Time elapsed: 0.062 s 8.44/1.49 % (16663)Instructions burned: 141 (million) 8.44/1.49 % (16663)------------------------------ 8.44/1.49 % (16663)------------------------------ 8.44/1.50 % (16667)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on Vampire---4 for (1788ds/906Mi) 8.44/1.51 % (16661)Instruction limit reached! 8.44/1.51 % (16661)------------------------------ 8.44/1.51 % (16661)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 8.44/1.51 % (16661)Termination reason: Unknown 8.44/1.51 % (16661)Termination phase: Saturation 8.44/1.51 8.44/1.51 % (16661)Memory used [KB]: 6908 8.44/1.51 % (16661)Time elapsed: 0.107 s 8.44/1.51 % (16661)Instructions burned: 281 (million) 8.44/1.51 % (16661)------------------------------ 8.44/1.51 % (16661)------------------------------ 8.44/1.52 % (16668)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 Vampire---4 for (1788ds/668Mi) 8.64/1.54 % (16647)Instruction limit reached! 8.64/1.54 % (16647)------------------------------ 8.64/1.54 % (16647)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 8.64/1.54 % (16647)Termination reason: Unknown 8.64/1.54 % (16647)Termination phase: Saturation 8.64/1.54 8.64/1.54 % (16647)Memory used [KB]: 7036 8.64/1.54 % (16647)Time elapsed: 0.320 s 8.64/1.54 % (16647)Instructions burned: 942 (million) 8.64/1.54 % (16647)------------------------------ 8.64/1.54 % (16647)------------------------------ 8.64/1.54 % (16660)Instruction limit reached! 8.64/1.54 % (16660)------------------------------ 8.64/1.54 % (16660)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 8.64/1.54 % (16660)Termination reason: Unknown 8.64/1.54 % (16660)Termination phase: Saturation 8.64/1.54 8.64/1.54 % (16660)Memory used [KB]: 10746 8.64/1.54 % (16660)Time elapsed: 0.145 s 8.64/1.54 % (16660)Instructions burned: 394 (million) 8.64/1.54 % (16660)------------------------------ 8.64/1.54 % (16660)------------------------------ 8.64/1.55 % (16669)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 Vampire---4 for (1788ds/1670Mi) 8.64/1.56 % (16670)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on Vampire---4 for (1788ds/794Mi) 10.26/1.63 % (16664)Instruction limit reached! 10.26/1.63 % (16664)------------------------------ 10.26/1.63 % (16664)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 10.26/1.63 % (16664)Termination reason: Unknown 10.26/1.63 % (16664)Termination phase: Saturation 10.26/1.63 10.26/1.63 % (16664)Memory used [KB]: 9210 10.26/1.63 % (16664)Time elapsed: 0.192 s 10.26/1.63 % (16664)Instructions burned: 389 (million) 10.26/1.63 % (16664)------------------------------ 10.26/1.63 % (16664)------------------------------ 10.26/1.65 % (16671)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 Vampire---4 for (1787ds/294Mi) 10.69/1.75 % (16665)Instruction limit reached! 10.69/1.75 % (16665)------------------------------ 10.69/1.75 % (16665)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 10.69/1.75 % (16665)Termination reason: Unknown 10.69/1.75 % (16665)Termination phase: Saturation 10.69/1.75 10.69/1.75 % (16665)Memory used [KB]: 8571 10.69/1.75 % (16665)Time elapsed: 0.291 s 10.69/1.75 % (16665)Instructions burned: 593 (million) 10.69/1.75 % (16665)------------------------------ 10.69/1.75 % (16665)------------------------------ 10.69/1.76 % (16672)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 Vampire---4 for (1785ds/970Mi) 10.69/1.77 % (16671)Instruction limit reached! 10.69/1.77 % (16671)------------------------------ 10.69/1.77 % (16671)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 10.69/1.77 % (16671)Termination reason: Unknown 10.69/1.77 % (16671)Termination phase: Saturation 10.69/1.77 10.69/1.77 % (16671)Memory used [KB]: 6908 10.69/1.77 % (16671)Time elapsed: 0.120 s 10.69/1.77 % (16671)Instructions burned: 296 (million) 10.69/1.77 % (16671)------------------------------ 10.69/1.77 % (16671)------------------------------ 11.42/1.77 % (16668)Instruction limit reached! 11.42/1.77 % (16668)------------------------------ 11.42/1.77 % (16668)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 11.42/1.77 % (16668)Termination reason: Unknown 11.42/1.77 % (16668)Termination phase: Saturation 11.42/1.77 11.42/1.77 % (16668)Memory used [KB]: 15479 11.42/1.77 % (16668)Time elapsed: 0.269 s 11.42/1.77 % (16668)Instructions burned: 671 (million) 11.42/1.77 % (16668)------------------------------ 11.42/1.77 % (16668)------------------------------ 11.42/1.78 % (16673)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 Vampire---4 for (1785ds/383Mi) 11.49/1.79 % (16674)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 Vampire---4 for (1785ds/961Mi) 12.13/1.94 % (16670)Instruction limit reached! 12.13/1.94 % (16670)------------------------------ 12.13/1.94 % (16670)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 12.13/1.94 % (16670)Termination reason: Unknown 12.13/1.94 % (16670)Termination phase: Saturation 12.13/1.94 12.13/1.94 % (16670)Memory used [KB]: 5117 12.13/1.94 % (16670)Time elapsed: 0.388 s 12.13/1.94 % (16670)Instructions burned: 795 (million) 12.13/1.94 % (16670)------------------------------ 12.13/1.94 % (16670)------------------------------ 12.13/1.95 % (16667)Instruction limit reached! 12.13/1.95 % (16667)------------------------------ 12.13/1.95 % (16667)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 12.13/1.95 % (16667)Termination reason: Unknown 12.13/1.95 % (16667)Termination phase: Saturation 12.13/1.95 12.13/1.95 % (16667)Memory used [KB]: 9850 12.13/1.95 % (16667)Time elapsed: 0.451 s 12.13/1.95 % (16667)Instructions burned: 906 (million) 12.13/1.95 % (16667)------------------------------ 12.13/1.95 % (16667)------------------------------ 12.13/1.96 % (16676)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=1083:si=on:rtra=on_0 on Vampire---4 for (1784ds/1083Mi) 12.13/1.96 % (16677)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=1398:si=on:rtra=on_0 on Vampire---4 for (1783ds/1398Mi) 12.13/1.97 % (16657)Instruction limit reached! 12.13/1.97 % (16657)------------------------------ 12.13/1.97 % (16657)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 12.13/1.97 % (16657)Termination reason: Unknown 12.13/1.97 % (16657)Termination phase: Saturation 12.13/1.97 12.13/1.97 % (16657)Memory used [KB]: 11641 12.13/1.97 % (16657)Time elapsed: 0.609 s 12.13/1.97 % (16657)Instructions burned: 1201 (million) 12.13/1.97 % (16657)------------------------------ 12.13/1.97 % (16657)------------------------------ 12.13/1.97 % (16673)Instruction limit reached! 12.13/1.97 % (16673)------------------------------ 12.13/1.97 % (16673)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 12.13/1.97 % (16673)Termination reason: Unknown 12.13/1.97 % (16673)Termination phase: Saturation 12.13/1.97 12.13/1.97 % (16673)Memory used [KB]: 10234 12.13/1.97 % (16673)Time elapsed: 0.218 s 12.13/1.97 % (16673)Instructions burned: 383 (million) 12.13/1.97 % (16673)------------------------------ 12.13/1.97 % (16673)------------------------------ 12.65/1.98 % (16678)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 Vampire---4 for (1783ds/562Mi) 12.65/1.99 % (16679)lrs+1010_1:2_au=on:e2e=on:sd=3:ss=axioms:st=3.0:i=1208:si=on:rtra=on_0 on Vampire---4 for (1783ds/1208Mi) 12.86/2.10 % (16672)Instruction limit reached! 12.86/2.10 % (16672)------------------------------ 12.86/2.10 % (16672)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 12.86/2.10 % (16672)Termination reason: Unknown 12.86/2.10 % (16672)Termination phase: Saturation 12.86/2.10 12.86/2.10 % (16672)Memory used [KB]: 10746 12.86/2.10 % (16672)Time elapsed: 0.344 s 12.86/2.10 % (16672)Instructions burned: 971 (million) 12.86/2.10 % (16672)------------------------------ 12.86/2.10 % (16672)------------------------------ 13.27/2.12 % (16680)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 Vampire---4 for (1782ds/348Mi) 13.27/2.13 % (16669)Instruction limit reached! 13.27/2.13 % (16669)------------------------------ 13.27/2.13 % (16669)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 13.27/2.13 % (16669)Termination reason: Unknown 13.27/2.13 % (16669)Termination phase: Saturation 13.27/2.13 13.27/2.13 % (16669)Memory used [KB]: 11641 13.27/2.13 % (16669)Time elapsed: 0.578 s 13.27/2.13 % (16669)Instructions burned: 1671 (million) 13.27/2.13 % (16669)------------------------------ 13.27/2.13 % (16669)------------------------------ 14.39/2.14 % (16681)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on Vampire---4 for (1781ds/343Mi) 14.39/2.20 % (16678)Instruction limit reached! 14.39/2.20 % (16678)------------------------------ 14.39/2.20 % (16678)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 14.39/2.20 % (16678)Termination reason: Unknown 14.39/2.20 % (16678)Termination phase: Saturation 14.39/2.20 14.39/2.20 % (16678)Memory used [KB]: 7547 14.39/2.20 % (16678)Time elapsed: 0.223 s 14.39/2.20 % (16678)Instructions burned: 564 (million) 14.39/2.20 % (16678)------------------------------ 14.39/2.20 % (16678)------------------------------ 14.39/2.22 % (16682)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 Vampire---4 for (1781ds/1655Mi) 14.99/2.25 % (16680)Instruction limit reached! 14.99/2.25 % (16680)------------------------------ 14.99/2.25 % (16680)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 14.99/2.25 % (16680)Termination reason: Unknown 14.99/2.25 % (16680)Termination phase: Saturation 14.99/2.25 14.99/2.25 % (16680)Memory used [KB]: 7419 14.99/2.25 % (16680)Time elapsed: 0.134 s 14.99/2.25 % (16680)Instructions burned: 350 (million) 14.99/2.25 % (16680)------------------------------ 14.99/2.25 % (16680)------------------------------ 14.99/2.26 % (16674)Instruction limit reached! 14.99/2.26 % (16674)------------------------------ 14.99/2.26 % (16674)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 14.99/2.26 % (16674)Termination reason: Unknown 14.99/2.26 % (16674)Termination phase: Saturation 14.99/2.26 14.99/2.26 % (16674)Memory used [KB]: 8827 14.99/2.26 % (16674)Time elapsed: 0.487 s 14.99/2.26 % (16674)Instructions burned: 961 (million) 14.99/2.26 % (16674)------------------------------ 14.99/2.26 % (16674)------------------------------ 14.99/2.26 % (16683)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on Vampire---4 for (1780ds/6454Mi) 14.99/2.28 % (16684)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on Vampire---4 for (1780ds/1539Mi) 15.35/2.30 % (16681)Instruction limit reached! 15.35/2.30 % (16681)------------------------------ 15.35/2.30 % (16681)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 15.35/2.30 % (16681)Termination reason: Unknown 15.35/2.30 % (16681)Termination phase: Saturation 15.35/2.30 15.35/2.30 % (16681)Memory used [KB]: 8315 15.35/2.30 % (16681)Time elapsed: 0.160 s 15.35/2.30 % (16681)Instructions burned: 344 (million) 15.35/2.30 % (16681)------------------------------ 15.35/2.30 % (16681)------------------------------ 15.35/2.32 % (16685)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 Vampire---4 for (1780ds/501Mi) 16.17/2.49 % (16676)Instruction limit reached! 16.17/2.49 % (16676)------------------------------ 16.17/2.49 % (16676)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 16.17/2.49 % (16676)Termination reason: Unknown 16.17/2.49 % (16676)Termination phase: Saturation 16.17/2.49 16.17/2.49 % (16676)Memory used [KB]: 9338 16.17/2.49 % (16676)Time elapsed: 0.559 s 16.17/2.49 % (16676)Instructions burned: 1084 (million) 16.17/2.49 % (16676)------------------------------ 16.17/2.49 % (16676)------------------------------ 16.28/2.51 % (16686)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 Vampire---4 for (1778ds/277Mi) 16.41/2.57 % (16685)Instruction limit reached! 16.41/2.57 % (16685)------------------------------ 16.41/2.57 % (16685)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 16.41/2.57 % (16685)Termination reason: Unknown 16.41/2.57 % (16685)Termination phase: Saturation 16.41/2.57 16.41/2.57 % (16685)Memory used [KB]: 9210 16.41/2.57 % (16685)Time elapsed: 0.251 s 16.41/2.57 % (16685)Instructions burned: 501 (million) 16.41/2.57 % (16685)------------------------------ 16.41/2.57 % (16685)------------------------------ 16.41/2.58 % (16687)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 Vampire---4 for (1777ds/136Mi) 16.87/2.60 % (16679)Instruction limit reached! 16.87/2.60 % (16679)------------------------------ 16.87/2.60 % (16679)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 16.87/2.60 % (16679)Termination reason: Unknown 16.87/2.60 % (16679)Termination phase: Saturation 16.87/2.60 16.87/2.60 % (16679)Memory used [KB]: 11257 16.87/2.60 % (16679)Time elapsed: 0.618 s 16.87/2.60 % (16679)Instructions burned: 1209 (million) 16.87/2.60 % (16679)------------------------------ 16.87/2.60 % (16679)------------------------------ 16.87/2.61 % (16686)Instruction limit reached! 16.87/2.61 % (16686)------------------------------ 16.87/2.61 % (16686)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 16.87/2.61 % (16686)Termination reason: Unknown 16.87/2.61 % (16686)Termination phase: Saturation 16.87/2.61 16.87/2.61 % (16686)Memory used [KB]: 7291 16.87/2.61 % (16686)Time elapsed: 0.109 s 16.87/2.61 % (16686)Instructions burned: 277 (million) 16.87/2.61 % (16686)------------------------------ 16.87/2.61 % (16686)------------------------------ 16.87/2.62 % (16688)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 Vampire---4 for (1777ds/401Mi) 16.87/2.63 % (16677)Instruction limit reached! 16.87/2.63 % (16677)------------------------------ 16.87/2.63 % (16677)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 16.87/2.63 % (16677)Termination reason: Unknown 16.87/2.63 % (16677)Termination phase: Saturation 16.87/2.63 16.87/2.63 % (16677)Memory used [KB]: 9978 16.87/2.63 % (16677)Time elapsed: 0.689 s 16.87/2.63 % (16677)Instructions burned: 1399 (million) 16.87/2.63 % (16677)------------------------------ 16.87/2.63 % (16677)------------------------------ 16.87/2.63 % (16689)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 Vampire---4 for (1777ds/4810Mi) 16.87/2.64 % (16687)Instruction limit reached! 16.87/2.64 % (16687)------------------------------ 16.87/2.64 % (16687)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 16.87/2.64 % (16687)Termination reason: Unknown 16.87/2.64 % (16687)Termination phase: Saturation 16.87/2.64 16.87/2.64 % (16687)Memory used [KB]: 6908 16.87/2.64 % (16687)Time elapsed: 0.060 s 16.87/2.64 % (16687)Instructions burned: 136 (million) 16.87/2.64 % (16687)------------------------------ 16.87/2.64 % (16687)------------------------------ 16.87/2.64 % (16690)lrs+1002_1:128_atotf=0.1:au=on:cbe=off:ntd=on:sp=const_frequency:i=2020:si=on:rtra=on_0 on Vampire---4 for (1777ds/2020Mi) 16.87/2.65 % (16691)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=375:si=on:rtra=on_0 on Vampire---4 for (1776ds/375Mi) 17.19/2.76 % (16688)Instruction limit reached! 17.19/2.76 % (16688)------------------------------ 17.19/2.76 % (16688)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 17.19/2.76 % (16688)Termination reason: Unknown 17.19/2.76 % (16688)Termination phase: Saturation 17.19/2.76 17.19/2.76 % (16688)Memory used [KB]: 6908 17.19/2.76 % (16688)Time elapsed: 0.145 s 17.19/2.76 % (16688)Instructions burned: 401 (million) 17.19/2.76 % (16688)------------------------------ 17.19/2.76 % (16688)------------------------------ 17.45/2.78 % (16692)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on Vampire---4 for (1775ds/8250Mi) 19.70/2.83 % (16691)Instruction limit reached! 19.70/2.83 % (16691)------------------------------ 19.70/2.83 % (16691)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 19.70/2.83 % (16691)Termination reason: Unknown 19.70/2.83 % (16691)Termination phase: Saturation 19.70/2.83 19.70/2.83 % (16691)Memory used [KB]: 8187 19.70/2.83 % (16691)Time elapsed: 0.180 s 19.70/2.83 % (16691)Instructions burned: 375 (million) 19.70/2.83 % (16691)------------------------------ 19.70/2.83 % (16691)------------------------------ 19.97/2.84 % (16693)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on Vampire---4 for (1775ds/187Mi) 20.36/2.93 % (16693)Instruction limit reached! 20.36/2.93 % (16693)------------------------------ 20.36/2.93 % (16693)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 20.36/2.93 % (16693)Termination reason: Unknown 20.36/2.93 % (16693)Termination phase: Saturation 20.36/2.93 20.36/2.93 % (16693)Memory used [KB]: 7547 20.36/2.93 % (16693)Time elapsed: 0.084 s 20.36/2.93 % (16693)Instructions burned: 187 (million) 20.36/2.93 % (16693)------------------------------ 20.36/2.93 % (16693)------------------------------ 20.36/2.94 % (16694)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on Vampire---4 for (1774ds/393Mi) 20.82/3.01 % (16682)Instruction limit reached! 20.82/3.01 % (16682)------------------------------ 20.82/3.01 % (16682)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 20.82/3.01 % (16682)Termination reason: Unknown 20.82/3.01 % (16682)Termination phase: Saturation 20.82/3.01 20.82/3.01 % (16682)Memory used [KB]: 12153 20.82/3.01 % (16682)Time elapsed: 0.779 s 20.82/3.01 % (16682)Instructions burned: 1655 (million) 20.82/3.01 % (16682)------------------------------ 20.82/3.01 % (16682)------------------------------ 20.82/3.02 % (16695)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on Vampire---4 for (1773ds/371Mi) 20.82/3.04 % (16684)Instruction limit reached! 20.82/3.04 % (16684)------------------------------ 20.82/3.04 % (16684)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 20.82/3.04 % (16684)Termination reason: Unknown 20.82/3.04 % (16684)Termination phase: Saturation 20.82/3.04 20.82/3.04 % (16684)Memory used [KB]: 9978 20.82/3.04 % (16684)Time elapsed: 0.752 s 20.82/3.04 % (16684)Instructions burned: 1540 (million) 20.82/3.04 % (16684)------------------------------ 20.82/3.04 % (16684)------------------------------ 21.48/3.05 % (16696)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on Vampire---4 for (1772ds/434Mi) 21.70/3.13 % (16694)Instruction limit reached! 21.70/3.13 % (16694)------------------------------ 21.70/3.13 % (16694)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 21.70/3.13 % (16694)Termination reason: Unknown 21.70/3.13 % (16694)Termination phase: Saturation 21.70/3.13 21.70/3.13 % (16694)Memory used [KB]: 8571 21.70/3.13 % (16694)Time elapsed: 0.187 s 21.70/3.13 % (16694)Instructions burned: 393 (million) 21.70/3.13 % (16694)------------------------------ 21.70/3.13 % (16694)------------------------------ 22.12/3.14 % (16697)lrs+10_1:8_av=off:fe=off:hud=5:piset=or:prag=on:i=452:si=on:rtra=on_0 on Vampire---4 for (1772ds/452Mi) 22.15/3.20 % (16695)Instruction limit reached! 22.15/3.20 % (16695)------------------------------ 22.15/3.20 % (16695)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 22.15/3.20 % (16695)Termination reason: Unknown 22.15/3.20 % (16695)Termination phase: Saturation 22.15/3.20 22.15/3.20 % (16695)Memory used [KB]: 8443 22.15/3.20 % (16695)Time elapsed: 0.176 s 22.15/3.20 % (16695)Instructions burned: 372 (million) 22.15/3.20 % (16695)------------------------------ 22.15/3.20 % (16695)------------------------------ 22.62/3.21 % (16698)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on Vampire---4 for (1771ds/5411Mi) 22.62/3.22 % (16666)Instruction limit reached! 22.62/3.22 % (16666)------------------------------ 22.62/3.22 % (16666)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 22.62/3.22 % (16666)Termination reason: Unknown 22.62/3.22 % (16666)Termination phase: Saturation 22.62/3.22 22.62/3.22 % (16666)Memory used [KB]: 8187 22.62/3.22 % (16666)Time elapsed: 1.744 s 22.62/3.22 % (16666)Instructions burned: 4759 (million) 22.62/3.22 % (16666)------------------------------ 22.62/3.22 % (16666)------------------------------ 22.62/3.23 % (16699)dis+1010_1:1_cnfonf=conj_eager:e2e=on:fe=axiom:fsr=off:ntd=on:nwc=10.0:s2a=on:sgt=5:sp=occurrence:ss=axioms:i=1110:si=on:rtra=on_0 on Vampire---4 for (1771ds/1110Mi) 22.85/3.26 % (16696)Instruction limit reached! 22.85/3.26 % (16696)------------------------------ 22.85/3.26 % (16696)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 22.85/3.26 % (16696)Termination reason: Unknown 22.85/3.26 % (16696)Termination phase: Saturation 22.85/3.26 22.85/3.26 % (16696)Memory used [KB]: 9466 22.85/3.26 % (16696)Time elapsed: 0.209 s 22.85/3.26 % (16696)Instructions burned: 434 (million) 22.85/3.26 % (16696)------------------------------ 22.85/3.26 % (16696)------------------------------ 22.85/3.28 % (16700)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on Vampire---4 for (1770ds/590Mi) 22.85/3.36 % (16697)Instruction limit reached! 22.85/3.36 % (16697)------------------------------ 22.85/3.36 % (16697)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 22.85/3.36 % (16697)Termination reason: Unknown 22.85/3.36 % (16697)Termination phase: Saturation 22.85/3.36 22.85/3.36 % (16697)Memory used [KB]: 3837 22.85/3.36 % (16697)Time elapsed: 0.218 s 22.85/3.36 % (16697)Instructions burned: 452 (million) 22.85/3.36 % (16697)------------------------------ 22.85/3.36 % (16697)------------------------------ 24.11/3.37 % (16701)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on Vampire---4 for (1769ds/432Mi) 25.39/3.56 % (16700)Instruction limit reached! 25.39/3.56 % (16700)------------------------------ 25.39/3.56 % (16700)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 25.39/3.56 % (16700)Termination reason: Unknown 25.39/3.56 % (16700)Termination phase: Saturation 25.39/3.56 25.39/3.56 % (16700)Memory used [KB]: 9338 25.39/3.56 % (16700)Time elapsed: 0.276 s 25.39/3.56 % (16700)Instructions burned: 591 (million) 25.39/3.56 % (16700)------------------------------ 25.39/3.56 % (16700)------------------------------ 25.39/3.58 % (16702)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=2517:si=on:rtra=on_0 on Vampire---4 for (1767ds/2517Mi) 25.39/3.58 % (16701)Instruction limit reached! 25.39/3.58 % (16701)------------------------------ 25.39/3.58 % (16701)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 25.39/3.58 % (16701)Termination reason: Unknown 25.39/3.58 % (16701)Termination phase: Saturation 25.39/3.58 25.39/3.58 % (16701)Memory used [KB]: 8315 25.39/3.58 % (16701)Time elapsed: 0.234 s 25.39/3.58 % (16701)Instructions burned: 433 (million) 25.39/3.58 % (16701)------------------------------ 25.39/3.58 % (16701)------------------------------ 25.88/3.60 % (16703)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on Vampire---4 for (1767ds/783Mi) 25.88/3.61 % (16690)Instruction limit reached! 25.88/3.61 % (16690)------------------------------ 25.88/3.61 % (16690)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 25.88/3.61 % (16690)Termination reason: Unknown 25.88/3.61 % (16690)Termination phase: Saturation 25.88/3.61 25.88/3.61 % (16690)Memory used [KB]: 8827 25.88/3.61 % (16690)Time elapsed: 0.966 s 25.88/3.61 % (16690)Instructions burned: 2020 (million) 25.88/3.61 % (16690)------------------------------ 25.88/3.61 % (16690)------------------------------ 25.88/3.62 % (16704)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on Vampire---4 for (1767ds/481Mi) 26.76/3.78 % (16699)Instruction limit reached! 26.76/3.78 % (16699)------------------------------ 26.76/3.78 % (16699)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 26.76/3.78 % (16699)Termination reason: Unknown 26.76/3.78 % (16699)Termination phase: Saturation 26.76/3.78 26.76/3.78 % (16699)Memory used [KB]: 9210 26.76/3.78 % (16699)Time elapsed: 0.552 s 26.76/3.78 % (16699)Instructions burned: 1110 (million) 26.76/3.78 % (16699)------------------------------ 26.76/3.78 % (16699)------------------------------ 26.76/3.80 % (16705)lrs+1010_1:64_aac=none:acc=on:au=on:c=on:cbe=off:ccuc=small_ones:chr=on:cnfonf=lazy_not_gen:fde=unused:hud=10:kws=precedence:nicw=on:piset=all_but_not_eq:sd=2:sp=reverse_arity:ss=axioms:i=536:si=on:rtra=on_0 on Vampire---4 for (1765ds/536Mi) 26.76/3.80 % (16704)Instruction limit reached! 26.76/3.80 % (16704)------------------------------ 26.76/3.80 % (16704)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 26.76/3.80 % (16704)Termination reason: Unknown 26.76/3.80 % (16704)Termination phase: Saturation 26.76/3.80 26.76/3.80 % (16704)Memory used [KB]: 10746 26.76/3.80 % (16704)Time elapsed: 0.182 s 26.76/3.80 % (16704)Instructions burned: 482 (million) 26.76/3.80 % (16704)------------------------------ 26.76/3.80 % (16704)------------------------------ 26.76/3.81 % (16706)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on Vampire---4 for (1765ds/157Mi) 27.34/3.88 % (16706)Instruction limit reached! 27.34/3.88 % (16706)------------------------------ 27.34/3.88 % (16706)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 27.34/3.88 % (16706)Termination reason: Unknown 27.34/3.88 % (16706)Termination phase: Saturation 27.34/3.88 27.34/3.88 % (16706)Memory used [KB]: 6908 27.34/3.88 % (16706)Time elapsed: 0.065 s 27.34/3.88 % (16706)Instructions burned: 157 (million) 27.34/3.88 % (16706)------------------------------ 27.34/3.88 % (16706)------------------------------ 27.60/3.89 % (16707)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on Vampire---4 for (1764ds/4350Mi) 28.93/3.99 % (16703)Instruction limit reached! 28.93/3.99 % (16703)------------------------------ 28.93/3.99 % (16703)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 28.93/3.99 % (16703)Termination reason: Unknown 28.93/3.99 % (16703)Termination phase: Saturation 28.93/3.99 28.93/3.99 % (16703)Memory used [KB]: 10490 28.93/3.99 % (16703)Time elapsed: 0.394 s 28.93/3.99 % (16703)Instructions burned: 784 (million) 28.93/3.99 % (16703)------------------------------ 28.93/3.99 % (16703)------------------------------ 28.93/4.00 % (16708)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on Vampire---4 for (1763ds/358Mi) 29.36/4.05 % (16705)Instruction limit reached! 29.36/4.05 % (16705)------------------------------ 29.36/4.05 % (16705)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 29.36/4.05 % (16705)Termination reason: Unknown 29.36/4.05 % (16705)Termination phase: Saturation 29.36/4.05 29.36/4.05 % (16705)Memory used [KB]: 8699 29.36/4.05 % (16705)Time elapsed: 0.255 s 29.36/4.05 % (16705)Instructions burned: 537 (million) 29.36/4.05 % (16705)------------------------------ 29.36/4.05 % (16705)------------------------------ 29.57/4.06 % (16709)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=700:si=on:rtra=on_0 on Vampire---4 for (1762ds/700Mi) 30.25/4.17 % (16708)Instruction limit reached! 30.25/4.17 % (16708)------------------------------ 30.25/4.17 % (16708)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 30.25/4.17 % (16708)Termination reason: Unknown 30.25/4.17 % (16708)Termination phase: Saturation 30.25/4.17 30.25/4.17 % (16708)Memory used [KB]: 8187 30.25/4.17 % (16708)Time elapsed: 0.168 s 30.25/4.17 % (16708)Instructions burned: 359 (million) 30.25/4.17 % (16708)------------------------------ 30.25/4.17 % (16708)------------------------------ 30.25/4.19 % (16710)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on Vampire---4 for (1761ds/406Mi) 31.03/4.31 % (16689)Instruction limit reached! 31.03/4.31 % (16689)------------------------------ 31.03/4.31 % (16689)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 31.03/4.31 % (16689)Termination reason: Unknown 31.03/4.31 % (16689)Termination phase: Saturation 31.03/4.31 31.03/4.31 % (16689)Memory used [KB]: 11385 31.03/4.31 % (16689)Time elapsed: 1.688 s 31.03/4.31 % (16689)Instructions burned: 4812 (million) 31.03/4.31 % (16689)------------------------------ 31.03/4.31 % (16689)------------------------------ 31.36/4.33 % (16711)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on Vampire---4 for (1760ds/283Mi) 31.51/4.37 % (16710)Refutation not found, incomplete strategy 31.51/4.37 % (16710)------------------------------ 31.51/4.37 % (16710)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 31.51/4.37 % (16710)Termination reason: Refutation not found, incomplete strategy 31.51/4.37 31.51/4.37 31.51/4.37 % (16710)Memory used [KB]: 7291 31.51/4.37 % (16710)Time elapsed: 0.186 s 31.51/4.37 % (16710)Instructions burned: 400 (million) 31.51/4.37 % (16710)------------------------------ 31.51/4.37 % (16710)------------------------------ 31.51/4.38 % (16712)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=641:si=on:rtra=on_0 on Vampire---4 for (1759ds/641Mi) 31.51/4.40 % (16709)Instruction limit reached! 31.51/4.40 % (16709)------------------------------ 31.51/4.40 % (16709)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 31.51/4.40 % (16709)Termination reason: Unknown 31.51/4.40 % (16709)Termination phase: Saturation 31.51/4.40 31.51/4.40 % (16709)Memory used [KB]: 7931 31.51/4.40 % (16709)Time elapsed: 0.341 s 31.51/4.40 % (16709)Instructions burned: 701 (million) 31.51/4.40 % (16709)------------------------------ 31.51/4.40 % (16709)------------------------------ 31.51/4.42 % (16713)lrs+1010_1:1_cbe=off:chr=on:er=known:hud=4:i=147:si=on:rtra=on_0 on Vampire---4 for (1759ds/147Mi) 32.44/4.46 % (16711)Instruction limit reached! 32.44/4.46 % (16711)------------------------------ 32.44/4.46 % (16711)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 32.44/4.46 % (16711)Termination reason: Unknown 32.44/4.46 % (16711)Termination phase: Saturation 32.44/4.46 32.44/4.46 % (16711)Memory used [KB]: 7931 32.44/4.46 % (16711)Time elapsed: 0.133 s 32.44/4.46 % (16711)Instructions burned: 283 (million) 32.44/4.46 % (16711)------------------------------ 32.44/4.46 % (16711)------------------------------ 32.44/4.48 % (16714)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on Vampire---4 for (1758ds/932Mi) 32.44/4.48 % (16713)Instruction limit reached! 32.44/4.48 % (16713)------------------------------ 32.44/4.48 % (16713)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 32.44/4.48 % (16713)Termination reason: Unknown 32.44/4.48 % (16713)Termination phase: Saturation 32.44/4.48 32.44/4.48 % (16713)Memory used [KB]: 7164 32.44/4.48 % (16713)Time elapsed: 0.066 s 32.44/4.48 % (16713)Instructions burned: 148 (million) 32.44/4.48 % (16713)------------------------------ 32.44/4.48 % (16713)------------------------------ 33.02/4.50 % (16715)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on Vampire---4 for (1758ds/2401Mi) 34.14/4.69 % (16712)Instruction limit reached! 34.14/4.69 % (16712)------------------------------ 34.14/4.69 % (16712)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 34.14/4.69 % (16712)Termination reason: Unknown 34.14/4.69 % (16712)Termination phase: Saturation 34.14/4.69 34.14/4.69 % (16712)Memory used [KB]: 8315 34.14/4.69 % (16712)Time elapsed: 0.306 s 34.14/4.69 % (16712)Instructions burned: 642 (million) 34.14/4.69 % (16712)------------------------------ 34.14/4.69 % (16712)------------------------------ 34.14/4.71 % (16716)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=576:si=on:rtra=on_0 on Vampire---4 for (1756ds/576Mi) 34.97/4.77 % (16714)First to succeed. 34.97/4.82 % (16702)Instruction limit reached! 34.97/4.82 % (16702)------------------------------ 34.97/4.82 % (16702)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 34.97/4.82 % (16702)Termination reason: Unknown 34.97/4.82 % (16702)Termination phase: Saturation 34.97/4.82 34.97/4.82 % (16702)Memory used [KB]: 11641 34.97/4.82 % (16702)Time elapsed: 1.242 s 34.97/4.82 % (16702)Instructions burned: 2517 (million) 34.97/4.82 % (16702)------------------------------ 34.97/4.82 % (16702)------------------------------ 34.97/4.83 % (16718)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on Vampire---4 for (1755ds/715Mi) 35.80/4.92 % (16716)Instruction limit reached! 35.80/4.92 % (16716)------------------------------ 35.80/4.92 % (16716)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 35.80/4.92 % (16716)Termination reason: Unknown 35.80/4.92 % (16716)Termination phase: Saturation 35.80/4.92 35.80/4.92 % (16716)Memory used [KB]: 8443 35.80/4.92 % (16716)Time elapsed: 0.218 s 35.80/4.92 % (16716)Instructions burned: 576 (million) 35.80/4.92 % (16716)------------------------------ 35.80/4.92 % (16716)------------------------------ 35.80/4.94 % (16719)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on Vampire---4 for (1754ds/1762Mi) 38.51/5.18 % (16718)Instruction limit reached! 38.51/5.18 % (16718)------------------------------ 38.51/5.18 % (16718)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 38.51/5.18 % (16718)Termination reason: Unknown 38.51/5.18 % (16718)Termination phase: Saturation 38.51/5.18 38.51/5.18 % (16718)Memory used [KB]: 4221 38.51/5.18 % (16718)Time elapsed: 0.352 s 38.51/5.18 % (16718)Instructions burned: 716 (million) 38.51/5.18 % (16718)------------------------------ 38.51/5.18 % (16718)------------------------------ 38.51/5.20 % (16721)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on Vampire---4 for (1751ds/503Mi) 39.75/5.44 % (16721)Instruction limit reached! 39.75/5.44 % (16721)------------------------------ 39.75/5.44 % (16721)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 39.75/5.44 % (16721)Termination reason: Unknown 39.75/5.44 % (16721)Termination phase: Saturation 39.75/5.44 39.75/5.44 % (16721)Memory used [KB]: 8443 39.75/5.44 % (16721)Time elapsed: 0.244 s 39.75/5.44 % (16721)Instructions burned: 503 (million) 39.75/5.44 % (16721)------------------------------ 39.75/5.44 % (16721)------------------------------ 39.75/5.46 % (16722)dis+1010_3039923:1048576_bsr=unit_only:cbe=off:cha=on:cnfonf=off:e2e=on:fsr=off:hud=1:ixr=off:kws=precedence:lma=on:nm=4:piset=or:s2a=on:sp=frequency:spb=goal_then_units:i=5104:si=on:rtra=on_0 on Vampire---4 for (1749ds/5104Mi) 40.74/5.52 % (16683)Instruction limit reached! 40.74/5.52 % (16683)------------------------------ 40.74/5.52 % (16683)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 40.74/5.52 % (16683)Termination reason: Unknown 40.74/5.52 % (16683)Termination phase: Saturation 40.74/5.52 40.74/5.52 % (16683)Memory used [KB]: 14711 40.74/5.52 % (16683)Time elapsed: 3.261 s 40.74/5.52 % (16683)Instructions burned: 6455 (million) 40.74/5.52 % (16683)------------------------------ 40.74/5.52 % (16683)------------------------------ 41.00/5.54 % (16723)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=312:si=on:rtra=on_0 on Vampire---4 for (1748ds/312Mi) 41.00/5.55 % (16698)Also succeeded, but the first one will report. 41.00/5.55 % (16714)Refutation found. Thanks to Tanya! 41.00/5.55 % SZS status Theorem for Vampire---4 41.00/5.55 % SZS output start Proof for Vampire---4 41.00/5.55 thf(func_def_0, type, in: $i > $i > $o). 41.00/5.55 thf(func_def_1, type, exu: ($i > $o) > $o). 41.00/5.55 thf(func_def_6, type, setadjoin: $i > $i > $i). 41.00/5.55 thf(func_def_8, type, powerset: $i > $i). 41.00/5.55 thf(func_def_10, type, setunion: $i > $i). 41.00/5.55 thf(func_def_19, type, descr: ($i > $o) > $i). 41.00/5.55 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i). 41.00/5.55 thf(func_def_26, type, prop2set: $o > $i). 41.00/5.55 thf(func_def_36, type, nonempty: $i > $o). 41.00/5.55 thf(func_def_69, type, set2prop: $i > $o). 41.00/5.55 thf(func_def_88, type, subset: $i > $i > $o). 41.00/5.55 thf(func_def_89, type, disjoint: $i > $i > $o). 41.00/5.55 thf(func_def_90, type, setsmeet: $i > $i > $o). 41.00/5.55 thf(func_def_114, type, binunion: $i > $i > $i). 41.00/5.55 thf(func_def_122, type, binintersect: $i > $i > $i). 41.00/5.55 thf(func_def_135, type, regular: $i > $o). 41.00/5.55 thf(func_def_136, type, setminus: $i > $i > $i). 41.00/5.55 thf(func_def_147, type, symdiff: $i > $i > $i). 41.00/5.55 thf(func_def_153, type, iskpair: $i > $o). 41.00/5.55 thf(func_def_158, type, kpair: $i > $i > $i). 41.00/5.55 thf(func_def_160, type, cartprod: $i > $i > $i). 41.00/5.55 thf(func_def_177, type, singleton: $i > $o). 41.00/5.55 thf(func_def_179, type, ex1: $i > ($i > $o) > $o). 41.00/5.55 thf(func_def_184, type, atmost1p: $i > $o). 41.00/5.55 thf(func_def_185, type, atleast2p: $i > $o). 41.00/5.55 thf(func_def_186, type, atmost2p: $i > $o). 41.00/5.55 thf(func_def_187, type, upairsetp: $i > $o). 41.00/5.55 thf(func_def_191, type, kfst: $i > $i). 41.00/5.55 thf(func_def_203, type, ksnd: $i > $i). 41.00/5.55 thf(func_def_213, type, breln: $i > $i > $i > $o). 41.00/5.55 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 41.00/5.55 thf(func_def_222, type, func: $i > $i > $i > $o). 41.00/5.55 thf(func_def_223, type, funcSet: $i > $i > $i). 41.00/5.55 thf(func_def_226, type, ap: $i > $i > $i > $i > $i). 41.00/5.55 thf(f1017,plain,( 41.00/5.55 $false), 41.00/5.55 inference(trivial_inequality_removal,[],[f1016])). 41.00/5.55 thf(f1016,plain,( 41.00/5.55 ($true = $false)), 41.00/5.55 inference(boolean_simplification,[],[f1015])). 41.00/5.55 thf(f1015,plain,( 41.00/5.55 ($true = (~ $true))), 41.00/5.55 inference(boolean_simplification,[],[f1014])). 41.00/5.55 thf(f1014,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => $true)))), 41.00/5.55 inference(boolean_simplification,[],[f1013])). 41.00/5.55 thf(f1013,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => $true))))), 41.00/5.55 inference(boolean_simplification,[],[f1012])). 41.00/5.55 thf(f1012,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => $true)))))), 41.00/5.55 inference(boolean_simplification,[],[f1011])). 41.00/5.55 thf(f1011,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) = (in @ Y1 @ (powerset @ Y0))))))) => $true))))))), 41.00/5.55 inference(boolean_simplification,[],[f1010])). 41.00/5.55 thf(f1010,plain,( 41.00/5.55 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => $true)))))) = $true)), 41.00/5.55 inference(boolean_simplification,[],[f1009])). 41.00/5.55 thf(f1009,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => $true))))))))), 41.00/5.55 inference(boolean_simplification,[],[f1008])). 41.00/5.55 thf(f1008,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => $true)))))))))), 41.00/5.55 inference(boolean_simplification,[],[f1007])). 41.00/5.55 thf(f1007,plain,( 41.00/5.55 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => $true))))))))) = $true)), 41.00/5.55 inference(boolean_simplification,[],[f1006])). 41.00/5.55 thf(f1006,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => $true)))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f1005])). 41.00/5.55 thf(f1005,plain,( 41.00/5.55 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => $true))))))))))) = $true)), 41.00/5.55 inference(boolean_simplification,[],[f1004])). 41.00/5.55 thf(f1004,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => $true)))))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f1003])). 41.00/5.55 thf(f1003,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => $true))))))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f1002])). 41.00/5.55 thf(f1002,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => $true)))))))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f1001])). 41.00/5.55 thf(f1001,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => $true))))))))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f1000])). 41.00/5.55 thf(f1000,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => $true)))))))))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f999])). 41.00/5.55 thf(f999,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => $true))))))))))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f998])). 41.00/5.55 thf(f998,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => $true)))))))))))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f997])). 41.00/5.55 thf(f997,plain,( 41.00/5.55 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => $true))))))))))))))))))) = $true)), 41.00/5.55 inference(boolean_simplification,[],[f996])). 41.00/5.55 thf(f996,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => $true)))))))))))))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f995])). 41.00/5.55 thf(f995,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => $true))))))))))))))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f994])). 41.00/5.55 thf(f994,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => $true)))))))))))))))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f993])). 41.00/5.55 thf(f993,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => $true))))))))))))))))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f992])). 41.00/5.55 thf(f992,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! 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@ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => $true)))))))))))))))))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f991])). 41.00/5.55 thf(f991,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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 @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (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 > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => $true))))))))))))))))))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f990])). 41.00/5.55 thf(f990,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! 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@ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) = (Y1 @ Y2))))))))) => $true)))))))))))))))))))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f989])). 41.00/5.55 thf(f989,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) = (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => $true))))))))))))))))))))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f988])). 41.00/5.55 thf(f988,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) = (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (~ (emptyset = (dsetconstr @ Y0 @ Y1))))))))))) => $true)))))))))))))))))))))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f987])). 41.00/5.55 thf(f987,plain,( 41.00/5.55 ($true = (~ ((!! 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@ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! 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@ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) = (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (~ (emptyset = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => $true))))))))))))))))))))))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f986])). 41.00/5.55 thf(f986,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! 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@ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! 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@ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) = (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! 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@ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (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 > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) = (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (~ (emptyset = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => $true))))))))))))))))))))))))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f984])). 41.00/5.55 thf(f984,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) = (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (~ (emptyset = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => $true)))))))))))))))))))))))))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f983])). 41.00/5.55 thf(f983,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) = (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (~ (emptyset = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((Y2 = Y1) => Y3) => (((in @ Y2 @ Y0) => Y3) => Y3))))))))))) => $true))))))))))))))))))))))))))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f982])). 41.00/5.55 thf(f982,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! 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@ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((Y2 = Y1) => Y3) => (((in @ Y2 @ Y0) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((Y1 = Y0) | (in @ Y1 @ Y2))))))))) => $true)))))))))))))))))))))))))))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f981])). 41.00/5.55 thf(f981,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! 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@ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((Y1 = Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => $true))))))))))))))))))))))))))))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f980])). 41.00/5.55 thf(f980,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! 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@ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) = (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (~ (emptyset = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((Y2 = Y1) => Y3) => (((in @ Y2 @ Y0) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((Y1 = Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => $true)))))))))))))))))))))))))))))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f979])). 41.00/5.55 thf(f979,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) = (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (~ (emptyset = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((Y2 = Y1) => Y3) => (((in @ Y2 @ Y0) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((Y1 = Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => $true))))))))))))))))))))))))))))))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f978])). 41.00/5.55 thf(f978,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) = (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (~ (emptyset = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((Y2 = Y1) => Y3) => (((in @ Y2 @ Y0) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((Y1 = Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => $true)))))))))))))))))))))))))))))))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f977])). 41.00/5.55 thf(f977,plain,( 41.00/5.55 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) = (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (~ (emptyset = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((Y2 = Y1) => Y3) => (((in @ Y2 @ Y0) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((Y1 = Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => $true))))))))))))))))))))))))))))))))))))))) = $true)), 41.00/5.55 inference(boolean_simplification,[],[f976])). 41.00/5.55 thf(f976,plain,( 41.00/5.55 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) = (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (~ (emptyset = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((Y2 = Y1) => Y3) => (((in @ Y2 @ Y0) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((Y1 = Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y0 @ Y2) => (in @ Y1 @ (setunion @ Y2)))))))))) => $true)))))))))))))))))))))))))))))))))))))))) = $true)), 41.00/5.55 inference(boolean_simplification,[],[f975])). 41.00/5.55 thf(f975,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! 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@ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) = (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (~ (emptyset = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((Y2 = Y1) => Y3) => (((in @ Y2 @ Y0) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((Y1 = Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y0 @ Y2) => (in @ Y1 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (powerset @ (setunion @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => $true))))))))))))))))))))))))))))))))))))))))))))) = $true)), 41.00/5.55 inference(boolean_simplification,[],[f970])). 41.00/5.55 thf(f970,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) = (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (~ (emptyset = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((Y2 = Y1) => Y3) => (((in @ Y2 @ Y0) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((Y1 = Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y0 @ Y2) => (in @ Y1 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (powerset @ (setunion @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f969])). 41.00/5.55 thf(f969,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) = (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (~ (emptyset = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((Y2 = Y1) => Y3) => (((in @ Y2 @ Y0) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((Y1 = Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y0 @ Y2) => (in @ Y1 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (powerset @ (setunion @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f968])). 41.00/5.55 thf(f968,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! 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@ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (in @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f967])). 41.00/5.55 thf(f967,plain,( 41.00/5.55 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) = (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (~ (emptyset = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((Y2 = Y1) => Y3) => (((in @ Y2 @ Y0) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((Y1 = Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y0 @ Y2) => (in @ Y1 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (powerset @ (setunion @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ 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))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 41.00/5.55 inference(boolean_simplification,[],[f966])). 41.00/5.55 thf(f966,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) = (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (~ (emptyset = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((Y2 = Y1) => Y3) => (((in @ Y2 @ Y0) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((Y1 = Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y0 @ Y2) => (in @ Y1 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (powerset @ (setunion @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ 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))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f965])). 41.00/5.55 thf(f965,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (~ (emptyset = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((Y2 = Y1) => Y3) => (((in @ Y2 @ Y0) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((Y1 = Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y0 @ Y2) => (in @ Y1 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (powerset @ (setunion @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ 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))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (((dsetconstr @ Y1 @ Y0) = emptyset) => $false)))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 41.00/5.55 inference(boolean_simplification,[],[f963])). 41.00/5.55 thf(f963,plain,( 41.00/5.55 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) = (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (~ (emptyset = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((Y2 = Y1) => Y3) => (((in @ Y2 @ Y0) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((Y1 = Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y0 @ Y2) => (in @ Y1 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (powerset @ (setunion @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ 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))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (((dsetconstr @ Y1 @ Y0) = emptyset) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ Y0)))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 41.00/5.55 inference(boolean_simplification,[],[f962])). 41.00/5.55 thf(f962,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) = (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (~ (emptyset = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((Y2 = Y1) => Y3) => (((in @ Y2 @ Y0) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((Y1 = Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y0 @ Y2) => (in @ Y1 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (powerset @ (setunion @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ 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))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (((dsetconstr @ Y1 @ Y0) = emptyset) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f961])). 41.00/5.55 thf(f961,plain,( 41.00/5.55 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) = (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (~ (emptyset = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((Y2 = Y1) => Y3) => (((in @ Y2 @ Y0) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((Y1 = Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y0 @ Y2) => (in @ Y1 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (powerset @ (setunion @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ 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))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (((dsetconstr @ Y1 @ Y0) = emptyset) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 41.00/5.55 inference(boolean_simplification,[],[f960])). 41.00/5.55 thf(f960,plain,( 41.00/5.55 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) = (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (~ (emptyset = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((Y2 = Y1) => Y3) => (((in @ Y2 @ Y0) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((Y1 = Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y0 @ Y2) => (in @ Y1 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (powerset @ (setunion @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ 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))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (((dsetconstr @ Y1 @ Y0) = emptyset) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 41.00/5.55 inference(boolean_simplification,[],[f959])). 41.00/5.55 thf(f959,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) = (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (~ (emptyset = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((Y2 = Y1) => Y3) => (((in @ Y2 @ Y0) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((Y1 = Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y0 @ Y2) => (in @ Y1 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (powerset @ (setunion @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ 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))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (((dsetconstr @ Y1 @ Y0) = emptyset) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1)))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f958])). 41.00/5.55 thf(f958,plain,( 41.00/5.55 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) = (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (~ (emptyset = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((Y2 = Y1) => Y3) => (((in @ Y2 @ Y0) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((Y1 = Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y0 @ Y2) => (in @ Y1 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (powerset @ (setunion @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ 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))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (((dsetconstr @ Y1 @ Y0) = emptyset) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1)))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 41.00/5.55 inference(boolean_simplification,[],[f957])). 41.00/5.55 thf(f957,plain,( 41.00/5.55 ($true = (~ ((!! 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@ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ 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))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (((dsetconstr @ Y1 @ Y0) = emptyset) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1)))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 41.00/5.55 inference(boolean_simplification,[],[f955])). 41.00/5.55 thf(f955,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ ($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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1)))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))) => (!! @ $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)))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f954])). 41.00/5.55 thf(f954,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! 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@ ($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 > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1)))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))) => (!! @ $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]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f953])). 41.00/5.55 thf(f953,plain,( 41.00/5.55 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! 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@ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (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 > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) = (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (~ (emptyset = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((Y2 = Y1) => Y3) => (((in @ Y2 @ Y0) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((Y1 = Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y0 @ Y2) => (in @ Y1 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (powerset @ (setunion @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ 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))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (((dsetconstr @ Y1 @ Y0) = emptyset) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1)))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))) => (!! @ $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]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 41.00/5.55 inference(boolean_simplification,[],[f952])). 41.00/5.55 thf(f952,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! 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@ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! 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@ $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))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (((dsetconstr @ Y1 @ Y0) = emptyset) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ Y0)))))) => ((!! 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@ $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]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 41.00/5.55 inference(boolean_simplification,[],[f948])). 41.00/5.55 thf(f948,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f944])). 41.00/5.55 thf(f944,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! 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@ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) = (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (~ (emptyset = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! 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@ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y0 @ Y2) => (in @ Y1 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (powerset @ (setunion @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ 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))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (((dsetconstr @ Y1 @ Y0) = emptyset) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! 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@ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((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 @ Y0) = (setunion @ Y1))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f943])). 41.00/5.55 thf(f943,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! 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@ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((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 @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f942])). 41.00/5.55 thf(f942,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y5) = (Y2 @ Y4))))))))) => ((dsetconstr @ Y1 @ Y2) = (dsetconstr @ Y0 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f937])). 41.00/5.55 thf(f937,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! 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@ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) = (Y1 @ Y2))))))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f924])). 41.00/5.55 thf(f924,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $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 @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (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 @ Y0 @ (powerset @ Y1)) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (subset @ (powerset @ Y0) @ (powerset @ Y1))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 41.00/5.55 inference(boolean_simplification,[],[f918])). 41.00/5.55 thf(f918,plain,( 41.00/5.55 ($true = (~ ((!! 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@ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (subset @ (powerset @ Y0) @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (subset @ (dsetconstr @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 41.00/5.55 inference(boolean_simplification,[],[f915])). 41.00/5.55 thf(f915,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (subset @ (powerset @ Y0) @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (subset @ (dsetconstr @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (binunion @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ (binunion @ Y3 @ Y2)) => (((in @ Y0 @ Y3) => Y1) => (((in @ Y0 @ Y2) => Y1) => Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y2) | (in @ Y1 @ Y0))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 41.00/5.55 inference(boolean_simplification,[],[f911])). 41.00/5.55 thf(f911,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! 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@ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) = (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! 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@ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))) => (!! @ $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]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (subset @ (powerset @ Y0) @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (subset @ (dsetconstr @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (binunion @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ (binunion @ Y3 @ Y2)) => (((in @ Y0 @ Y3) => Y1) => (((in @ Y0 @ Y2) => Y1) => Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y2) | (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (in @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y1 @ Y2) => (subset @ Y1 @ (binintersect @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 41.00/5.55 inference(boolean_simplification,[],[f906])). 41.00/5.55 thf(f906,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! 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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)))) => (((dsetconstr @ Y1 @ Y0) = emptyset) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1)))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))) => (!! @ $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]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((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 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y5) = (Y2 @ Y4))))))))) => ((dsetconstr @ Y1 @ Y2) = (dsetconstr @ Y0 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y0) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y0) => ((~ (in @ Y1 @ Y0)) => (~ (in @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => (~ (subset @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (subset @ (powerset @ Y0) @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (subset @ (dsetconstr @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (binunion @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ (binunion @ Y3 @ Y2)) => (((in @ Y0 @ Y3) => Y1) => (((in @ Y0 @ Y2) => Y1) => Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y2) | (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (in @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y1 @ Y2) => (subset @ Y1 @ (binintersect @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 41.00/5.55 inference(boolean_simplification,[],[f904])). 41.00/5.55 thf(f904,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (binunion @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ (binunion @ Y3 @ Y2)) => (((in @ Y0 @ Y3) => Y1) => (((in @ Y0 @ Y2) => Y1) => Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y2) | (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (in @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (subset @ (powerset @ Y0) @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (subset @ (dsetconstr @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (binunion @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ (binunion @ Y3 @ Y2)) => (((in @ Y0 @ Y3) => Y1) => (((in @ Y0 @ Y2) => Y1) => Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y2) | (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (in @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y1 @ Y2) => (subset @ Y1 @ (binintersect @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 41.00/5.55 inference(boolean_simplification,[],[f902])). 41.00/5.55 thf(f902,plain,( 41.00/5.55 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) = (Y1 @ Y2))))))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y0 @ Y2) => (in @ Y1 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (powerset @ (setunion @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ 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))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! 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@ $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 @ Y2 @ Y0) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y0) => ((~ (in @ Y1 @ Y0)) => (~ (in @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => (~ (subset @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (subset @ (powerset @ Y0) @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (subset @ (dsetconstr @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (binunion @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ (binunion @ Y3 @ Y2)) => (((in @ Y0 @ Y3) => Y1) => (((in @ Y0 @ Y2) => Y1) => Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y2) | (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (in @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y1 @ Y2) => (subset @ Y1 @ (binintersect @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 41.00/5.56 inference(boolean_simplification,[],[f900])). 41.00/5.56 thf(f900,plain,( 41.00/5.56 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (binunion @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ (binunion @ Y3 @ Y2)) => (((in @ Y0 @ Y3) => Y1) => (((in @ Y0 @ Y2) => Y1) => Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y2) | (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (in @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y1 @ Y2) => (subset @ Y1 @ (binintersect @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y0 @ Y1) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y0) => (subset @ Y0 @ Y1)))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 41.00/5.56 inference(boolean_simplification,[],[f898])). 41.00/5.56 thf(f898,plain,( 41.00/5.56 ($true = (~ ((!! 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@ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y0 @ Y2) => (in @ Y1 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (powerset @ (setunion @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ 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))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (((dsetconstr @ Y1 @ Y0) = emptyset) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1)))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))) => (!! @ $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]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((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 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y5) = (Y2 @ Y4))))))))) => ((dsetconstr @ Y1 @ Y2) = (dsetconstr @ Y0 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y0) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y0) => ((~ (in @ Y1 @ Y0)) => (~ (in @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => (~ (subset @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (subset @ (powerset @ Y0) @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (subset @ (dsetconstr @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (binunion @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ (binunion @ Y3 @ Y2)) => (((in @ Y0 @ Y3) => Y1) => (((in @ Y0 @ Y2) => Y1) => Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y2) | (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (in @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y1 @ Y2) => (subset @ Y1 @ (binintersect @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y0 @ Y1) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y0 @ Y1) @ (binintersect @ Y0 @ Y2)) = (binintersect @ Y0 @ (binunion @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => (in @ Y2 @ (setminus @ Y0 @ Y1)))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 41.00/5.56 inference(boolean_simplification,[],[f896])). 41.00/5.56 thf(f896,plain,( 41.00/5.56 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) = (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (~ (emptyset = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((Y2 = Y1) => Y3) => (((in @ Y2 @ Y0) => Y3) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((Y1 = Y0) | (in @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y0 @ Y2) => (in @ Y1 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (powerset @ (setunion @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1)))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! 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@ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((emptyset = emptyset) => ((!! 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@ $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 @ Y5) = (Y2 @ Y4))))))))) => ((dsetconstr @ Y1 @ Y2) = (dsetconstr @ Y0 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y0) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y0 @ Y1) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y0 @ Y1) @ (binintersect @ Y0 @ Y2)) = (binintersect @ Y0 @ (binunion @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => (in @ Y2 @ (setminus @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 41.00/5.56 inference(boolean_simplification,[],[f895])). 41.00/5.56 thf(f895,plain,( 41.00/5.56 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (Y1 = Y0))))))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => ((in @ Y0 @ Y2) => (in @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y0 @ Y2) => (in @ Y1 @ (setunion @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setunion @ Y1)) => (!! @ $o @ (^[Y2 : $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ Y3) => ((in @ Y3 @ Y1) => Y2)))) => Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ Y1 @ (powerset @ (setunion @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y1 = Y2) = (Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: ($true & (in @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (Y1 = Y0)) => (~ (in @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (in @ 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))) => ((Y2 = Y1) | (Y1 = Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (Y0 @ Y2)))) => (((dsetconstr @ Y1 @ Y0) = emptyset) => $false)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ emptyset) => (Y1 @ Y0)))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (~ (Y0 @ Y2))))) => (~ (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1)))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))) => (!! @ $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]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ Y0) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((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 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y5) = (Y2 @ Y4))))))))) => ((dsetconstr @ Y1 @ Y2) = (dsetconstr @ Y0 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y0) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y0) => ((~ (in @ Y1 @ Y0)) => (~ (in @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => (~ (subset @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (subset @ (powerset @ Y0) @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (subset @ (dsetconstr @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (binunion @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ (binunion @ Y3 @ Y2)) => (((in @ Y0 @ Y3) => Y1) => (((in @ Y0 @ Y2) => Y1) => Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y2) | (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (in @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y1 @ Y2) => (subset @ Y1 @ (binintersect @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y0 @ Y1) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y0 @ Y1) @ (binintersect @ Y0 @ Y2)) = (binintersect @ Y0 @ (binunion @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => (in @ Y2 @ (setminus @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 41.00/5.56 inference(boolean_simplification,[],[f893])). 41.00/5.56 thf(f893,plain,( 41.00/5.56 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! 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@ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (~ (Y1 @ Y2)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) & (in @ Y2 @ Y1)))) => (~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2)))))))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) => ((!! @ $o @ (^[Y0 : $o]: (Y0 => (set2prop @ (prop2set @ Y0))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (in @ Y2 @ Y1))))) => (!! @ $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]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! 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@ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) = (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))))))))) => ((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 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))) => ((omega = omega) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (setadjoin @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y0 @ Y1) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ emptyset) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (in @ Y0 @ (powerset @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (subset @ (powerset @ Y0) @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (in @ (dsetconstr @ Y0 @ Y1) @ (powerset @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (subset @ (dsetconstr @ Y0 @ Y1) @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => (in @ Y0 @ (binunion @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (binunion @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y0 @ (binunion @ Y3 @ Y2)) => (((in @ Y0 @ Y3) => Y1) => (((in @ Y0 @ Y2) => Y1) => Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binunion @ Y2 @ Y0)) => ((in @ Y1 @ Y2) | (in @ Y1 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y1 @ (binunion @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => ((in @ Y0 @ Y2) => (in @ Y0 @ (binintersect @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y0) => ((subset @ Y1 @ Y2) => (subset @ Y1 @ (binintersect @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))) => ((!! @ $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 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y0 @ Y1) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y0 @ Y1) @ (binintersect @ Y0 @ Y2)) = (binintersect @ Y0 @ (binunion @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => (in @ Y2 @ (setminus @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y0 @ Y1))) => ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y2 @ Y1))) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (~ (in @ Y1 @ (setminus @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => (in @ Y2 @ (symdiff @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 41.00/5.56 inference(boolean_simplification,[],[f884])). 41.00/5.56 thf(f884,plain,( 41.00/5.56 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) = (Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((~ (emptyset = Y0)) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (~ (emptyset = (dsetconstr @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (~ (emptyset = Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (setadjoin @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((Y2 = Y1) => Y3) => (((in @ Y2 @ Y0) => Y3) => Y3))))))))))) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y0 @ Y1))) => ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y2 @ Y1))) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (~ (in @ Y1 @ (setminus @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => Y3)) => Y3))))))))))) => ((!! 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@ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) & (!! 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@ $i @ (^[Y3 : $i]: ((Y0 @ Y3) => (Y2 = Y3))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3))))))) => ((descr @ Y0) = (descr @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((Y4 = Y5) => ((Y3 @ Y5) = (Y2 @ Y4))))))))) => ((dsetconstr @ Y1 @ Y2) = (dsetconstr @ Y0 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (subset @ emptyset)) => ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y0 @ Y1) = Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y0) => (subset @ Y0 @ Y1)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y0 @ Y1) @ (binintersect @ Y0 @ Y2)) = (binintersect @ Y0 @ (binunion @ Y1 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => (in @ Y2 @ (setminus @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y0 @ Y1))) => ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y2 @ Y1))) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (~ (in @ Y1 @ (setminus @ Y2 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => (in @ Y2 @ (symdiff @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (~ (in @ Y2 @ (symdiff @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y0)) => ((~ (in @ Y2 @ Y1)) => (~ (in @ Y2 @ (symdiff @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 41.00/5.56 inference(boolean_simplification,[],[f879])). 41.00/5.56 thf(f879,plain,( 41.00/5.56 ($true = (~ ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => (in @ Y2 @ (symdiff @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (~ (in @ Y2 @ (symdiff @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y0)) => ((~ (in @ Y2 @ Y1)) => (~ (in @ Y2 @ (symdiff @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! 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@ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => Y3)) => Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => (in @ Y2 @ (symdiff @ Y0 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (~ (in @ Y2 @ (symdiff @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y0)) => ((~ (in @ Y2 @ Y1)) => (~ (in @ Y2 @ (symdiff @ Y0 @ Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y1 @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ Y1))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y0)))))))))) => ((!! @ $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 @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y0)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y0 @ Y2))))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 41.00/5.56 inference(boolean_simplification,[],[f870])). 41.00/5.56 thf(f870,plain,( 41.00/5.56 ($true = (~ ((!! 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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]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 41.00/5.56 inference(boolean_simplification,[],[f859])). 41.00/5.56 thf(f859,plain,( 41.00/5.56 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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 > $o) @ (^[Y1 : $i > $o]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))) => (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y2 @ Y3) => (Y0 = Y3))))) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y1 @ Y2)) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y1 @ Y2)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ Y0 @ Y1))))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 41.00/5.56 inference(boolean_simplification,[],[f857])). 41.00/5.56 thf(f857,plain,( 41.00/5.56 ($true = (~ ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y0 @ Y1) = (kpair @ Y3 @ Y2)) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) = (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y3 = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) = (setadjoin @ Y2 @ emptyset)) => (Y1 = Y0)))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 41.00/5.56 inference(boolean_simplification,[],[f845])). 41.00/5.56 thf(f845,plain,( 41.00/5.56 ((~ ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (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 @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => (Y1 = Y0)))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 41.00/5.56 inference(boolean_simplification,[],[f844])). 41.00/5.56 thf(f844,plain,( 41.00/5.56 ($true = (~ ((!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y0 @ Y1) = (kpair @ Y3 @ Y2)) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) = (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y3 = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ 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 @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y0 @ Y3)) => (Y3 = 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 @ Y1 @ (cartprod @ Y0 @ Y2)) => (in @ (ksnd @ Y1) @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y0 @ Y2) @ (cartprod @ Y3 @ Y1)) => (in @ Y0 @ Y3)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y1 @ Y2)) => (in @ Y3 @ Y2)))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 41.00/5.57 inference(boolean_simplification,[],[f837])). 41.00/5.57 thf(f837,plain,( 41.00/5.57 ((~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! 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@ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (Y0 @ (descr @ Y0))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((Y1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y2 @ Y1)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ Y1)) => (Y1 @ Y0)))))))) => ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y0 @ Y1) = (kpair @ Y3 @ Y2)) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) = (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y3 = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ 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 @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y0 @ Y3)) => (Y3 = 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 @ Y1 @ (cartprod @ Y0 @ Y2)) => (in @ (ksnd @ Y1) @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y0 @ Y2) @ (cartprod @ Y3 @ Y1)) => (in @ Y0 @ Y3)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y1 @ Y2)) => (in @ Y3 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((kpair @ Y1 @ Y3) = (kpair @ Y1 @ Y3)))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 41.00/5.57 inference(boolean_simplification,[],[f836])). 41.00/5.57 thf(f836,plain,( 41.00/5.57 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ omega) => (in @ (setadjoin @ Y0 @ Y0) @ omega)))) => ((!! @ $i @ (^[Y0 : $i]: (((!! @ $i @ (^[Y1 : $i]: (((in @ Y1 @ Y0) & (in @ Y1 @ omega)) => (in @ (setadjoin @ Y1 @ Y1) @ Y0)))) & (in @ emptyset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ omega) => (in @ Y1 @ Y0))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! 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@ $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 @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y0 @ Y1) = (kpair @ Y3 @ Y2)) => (Y3 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) = (setadjoin @ Y1 @ emptyset))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ (setadjoin @ Y0 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y3 = Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ 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 @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => (Y1 = Y0)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y0 @ Y3)) => (Y3 = 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 @ Y1 @ (cartprod @ Y0 @ Y2)) => (in @ (ksnd @ Y1) @ Y2)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y0 @ Y2) @ (cartprod @ Y3 @ Y1)) => (in @ Y0 @ Y3)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y1 @ Y2)) => (in @ Y3 @ Y2)))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((kpair @ Y1 @ Y3) = (kpair @ Y1 @ Y3)))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((kfst @ (kpair @ Y1 @ Y3)) = Y1))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((ksnd @ (kpair @ Y1 @ Y3)) = Y3))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ 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 @ Y2 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((Y3 @ Y2 @ Y4) => (in @ (kpair @ Y2 @ Y4) @ (dpsetconstr @ Y1 @ Y0 @ Y3))))))))))))))) => $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 41.00/5.57 inference(boolean_simplification,[],[f832])). 41.00/5.57 thf(f832,plain,( 41.00/5.57 ($true = (~ ((!! 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@ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y2 @ Y4) => (Y3 = Y4)))))))))) => (?? @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) = (?? @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) & (in @ Y4 @ Y1)))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & (~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (in @ Y2 @ Y0))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! 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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 @ Y2 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((Y3 @ Y2 @ Y4) => (in @ (kpair @ Y2 @ Y4) @ (dpsetconstr @ Y1 @ Y0 @ Y3))))))))))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y1 @ Y0 @ Y2) @ (cartprod @ Y1 @ Y0)))))))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y0 @ Y1 @ Y2) @ (cartprod @ Y0 @ Y1)))))))) => ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y2 @ Y3 @ Y0)) => (Y0 @ Y1 @ Y4)))))))))))))) => $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 41.00/5.57 inference(boolean_simplification,[],[f829])). 41.00/5.57 thf(f829,plain,( 41.00/5.57 ($true = (~ ((!! 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@ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (setunion @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))) @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $true)), 41.00/5.57 inference(beta_eta_normalization,[],[f824])). 41.00/5.57 thf(f824,plain,( 41.00/5.57 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) = (in @ Y2 @ Y1)))) => (Y1 = Y0)))))) => ((!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))) => ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) = ((in @ Y1 @ Y2) | (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]: ((?? @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) & (in @ Y2 @ Y1)))) = (in @ Y0 @ (setunion @ Y1))))))) => ((in @ emptyset @ omega) => ((!! 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[X0 : $i > $i > $o,X1,X2,X3,X4] : ((in @ (kpair @ X4 @ X1) @ (dpsetconstr @ X2 @ X3 @ (^[X5 : $i, X6 : $i] : (X0 @ X5 @ X6)))) => (in @ X1 @ X3)) = dpsetconstrEL2)), 41.00/5.57 inference(rectify,[],[f192])). 41.00/5.57 thf(f192,axiom,( 41.00/5.57 (! [X0 : $i > $i > $o,X2,X3,X4,X1] : ((in @ (kpair @ X1 @ X2) @ (dpsetconstr @ X3 @ X4 @ (^[X8 : $i, X10 : $i] : (X0 @ X8 @ X10)))) => (in @ X2 @ X4)) = dpsetconstrEL2)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',dpsetconstrEL2)). 41.00/5.57 thf(f678,plain,( 41.00/5.57 (dpsetconstrEL1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: ((in @ (kpair @ Y3 @ Y0) @ (dpsetconstr @ Y1 @ Y2 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y4 @ Y5 @ Y6)))))) => (in @ Y3 @ Y1)))))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f205])). 41.00/5.57 thf(f205,plain,( 41.00/5.57 (dpsetconstrEL1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: ((in @ (kpair @ Y3 @ Y0) @ (dpsetconstr @ Y1 @ Y2 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y4 @ Y5 @ Y6)))))) => (in @ Y3 @ Y1)))))))))))))), 41.00/5.57 inference(fool_elimination,[],[f204])). 41.00/5.57 thf(f204,plain,( 41.00/5.57 (! [X0 : $i > $i > $o,X1,X2,X3,X4] : ((in @ (kpair @ X1 @ X4) @ (dpsetconstr @ X3 @ X2 @ (^[X5 : $i, X6 : $i] : (X0 @ X5 @ X6)))) => (in @ X1 @ X3)) = dpsetconstrEL1)), 41.00/5.57 inference(rectify,[],[f191])). 41.00/5.57 thf(f191,axiom,( 41.00/5.57 (! [X0 : $i > $i > $o,X1,X4,X3,X2] : ((in @ (kpair @ X1 @ X2) @ (dpsetconstr @ X3 @ X4 @ (^[X8 : $i, X10 : $i] : (X0 @ X8 @ X10)))) => (in @ X1 @ X3)) = dpsetconstrEL1)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',dpsetconstrEL1)). 41.00/5.57 thf(f638,plain,( 41.00/5.57 (dpsetconstrERa = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y2 @ Y3 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y0 @ Y5 @ Y6)))))) => (Y0 @ Y1 @ Y4)))))))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f337])). 41.00/5.57 thf(f337,plain,( 41.00/5.57 (dpsetconstrERa = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((in @ (kpair @ Y1 @ Y4) @ (dpsetconstr @ Y2 @ Y3 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y0 @ Y5 @ Y6)))))) => (Y0 @ Y1 @ Y4)))))))))))))))), 41.00/5.57 inference(fool_elimination,[],[f336])). 41.00/5.57 thf(f336,plain,( 41.00/5.57 (! [X0,X1,X2,X3 : $i > $i > $o] : ((in @ X2 @ X1) => ! [X4] : ((in @ X4 @ X0) => ((in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X1 @ X0 @ (^[X5 : $i, X6 : $i] : (X3 @ X5 @ X6)))) => (X3 @ X2 @ X4)))) = dpsetconstrERa)), 41.00/5.57 inference(rectify,[],[f190])). 41.00/5.57 thf(f190,axiom,( 41.00/5.57 (! [X4,X3,X1,X0 : $i > $i > $o] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => ((in @ (kpair @ X1 @ X2) @ (dpsetconstr @ X3 @ X4 @ (^[X8 : $i, X10 : $i] : (X0 @ X8 @ X10)))) => (X0 @ X1 @ X2)))) = dpsetconstrERa)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',dpsetconstrERa)). 41.00/5.57 thf(f819,plain,( 41.00/5.57 (setOfPairsIsBReln = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y0 @ Y1 @ (dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y2 @ Y3 @ Y4)))))))))))))), 41.00/5.57 inference(definition_unfolding,[],[f709,f725])). 41.00/5.57 thf(f709,plain,( 41.00/5.57 (setOfPairsIsBReln = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (breln @ Y0 @ Y1 @ (dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y2 @ Y3 @ Y4)))))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f519])). 41.00/5.57 thf(f519,plain,( 41.00/5.57 (setOfPairsIsBReln = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (breln @ Y0 @ Y1 @ (dpsetconstr @ Y0 @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y2 @ Y3 @ Y4)))))))))))))), 41.00/5.57 inference(fool_elimination,[],[f518])). 41.00/5.57 thf(f518,plain,( 41.00/5.57 (setOfPairsIsBReln = ! [X0 : $i > $i > $o,X1,X2] : (breln @ X2 @ X1 @ (dpsetconstr @ X2 @ X1 @ (^[X3 : $i, X4 : $i] : (X0 @ X3 @ X4)))))), 41.00/5.57 inference(rectify,[],[f189])). 41.00/5.57 thf(f189,axiom,( 41.00/5.57 (setOfPairsIsBReln = ! [X0 : $i > $i > $o,X4,X3] : (breln @ X3 @ X4 @ (dpsetconstr @ X3 @ X4 @ (^[X1 : $i, X2 : $i] : (X0 @ X1 @ X2)))))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',setOfPairsIsBReln)). 41.00/5.57 thf(f699,plain,( 41.00/5.57 (dpsetconstrSub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y1 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y2 @ Y3 @ Y4))))) @ (cartprod @ Y1 @ Y0)))))))))), 41.00/5.57 inference(cnf_transformation,[],[f513])). 41.00/5.57 thf(f513,plain,( 41.00/5.57 (dpsetconstrSub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (subset @ (dpsetconstr @ Y1 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (Y2 @ Y3 @ Y4))))) @ (cartprod @ Y1 @ Y0)))))))))), 41.00/5.57 inference(fool_elimination,[],[f512])). 41.00/5.57 thf(f512,plain,( 41.00/5.57 (dpsetconstrSub = ! [X0 : $i > $i > $o,X1,X2] : (subset @ (dpsetconstr @ X1 @ X2 @ (^[X3 : $i, X4 : $i] : (X0 @ X3 @ X4))) @ (cartprod @ X1 @ X2)))), 41.00/5.57 inference(rectify,[],[f188])). 41.00/5.57 thf(f188,axiom,( 41.00/5.57 (dpsetconstrSub = ! [X0 : $i > $i > $o,X3,X4] : (subset @ (dpsetconstr @ X3 @ X4 @ (^[X1 : $i, X2 : $i] : (X0 @ X1 @ X2))) @ (cartprod @ X3 @ X4)))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',dpsetconstrSub)). 41.00/5.57 thf(f716,plain,( 41.00/5.57 (dpsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((Y3 @ Y2 @ Y4) => (in @ (kpair @ Y2 @ Y4) @ (dpsetconstr @ Y1 @ Y0 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y3 @ Y5 @ Y6))))))))))))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f585])). 41.00/5.57 thf(f585,plain,( 41.00/5.57 (dpsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((Y3 @ Y2 @ Y4) => (in @ (kpair @ Y2 @ Y4) @ (dpsetconstr @ Y1 @ Y0 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y3 @ Y5 @ Y6))))))))))))))))))))), 41.00/5.57 inference(fool_elimination,[],[f584])). 41.00/5.57 thf(f584,plain,( 41.00/5.57 (dpsetconstrI = ! [X0 : $i > $i > $o,X1,X2,X3] : ((in @ X1 @ X2) => ! [X4] : ((in @ X4 @ X3) => ((X0 @ X1 @ X4) => (in @ (kpair @ X1 @ X4) @ (dpsetconstr @ X2 @ X3 @ (^[X5 : $i, X6 : $i] : (X0 @ X5 @ X6))))))))), 41.00/5.57 inference(rectify,[],[f187])). 41.00/5.57 thf(f187,axiom,( 41.00/5.57 (dpsetconstrI = ! [X0 : $i > $i > $o,X1,X3,X4] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => ((X0 @ X1 @ X2) => (in @ (kpair @ X1 @ X2) @ (dpsetconstr @ X3 @ X4 @ (^[X8 : $i, X10 : $i] : (X0 @ X8 @ X10))))))))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',dpsetconstrI)). 41.00/5.57 thf(f741,plain,( 41.00/5.57 (cartprodpairsurjEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => ((kpair @ (kfst @ Y1) @ (ksnd @ Y1)) = Y1)))))))))), 41.00/5.57 inference(cnf_transformation,[],[f280])). 41.00/5.57 thf(f280,plain,( 41.00/5.57 (cartprodpairsurjEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => ((kpair @ (kfst @ Y1) @ (ksnd @ Y1)) = Y1)))))))))), 41.00/5.57 inference(fool_elimination,[],[f279])). 41.00/5.57 thf(f279,plain,( 41.00/5.57 (cartprodpairsurjEq = ! [X0,X1,X2] : ((in @ X1 @ (cartprod @ X0 @ X2)) => ((kpair @ (kfst @ X1) @ (ksnd @ X1)) = X1)))), 41.00/5.57 inference(rectify,[],[f185])). 41.00/5.57 thf(f185,axiom,( 41.00/5.57 (cartprodpairsurjEq = ! [X3,X10,X4] : ((in @ X10 @ (cartprod @ X3 @ X4)) => ((kpair @ (kfst @ X10) @ (ksnd @ X10)) = X10)))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',cartprodpairsurjEq)). 41.00/5.57 thf(f643,plain,( 41.00/5.57 (cartprodsndpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((ksnd @ (kpair @ Y1 @ Y3)) = Y3))))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f501])). 41.00/5.57 thf(f501,plain,( 41.00/5.57 (cartprodsndpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((ksnd @ (kpair @ Y1 @ Y3)) = Y3))))))))))))), 41.00/5.57 inference(fool_elimination,[],[f500])). 41.00/5.57 thf(f500,plain,( 41.00/5.57 (cartprodsndpairEq = ! [X0,X1,X2] : ((in @ X1 @ X2) => ! [X3] : ((in @ X3 @ X0) => ((ksnd @ (kpair @ X1 @ X3)) = X3))))), 41.00/5.57 inference(rectify,[],[f184])). 41.00/5.57 thf(f184,axiom,( 41.00/5.57 (cartprodsndpairEq = ! [X4,X1,X3] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => ((ksnd @ (kpair @ X1 @ X2)) = X2))))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',cartprodsndpairEq)). 41.00/5.57 thf(f677,plain,( 41.00/5.57 (cartprodfstpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((kfst @ (kpair @ Y1 @ Y3)) = Y1))))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f527])). 41.00/5.57 thf(f527,plain,( 41.00/5.57 (cartprodfstpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((kfst @ (kpair @ Y1 @ Y3)) = Y1))))))))))))), 41.00/5.57 inference(fool_elimination,[],[f526])). 41.00/5.57 thf(f526,plain,( 41.00/5.57 (! [X0,X1,X2] : ((in @ X1 @ X2) => ! [X3] : ((in @ X3 @ X0) => ((kfst @ (kpair @ X1 @ X3)) = X1))) = cartprodfstpairEq)), 41.00/5.57 inference(rectify,[],[f183])). 41.00/5.57 thf(f183,axiom,( 41.00/5.57 (! [X4,X1,X3] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => ((kfst @ (kpair @ X1 @ X2)) = X1))) = cartprodfstpairEq)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',cartprodfstpairEq)). 41.00/5.57 thf(f763,plain,( 41.00/5.57 (cartprodmempaircEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((kpair @ Y1 @ Y3) = (kpair @ Y1 @ Y3)))))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f479])). 41.00/5.57 thf(f479,plain,( 41.00/5.57 (cartprodmempaircEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((kpair @ Y1 @ Y3) = (kpair @ Y1 @ Y3)))))))))))))), 41.00/5.57 inference(fool_elimination,[],[f478])). 41.00/5.57 thf(f478,plain,( 41.00/5.57 (cartprodmempaircEq = ! [X0,X1,X2] : ((in @ X1 @ X0) => ! [X3] : ((in @ X3 @ X2) => ((kpair @ X1 @ X3) = (kpair @ X1 @ X3)))))), 41.00/5.57 inference(rectify,[],[f182])). 41.00/5.57 thf(f182,axiom,( 41.00/5.57 (cartprodmempaircEq = ! [X3,X1,X4] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => ((kpair @ X1 @ X2) = (kpair @ X1 @ X2)))))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',cartprodmempaircEq)). 41.00/5.57 thf(f621,plain,( 41.00/5.57 (cartprodpairmemER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y1 @ Y2)) => (in @ Y3 @ Y2)))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f424])). 41.00/5.57 thf(f424,plain,( 41.00/5.57 (cartprodpairmemER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y0 @ Y3) @ (cartprod @ Y1 @ Y2)) => (in @ Y3 @ Y2)))))))))))), 41.00/5.57 inference(fool_elimination,[],[f423])). 41.00/5.57 thf(f423,plain,( 41.00/5.57 (! [X0,X1,X2,X3] : ((in @ (kpair @ X3 @ X0) @ (cartprod @ X2 @ X1)) => (in @ X0 @ X1)) = cartprodpairmemER)), 41.00/5.57 inference(rectify,[],[f181])). 41.00/5.57 thf(f181,axiom,( 41.00/5.57 (! [X2,X4,X3,X1] : ((in @ (kpair @ X1 @ X2) @ (cartprod @ X3 @ X4)) => (in @ X2 @ X4)) = cartprodpairmemER)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',cartprodpairmemER)). 41.00/5.57 thf(f636,plain,( 41.00/5.57 (cartprodpairmemEL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y0 @ Y2) @ (cartprod @ Y3 @ Y1)) => (in @ Y0 @ Y3)))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f489])). 41.00/5.57 thf(f489,plain,( 41.00/5.57 (cartprodpairmemEL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ (kpair @ Y0 @ Y2) @ (cartprod @ Y3 @ Y1)) => (in @ Y0 @ Y3)))))))))))), 41.00/5.57 inference(fool_elimination,[],[f488])). 41.00/5.57 thf(f488,plain,( 41.00/5.57 (! [X0,X1,X2,X3] : ((in @ (kpair @ X3 @ X1) @ (cartprod @ X0 @ X2)) => (in @ X3 @ X0)) = cartprodpairmemEL)), 41.00/5.57 inference(rectify,[],[f180])). 41.00/5.57 thf(f180,axiom,( 41.00/5.57 (! [X3,X2,X4,X1] : ((in @ (kpair @ X1 @ X2) @ (cartprod @ X3 @ X4)) => (in @ X1 @ X3)) = cartprodpairmemEL)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',cartprodpairmemEL)). 41.00/5.57 thf(f779,plain,( 41.00/5.57 (cartprodsndin = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (in @ (ksnd @ Y1) @ Y2)))))))))), 41.00/5.57 inference(cnf_transformation,[],[f457])). 41.00/5.57 thf(f457,plain,( 41.00/5.57 (cartprodsndin = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (in @ (ksnd @ Y1) @ Y2)))))))))), 41.00/5.57 inference(fool_elimination,[],[f456])). 41.00/5.57 thf(f456,plain,( 41.00/5.57 (cartprodsndin = ! [X0,X1,X2] : ((in @ X1 @ (cartprod @ X2 @ X0)) => (in @ (ksnd @ X1) @ X0)))), 41.00/5.57 inference(rectify,[],[f179])). 41.00/5.57 thf(f179,axiom,( 41.00/5.57 (cartprodsndin = ! [X4,X10,X3] : ((in @ X10 @ (cartprod @ X3 @ X4)) => (in @ (ksnd @ X10) @ X4)))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',cartprodsndin)). 41.00/5.57 thf(f598,plain,( 41.00/5.57 (kpairsurjEq = (!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => ((kpair @ (kfst @ Y0) @ (ksnd @ Y0)) = Y0)))))), 41.00/5.57 inference(cnf_transformation,[],[f266])). 41.00/5.57 thf(f266,plain,( 41.00/5.57 (kpairsurjEq = (!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => ((kpair @ (kfst @ Y0) @ (ksnd @ Y0)) = Y0)))))), 41.00/5.57 inference(fool_elimination,[],[f265])). 41.00/5.57 thf(f265,plain,( 41.00/5.57 (! [X0] : ((iskpair @ X0) => ((kpair @ (kfst @ X0) @ (ksnd @ X0)) = X0)) = kpairsurjEq)), 41.00/5.57 inference(rectify,[],[f178])). 41.00/5.57 thf(f178,axiom,( 41.00/5.57 (! [X10] : ((iskpair @ X10) => ((kpair @ (kfst @ X10) @ (ksnd @ X10)) = X10)) = kpairsurjEq)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',kpairsurjEq)). 41.00/5.57 thf(f625,plain,( 41.00/5.57 (ksndpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y0 @ Y1)) = Y1))))))), 41.00/5.57 inference(cnf_transformation,[],[f487])). 41.00/5.57 thf(f487,plain,( 41.00/5.57 (ksndpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((ksnd @ (kpair @ Y0 @ Y1)) = Y1))))))), 41.00/5.57 inference(fool_elimination,[],[f486])). 41.00/5.57 thf(f486,plain,( 41.00/5.57 (ksndpairEq = ! [X0,X1] : ((ksnd @ (kpair @ X1 @ X0)) = X0))), 41.00/5.57 inference(rectify,[],[f177])). 41.00/5.57 thf(f177,axiom,( 41.00/5.57 (ksndpairEq = ! [X2,X1] : ((ksnd @ (kpair @ X1 @ X2)) = X2))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',ksndpairEq)). 41.00/5.57 thf(f818,plain,( 41.00/5.57 (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))))))))), 41.00/5.57 inference(definition_unfolding,[],[f669,f702])). 41.00/5.57 thf(f669,plain,( 41.00/5.57 (ksndsingleton = (!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (singleton @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: ((kpair @ (kfst @ Y0) @ Y1) = Y0))))))))), 41.00/5.57 inference(cnf_transformation,[],[f294])). 41.00/5.57 thf(f294,plain,( 41.00/5.57 (ksndsingleton = (!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (singleton @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: ((kpair @ (kfst @ Y0) @ Y1) = Y0))))))))), 41.00/5.57 inference(fool_elimination,[],[f293])). 41.00/5.57 thf(f293,plain,( 41.00/5.57 (! [X0] : ((iskpair @ X0) => (singleton @ (dsetconstr @ (setunion @ X0) @ (^[X1 : $i] : (((kpair @ (kfst @ X0) @ X1) = X0)))))) = ksndsingleton)), 41.00/5.57 inference(rectify,[],[f176])). 41.00/5.57 thf(f176,axiom,( 41.00/5.57 (! [X10] : ((iskpair @ X10) => (singleton @ (dsetconstr @ (setunion @ X10) @ (^[X1 : $i] : (((kpair @ (kfst @ X10) @ X1) = X10)))))) = ksndsingleton)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',ksndsingleton)). 41.00/5.57 thf(f675,plain,( 41.00/5.57 (setukpairinjR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y0 @ Y3)) => (Y3 = Y1)))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f292])). 41.00/5.57 thf(f292,plain,( 41.00/5.57 (setukpairinjR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y2 @ Y1) = (kpair @ Y0 @ Y3)) => (Y3 = Y1)))))))))))), 41.00/5.57 inference(fool_elimination,[],[f291])). 41.00/5.57 thf(f291,plain,( 41.00/5.57 (setukpairinjR = ! [X0,X1,X2,X3] : (((kpair @ X1 @ X2) = (kpair @ X3 @ X0)) => (X0 = X2)))), 41.00/5.57 inference(rectify,[],[f175])). 41.00/5.57 thf(f175,axiom,( 41.00/5.57 (setukpairinjR = ! [X2,X8,X10,X1] : (((kpair @ X1 @ X2) = (kpair @ X8 @ X10)) => (X2 = X10)))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',setukpairinjR)). 41.00/5.57 thf(f658,plain,( 41.00/5.57 (setukpairinjR2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => (Y1 = Y0)))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f290])). 41.00/5.57 thf(f290,plain,( 41.00/5.57 (setukpairinjR2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y3 @ emptyset) @ (setadjoin @ (setadjoin @ Y3 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))) => (Y1 = Y0)))))))))))), 41.00/5.57 inference(fool_elimination,[],[f289])). 41.00/5.57 thf(f289,plain,( 41.00/5.57 (setukpairinjR2 = ! [X0,X1,X2,X3] : (((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset)) @ emptyset))) => (X2 = X3)))), 41.00/5.57 inference(rectify,[],[f174])). 41.00/5.57 thf(f174,axiom,( 41.00/5.57 (setukpairinjR2 = ! [X8,X1,X10,X2] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X8 @ emptyset) @ (setadjoin @ (setadjoin @ X8 @ (setadjoin @ X10 @ emptyset)) @ emptyset))) => (X2 = X10)))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',setukpairinjR2)). 41.00/5.57 thf(f701,plain,( 41.00/5.57 (upairequniteq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) = (setadjoin @ Y2 @ emptyset)) => (Y1 = Y0)))))))))), 41.00/5.57 inference(cnf_transformation,[],[f288])). 41.00/5.57 thf(f288,plain,( 41.00/5.57 (upairequniteq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) = (setadjoin @ Y2 @ emptyset)) => (Y1 = Y0)))))))))), 41.00/5.57 inference(fool_elimination,[],[f287])). 41.00/5.57 thf(f287,plain,( 41.00/5.57 (upairequniteq = ! [X0,X1,X2] : (((setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)) = (setadjoin @ X0 @ emptyset)) => (X1 = X2)))), 41.00/5.57 inference(rectify,[],[f173])). 41.00/5.57 thf(f173,axiom,( 41.00/5.57 (upairequniteq = ! [X8,X2,X1] : (((setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) = (setadjoin @ X8 @ emptyset)) => (X1 = X2)))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',upairequniteq)). 41.00/5.57 thf(f597,plain,( 41.00/5.57 (setukpairinjR1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y3 = Y0))))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f497])). 41.00/5.57 thf(f497,plain,( 41.00/5.57 (setukpairinjR1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y2 @ emptyset) @ (setadjoin @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => ((Y3 = Y2) => (Y3 = Y0))))))))))))), 41.00/5.57 inference(fool_elimination,[],[f496])). 41.00/5.57 thf(f496,plain,( 41.00/5.57 (! [X0,X1,X2,X3] : (((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset))) => ((X0 = X1) => (X0 = X3))) = setukpairinjR1)), 41.00/5.57 inference(rectify,[],[f172])). 41.00/5.57 thf(f172,axiom,( 41.00/5.57 (! [X10,X8,X1,X2] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X8 @ emptyset) @ (setadjoin @ (setadjoin @ X8 @ (setadjoin @ X10 @ emptyset)) @ emptyset))) => ((X8 = X10) => (X2 = X10))) = setukpairinjR1)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',setukpairinjR1)). 41.00/5.57 thf(f615,plain,( 41.00/5.57 (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)))))))))), 41.00/5.57 inference(cnf_transformation,[],[f365])). 41.00/5.57 thf(f365,plain,( 41.00/5.57 (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)))))))))), 41.00/5.57 inference(fool_elimination,[],[f364])). 41.00/5.57 thf(f364,plain,( 41.00/5.57 (setukpairinjR12 = ! [X0,X1] : ((X0 = X1) => ((setadjoin @ (setadjoin @ X1 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset)))))), 41.00/5.57 inference(rectify,[],[f171])). 41.00/5.57 thf(f171,axiom,( 41.00/5.57 (setukpairinjR12 = ! [X2,X1] : ((X1 = X2) => ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X1 @ emptyset) @ emptyset))))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',setukpairinjR12)). 41.00/5.57 thf(f715,plain,( 41.00/5.57 (setukpairinjR11 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) = (setadjoin @ Y1 @ emptyset))))))))), 41.00/5.57 inference(cnf_transformation,[],[f595])). 41.00/5.57 thf(f595,plain,( 41.00/5.57 (setukpairinjR11 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) = (setadjoin @ Y1 @ emptyset))))))))), 41.00/5.57 inference(fool_elimination,[],[f594])). 41.00/5.57 thf(f594,plain,( 41.00/5.57 (setukpairinjR11 = ! [X0,X1] : ((X0 = X1) => ((setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) = (setadjoin @ X0 @ emptyset))))), 41.00/5.57 inference(rectify,[],[f170])). 41.00/5.57 thf(f170,axiom,( 41.00/5.57 (setukpairinjR11 = ! [X1,X2] : ((X1 = X2) => ((setadjoin @ X1 @ emptyset) = (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)))))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',setukpairinjR11)). 41.00/5.57 thf(f626,plain,( 41.00/5.57 (setukpairinjL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y0 @ Y1) = (kpair @ Y3 @ Y2)) => (Y3 = Y0)))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f587])). 41.00/5.57 thf(f587,plain,( 41.00/5.57 (setukpairinjL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((kpair @ Y0 @ Y1) = (kpair @ Y3 @ Y2)) => (Y3 = Y0)))))))))))), 41.00/5.57 inference(fool_elimination,[],[f586])). 41.00/5.57 thf(f586,plain,( 41.00/5.57 (setukpairinjL = ! [X0,X1,X2,X3] : (((kpair @ X3 @ X2) = (kpair @ X0 @ X1)) => (X0 = X3)))), 41.00/5.57 inference(rectify,[],[f169])). 41.00/5.57 thf(f169,axiom,( 41.00/5.57 (setukpairinjL = ! [X1,X2,X10,X8] : (((kpair @ X1 @ X2) = (kpair @ X8 @ X10)) => (X1 = X8)))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',setukpairinjL)). 41.00/5.57 thf(f781,plain,( 41.00/5.57 (setukpairinjL2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y1 = Y0)))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f503])). 41.00/5.57 thf(f503,plain,( 41.00/5.57 (setukpairinjL2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset))) => (Y1 = Y0)))))))))))), 41.00/5.57 inference(fool_elimination,[],[f502])). 41.00/5.57 thf(f502,plain,( 41.00/5.57 (! [X0,X1,X2,X3] : (((setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset)) @ emptyset))) => (X2 = X3)) = setukpairinjL2)), 41.00/5.57 inference(rectify,[],[f168])). 41.00/5.57 thf(f168,axiom,( 41.00/5.57 (! [X2,X10,X1,X8] : (((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)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',setukpairinjL2)). 41.00/5.57 thf(f693,plain,( 41.00/5.57 (cartprodfstin = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (in @ (kfst @ Y0) @ Y1)))))))))), 41.00/5.57 inference(cnf_transformation,[],[f262])). 41.00/5.57 thf(f262,plain,( 41.00/5.57 (cartprodfstin = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (cartprod @ Y1 @ Y2)) => (in @ (kfst @ Y0) @ Y1)))))))))), 41.00/5.57 inference(fool_elimination,[],[f261])). 41.00/5.57 thf(f261,plain,( 41.00/5.57 (! [X0,X1,X2] : ((in @ X2 @ (cartprod @ X1 @ X0)) => (in @ (kfst @ X2) @ X1)) = cartprodfstin)), 41.00/5.57 inference(rectify,[],[f167])). 41.00/5.57 thf(f167,axiom,( 41.00/5.57 (! [X4,X3,X10] : ((in @ X10 @ (cartprod @ X3 @ X4)) => (in @ (kfst @ X10) @ X3)) = cartprodfstin)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',cartprodfstin)). 41.00/5.57 thf(f724,plain,( 41.00/5.57 (kfstpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y1 @ Y0)) = Y1))))))), 41.00/5.57 inference(cnf_transformation,[],[f221])). 41.00/5.57 thf(f221,plain,( 41.00/5.57 (kfstpairEq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((kfst @ (kpair @ Y1 @ Y0)) = Y1))))))), 41.00/5.57 inference(fool_elimination,[],[f220])). 41.00/5.57 thf(f220,plain,( 41.00/5.57 (kfstpairEq = ! [X0,X1] : ((kfst @ (kpair @ X0 @ X1)) = X0))), 41.00/5.57 inference(rectify,[],[f166])). 41.00/5.57 thf(f166,axiom,( 41.00/5.57 (kfstpairEq = ! [X1,X2] : ((kfst @ (kpair @ X1 @ X2)) = X1))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',kfstpairEq)). 41.00/5.57 thf(f817,plain,( 41.00/5.57 (theprop = (!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & ((setadjoin @ Y2 @ emptyset) = Y1))))) @ Y0) => (in @ (setunion @ Y0) @ Y0)))))), 41.00/5.57 inference(definition_unfolding,[],[f641,f702])). 41.00/5.57 thf(f641,plain,( 41.00/5.57 (theprop = (!! @ $i @ (^[Y0 : $i]: ((singleton @ Y0) => (in @ (setunion @ Y0) @ Y0)))))), 41.00/5.57 inference(cnf_transformation,[],[f459])). 41.00/5.57 thf(f459,plain,( 41.00/5.57 (theprop = (!! @ $i @ (^[Y0 : $i]: ((singleton @ Y0) => (in @ (setunion @ Y0) @ Y0)))))), 41.00/5.57 inference(fool_elimination,[],[f458])). 41.00/5.57 thf(f458,plain,( 41.00/5.57 (theprop = ! [X0] : ((singleton @ X0) => (in @ (setunion @ X0) @ X0)))), 41.00/5.57 inference(rectify,[],[f165])). 41.00/5.57 thf(f165,axiom,( 41.00/5.57 (theprop = ! [X11] : ((singleton @ X11) => (in @ (setunion @ X11) @ X11)))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',theprop)). 41.00/5.57 thf(f816,plain,( 41.00/5.57 (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))))))))), 41.00/5.57 inference(definition_unfolding,[],[f777,f702])). 41.00/5.57 thf(f777,plain,( 41.00/5.57 (kfstsingleton = (!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (singleton @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: (in @ (setadjoin @ Y1 @ emptyset) @ Y0))))))))), 41.00/5.57 inference(cnf_transformation,[],[f331])). 41.00/5.57 thf(f331,plain,( 41.00/5.57 (kfstsingleton = (!! @ $i @ (^[Y0 : $i]: ((iskpair @ Y0) => (singleton @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: (in @ (setadjoin @ Y1 @ emptyset) @ Y0))))))))), 41.00/5.57 inference(fool_elimination,[],[f330])). 41.00/5.57 thf(f330,plain,( 41.00/5.57 (! [X0] : ((iskpair @ X0) => (singleton @ (dsetconstr @ (setunion @ X0) @ (^[X1 : $i] : (in @ (setadjoin @ X1 @ emptyset) @ X0))))) = kfstsingleton)), 41.00/5.57 inference(rectify,[],[f164])). 41.00/5.57 thf(f164,axiom,( 41.00/5.57 (! [X10] : ((iskpair @ X10) => (singleton @ (dsetconstr @ (setunion @ X10) @ (^[X1 : $i] : (in @ (setadjoin @ X1 @ emptyset) @ X10))))) = kfstsingleton)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',kfstsingleton)). 41.00/5.57 thf(f786,plain,( 41.00/5.57 (setukpairinjL1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = Y0)))))))))), 41.00/5.57 inference(cnf_transformation,[],[f243])). 41.00/5.57 thf(f243,plain,( 41.00/5.57 (setukpairinjL1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset))) => (Y1 = Y0)))))))))), 41.00/5.57 inference(fool_elimination,[],[f242])). 41.00/5.57 thf(f242,plain,( 41.00/5.57 (setukpairinjL1 = ! [X0,X1,X2] : ((in @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset)) @ emptyset))) => (X1 = X2)))), 41.00/5.57 inference(rectify,[],[f163])). 41.00/5.57 thf(f163,axiom,( 41.00/5.57 (setukpairinjL1 = ! [X2,X8,X1] : ((in @ (setadjoin @ X8 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset))) => (X1 = X8)))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',setukpairinjL1)). 41.00/5.57 thf(f787,plain,( 41.00/5.57 (singletonsuniq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))))), 41.00/5.57 inference(cnf_transformation,[],[f449])). 41.00/5.57 thf(f449,plain,( 41.00/5.57 (singletonsuniq = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((setadjoin @ Y0 @ emptyset) = (setadjoin @ Y1 @ emptyset)) => (Y1 = Y0)))))))), 41.00/5.57 inference(fool_elimination,[],[f448])). 41.00/5.57 thf(f448,plain,( 41.00/5.57 (! [X0,X1] : (((setadjoin @ X1 @ emptyset) = (setadjoin @ X0 @ emptyset)) => (X0 = X1)) = singletonsuniq)), 41.00/5.57 inference(rectify,[],[f162])). 41.00/5.57 thf(f162,axiom,( 41.00/5.57 (! [X2,X1] : (((setadjoin @ X2 @ emptyset) = (setadjoin @ X1 @ emptyset)) => (X1 = X2)) = singletonsuniq)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',singletonsuniq)). 41.00/5.57 thf(f815,plain,( 41.00/5.57 (ex1I2 = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => ((^[Y2 : $i]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & ((setadjoin @ Y5 @ emptyset) = Y4))))) @ (dsetconstr @ Y2 @ (^[Y4 : $i]: (Y3 @ Y4))))))) @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))))), 41.00/5.57 inference(definition_unfolding,[],[f766,f812])). 41.00/5.57 thf(f766,plain,( 41.00/5.57 (ex1I2 = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (ex1 @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f397])). 41.00/5.57 thf(f397,plain,( 41.00/5.57 (ex1I2 = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((Y1 @ Y2) => ((Y1 @ Y3) => (Y2 = Y3))))))))) => ((?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) => (ex1 @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))))), 41.00/5.57 inference(fool_elimination,[],[f396])). 41.00/5.57 thf(f396,plain,( 41.00/5.57 (! [X0 : $i > $o,X1] : (! [X2] : ((in @ X2 @ X1) => ! [X3] : ((in @ X3 @ X1) => ((X0 @ X2) => ((X0 @ X3) => (X2 = X3))))) => (? [X4] : ((in @ X4 @ X1) & (X0 @ X4)) => (ex1 @ X1 @ (^[X5 : $i] : (X0 @ X5))))) = ex1I2)), 41.00/5.57 inference(rectify,[],[f161])). 41.00/5.57 thf(f161,axiom,( 41.00/5.57 (! [X0 : $i > $o,X3] : (! [X1] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X3) => ((X0 @ X1) => ((X0 @ X2) => (X1 = X2))))) => (? [X1] : ((in @ X1 @ X3) & (X0 @ X1)) => (ex1 @ X3 @ (^[X1 : $i] : (X0 @ X1))))) = ex1I2)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',ex1I2)). 41.00/5.57 thf(f814,plain,( 41.00/5.57 (ex1I = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y2 @ Y3) => (Y0 = Y3))))) => ((^[Y3 : $i]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) & ((setadjoin @ Y6 @ emptyset) = Y5))))) @ (dsetconstr @ Y3 @ (^[Y5 : $i]: (Y4 @ Y5))))))) @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))), 41.00/5.57 inference(definition_unfolding,[],[f788,f812])). 41.00/5.57 thf(f788,plain,( 41.00/5.57 (ex1I = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y2 @ Y3) => (Y0 = Y3))))) => (ex1 @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f439])). 41.00/5.57 thf(f439,plain,( 41.00/5.57 (ex1I = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((Y2 @ Y3) => (Y0 = Y3))))) => (ex1 @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))), 41.00/5.57 inference(fool_elimination,[],[f438])). 41.00/5.57 thf(f438,plain,( 41.00/5.57 (! [X0 : $i > $o,X1,X2] : ((in @ X2 @ X1) => ((X0 @ X2) => (! [X3] : ((in @ X3 @ X1) => ((X0 @ X3) => (X2 = X3))) => (ex1 @ X1 @ (^[X4 : $i] : (X0 @ X4)))))) = ex1I)), 41.00/5.57 inference(rectify,[],[f160])). 41.00/5.57 thf(f160,axiom,( 41.00/5.57 (! [X0 : $i > $o,X3,X1] : ((in @ X1 @ X3) => ((X0 @ X1) => (! [X2] : ((in @ X2 @ X3) => ((X0 @ X2) => (X1 = X2))) => (ex1 @ X3 @ (^[X2 : $i] : (X0 @ X2)))))) = ex1I)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',ex1I)). 41.00/5.57 thf(f813,plain,( 41.00/5.57 (ex1E1 = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (((^[Y2 : $i]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y4) & ((setadjoin @ Y5 @ emptyset) = Y4))))) @ (dsetconstr @ Y2 @ (^[Y4 : $i]: (Y3 @ Y4))))))) @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) => (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))))))))), 41.00/5.57 inference(definition_unfolding,[],[f671,f812])). 41.00/5.57 thf(f671,plain,( 41.00/5.57 (ex1E1 = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((ex1 @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) => (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f219])). 41.00/5.57 thf(f219,plain,( 41.00/5.57 (ex1E1 = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((ex1 @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))) => (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0))))))))))), 41.00/5.57 inference(fool_elimination,[],[f218])). 41.00/5.57 thf(f218,plain,( 41.00/5.57 (! [X0 : $i > $o,X1] : ((ex1 @ X1 @ (^[X2 : $i] : (X0 @ X2))) => ? [X3] : ((in @ X3 @ X1) & (X0 @ X3))) = ex1E1)), 41.00/5.57 inference(rectify,[],[f159])). 41.00/5.57 thf(f159,axiom,( 41.00/5.57 (! [X0 : $i > $o,X3] : ((ex1 @ X3 @ (^[X1 : $i] : (X0 @ X1))) => ? [X1] : ((in @ X1 @ X3) & (X0 @ X1))) = ex1E1)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',ex1E1)). 41.00/5.57 thf(f811,plain,( 41.00/5.57 (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)))))))))))), 41.00/5.57 inference(definition_unfolding,[],[f685,f702])). 41.00/5.57 thf(f685,plain,( 41.00/5.57 (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)))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f575])). 41.00/5.57 thf(f575,plain,( 41.00/5.57 (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)))))))))))), 41.00/5.57 inference(fool_elimination,[],[f574])). 41.00/5.57 thf(f574,plain,( 41.00/5.57 (! [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)))))) = singletonprop)), 41.00/5.57 inference(rectify,[],[f157])). 41.00/5.57 thf(f157,axiom,( 41.00/5.57 (! [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)))))) = singletonprop)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',singletonprop)). 41.00/5.57 thf(f647,plain,( 41.00/5.57 (setunionsingleton = (!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))))), 41.00/5.57 inference(cnf_transformation,[],[f589])). 41.00/5.57 thf(f589,plain,( 41.00/5.57 (setunionsingleton = (!! @ $i @ (^[Y0 : $i]: ((setunion @ (setadjoin @ Y0 @ emptyset)) = Y0))))), 41.00/5.57 inference(fool_elimination,[],[f588])). 41.00/5.57 thf(f588,plain,( 41.00/5.57 (! [X0] : ((setunion @ (setadjoin @ X0 @ emptyset)) = X0) = setunionsingleton)), 41.00/5.57 inference(rectify,[],[f155])). 41.00/5.57 thf(f155,axiom,( 41.00/5.57 (! [X1] : ((setunion @ (setadjoin @ X1 @ emptyset)) = X1) = setunionsingleton)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',setunionsingleton)). 41.00/5.57 thf(f756,plain,( 41.00/5.57 (setunionsingleton2 = (!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))))), 41.00/5.57 inference(cnf_transformation,[],[f555])). 41.00/5.57 thf(f555,plain,( 41.00/5.57 (setunionsingleton2 = (!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ (setunion @ (setadjoin @ Y0 @ emptyset))))))), 41.00/5.57 inference(fool_elimination,[],[f554])). 41.00/5.57 thf(f554,plain,( 41.00/5.57 (! [X0] : (subset @ X0 @ (setunion @ (setadjoin @ X0 @ emptyset))) = setunionsingleton2)), 41.00/5.57 inference(rectify,[],[f154])). 41.00/5.57 thf(f154,axiom,( 41.00/5.57 (! [X3] : (subset @ X3 @ (setunion @ (setadjoin @ X3 @ emptyset))) = setunionsingleton2)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',setunionsingleton2)). 41.00/5.57 thf(f760,plain,( 41.00/5.57 (setunionsingleton1 = (!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))))), 41.00/5.57 inference(cnf_transformation,[],[f237])). 41.00/5.57 thf(f237,plain,( 41.00/5.57 (setunionsingleton1 = (!! @ $i @ (^[Y0 : $i]: (subset @ (setunion @ (setadjoin @ Y0 @ emptyset)) @ Y0))))), 41.00/5.57 inference(fool_elimination,[],[f236])). 41.00/5.57 thf(f236,plain,( 41.00/5.57 (setunionsingleton1 = ! [X0] : (subset @ (setunion @ (setadjoin @ X0 @ emptyset)) @ X0))), 41.00/5.57 inference(rectify,[],[f153])). 41.00/5.57 thf(f153,axiom,( 41.00/5.57 (setunionsingleton1 = ! [X3] : (subset @ (setunion @ (setadjoin @ X3 @ emptyset)) @ X3))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',setunionsingleton1)). 41.00/5.57 thf(f733,plain,( 41.00/5.57 (setunionE2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f361])). 41.00/5.57 thf(f361,plain,( 41.00/5.57 (setunionE2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) & (in @ Y2 @ Y0))))))))))), 41.00/5.57 inference(fool_elimination,[],[f360])). 41.00/5.57 thf(f360,plain,( 41.00/5.57 (! [X0,X1] : ((in @ X0 @ (setunion @ X1)) => ? [X2] : ((in @ X2 @ X1) & (in @ X0 @ X2))) = setunionE2)), 41.00/5.57 inference(rectify,[],[f152])). 41.00/5.57 thf(f152,axiom,( 41.00/5.57 (! [X1,X3] : ((in @ X1 @ (setunion @ X3)) => ? [X11] : ((in @ X11 @ X3) & (in @ X1 @ X11))) = setunionE2)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',setunionE2)). 41.00/5.57 thf(f596,plain,( 41.00/5.57 (cartprodmempair = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (iskpair @ Y1)))))))))), 41.00/5.57 inference(cnf_transformation,[],[f577])). 41.00/5.57 thf(f577,plain,( 41.00/5.57 (cartprodmempair = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y0 @ Y2)) => (iskpair @ Y1)))))))))), 41.00/5.57 inference(fool_elimination,[],[f576])). 41.00/5.57 thf(f576,plain,( 41.00/5.57 (cartprodmempair = ! [X0,X1,X2] : ((in @ X1 @ (cartprod @ X2 @ X0)) => (iskpair @ X1)))), 41.00/5.57 inference(rectify,[],[f151])). 41.00/5.57 thf(f151,axiom,( 41.00/5.57 (cartprodmempair = ! [X4,X10,X3] : ((in @ X10 @ (cartprod @ X3 @ X4)) => (iskpair @ X10)))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',cartprodmempair)). 41.00/5.57 thf(f645,plain,( 41.00/5.57 (cartprodmempair1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y1)))))))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f505])). 41.00/5.57 thf(f505,plain,( 41.00/5.57 (cartprodmempair1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (cartprod @ Y2 @ Y0)) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) & (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) & ((kpair @ Y3 @ Y4) = Y1)))))))))))))))), 41.00/5.57 inference(fool_elimination,[],[f504])). 41.00/5.57 thf(f504,plain,( 41.00/5.57 (cartprodmempair1 = ! [X0,X1,X2] : ((in @ X1 @ (cartprod @ X0 @ X2)) => ? [X3] : (? [X4] : (((kpair @ X3 @ X4) = X1) & (in @ X4 @ X2)) & (in @ X3 @ X0))))), 41.00/5.57 inference(rectify,[],[f150])). 41.00/5.57 thf(f150,axiom,( 41.00/5.57 (cartprodmempair1 = ! [X3,X10,X4] : ((in @ X10 @ (cartprod @ X3 @ X4)) => ? [X1] : (? [X2] : (((kpair @ X1 @ X2) = X10) & (in @ X2 @ X4)) & (in @ X1 @ X3))))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',cartprodmempair1)). 41.00/5.57 thf(f601,plain,( 41.00/5.57 (cartprodpairin = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y2 @ Y3) @ (cartprod @ Y0 @ Y1)))))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f270])). 41.00/5.57 thf(f270,plain,( 41.00/5.57 (cartprodpairin = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (kpair @ Y2 @ Y3) @ (cartprod @ Y0 @ Y1)))))))))))))), 41.00/5.57 inference(fool_elimination,[],[f269])). 41.00/5.57 thf(f269,plain,( 41.00/5.57 (! [X0,X1,X2] : ((in @ X0 @ X2) => ! [X3] : ((in @ X3 @ X1) => (in @ (kpair @ X0 @ X3) @ (cartprod @ X2 @ X1)))) = cartprodpairin)), 41.00/5.57 inference(rectify,[],[f149])). 41.00/5.57 thf(f149,axiom,( 41.00/5.57 (! [X1,X4,X3] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => (in @ (kpair @ X1 @ X2) @ (cartprod @ X3 @ X4)))) = cartprodpairin)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',cartprodpairin)). 41.00/5.57 thf(f729,plain,( 41.00/5.57 (ubforcartprodlem3 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y2 @ Y3) @ (powerset @ (powerset @ (binunion @ Y1 @ Y0)))))))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f463])). 41.00/5.57 thf(f463,plain,( 41.00/5.57 (ubforcartprodlem3 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y2 @ Y3) @ (powerset @ (powerset @ (binunion @ Y1 @ Y0)))))))))))))))), 41.00/5.57 inference(fool_elimination,[],[f462])). 41.00/5.57 thf(f462,plain,( 41.00/5.57 (! [X0,X1,X2] : ((in @ X0 @ X1) => ! [X3] : ((in @ X3 @ X2) => (in @ (kpair @ X0 @ X3) @ (powerset @ (powerset @ (binunion @ X1 @ X2)))))) = ubforcartprodlem3)), 41.00/5.57 inference(rectify,[],[f148])). 41.00/5.57 thf(f148,axiom,( 41.00/5.57 (! [X1,X3,X4] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => (in @ (kpair @ X1 @ X2) @ (powerset @ (powerset @ (binunion @ X3 @ X4)))))) = ubforcartprodlem3)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',ubforcartprodlem3)). 41.00/5.57 thf(f682,plain,( 41.00/5.57 (ubforcartprodlem2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f434])). 41.00/5.57 thf(f434,plain,( 41.00/5.57 (ubforcartprodlem2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))))), 41.00/5.57 inference(fool_elimination,[],[f433])). 41.00/5.57 thf(f433,plain,( 41.00/5.57 (! [X0,X1,X2] : ((in @ X2 @ X1) => ! [X3] : ((in @ X3 @ X0) => (in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1 @ X0)))))) = ubforcartprodlem2)), 41.00/5.57 inference(rectify,[],[f147])). 41.00/5.57 thf(f147,axiom,( 41.00/5.57 (! [X4,X3,X1] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => (in @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X3 @ X4)))))) = ubforcartprodlem2)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',ubforcartprodlem2)). 41.00/5.57 thf(f790,plain,( 41.00/5.57 (ubforcartprodlem1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y0 @ Y2))))))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f399])). 41.00/5.57 thf(f399,plain,( 41.00/5.57 (ubforcartprodlem1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (subset @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ Y0 @ Y2))))))))))))))), 41.00/5.57 inference(fool_elimination,[],[f398])). 41.00/5.57 thf(f398,plain,( 41.00/5.57 (ubforcartprodlem1 = ! [X0,X1,X2] : ((in @ X1 @ X2) => ! [X3] : ((in @ X3 @ X0) => (subset @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X2 @ X0))))))), 41.00/5.57 inference(rectify,[],[f146])). 41.00/5.57 thf(f146,axiom,( 41.00/5.57 (ubforcartprodlem1 = ! [X4,X1,X3] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => (subset @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X3 @ X4))))))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',ubforcartprodlem1)). 41.00/5.57 thf(f653,plain,( 41.00/5.57 (upairinpowunion = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f343])). 41.00/5.57 thf(f343,plain,( 41.00/5.57 (upairinpowunion = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ (powerset @ (binunion @ Y2 @ Y0))))))))))))))), 41.00/5.57 inference(fool_elimination,[],[f342])). 41.00/5.57 thf(f342,plain,( 41.00/5.57 (! [X0,X1,X2] : ((in @ X1 @ X0) => ! [X3] : ((in @ X3 @ X2) => (in @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X0 @ X2))))) = upairinpowunion)), 41.00/5.57 inference(rectify,[],[f145])). 41.00/5.57 thf(f145,axiom,( 41.00/5.57 (! [X3,X1,X4] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => (in @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ (powerset @ (binunion @ X3 @ X4))))) = upairinpowunion)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',upairinpowunion)). 41.00/5.57 thf(f753,plain,( 41.00/5.57 (upairsubunion = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y0)))))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f215])). 41.00/5.57 thf(f215,plain,( 41.00/5.57 (upairsubunion = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (subset @ (setadjoin @ Y2 @ (setadjoin @ Y3 @ emptyset)) @ (binunion @ Y1 @ Y0)))))))))))))), 41.00/5.57 inference(fool_elimination,[],[f214])). 41.00/5.57 thf(f214,plain,( 41.00/5.57 (! [X0,X1,X2] : ((in @ X0 @ X1) => ! [X3] : ((in @ X3 @ X2) => (subset @ (setadjoin @ X0 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X1 @ X2)))) = upairsubunion)), 41.00/5.57 inference(rectify,[],[f144])). 41.00/5.57 thf(f144,axiom,( 41.00/5.57 (! [X1,X3,X4] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => (subset @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ (binunion @ X3 @ X4)))) = upairsubunion)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',upairsubunion)). 41.00/5.57 thf(f698,plain,( 41.00/5.57 (upairset2E = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f420])). 41.00/5.57 thf(f420,plain,( 41.00/5.57 (upairset2E = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y2 @ (setadjoin @ Y1 @ emptyset))) => ((Y2 = Y0) | (Y1 = Y0))))))))))), 41.00/5.57 inference(fool_elimination,[],[f419])). 41.00/5.57 thf(f419,plain,( 41.00/5.57 (upairset2E = ! [X0,X1,X2] : ((in @ X2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) => ((X1 = X2) | (X0 = X2))))), 41.00/5.57 inference(rectify,[],[f143])). 41.00/5.57 thf(f143,axiom,( 41.00/5.57 (upairset2E = ! [X1,X2,X8] : ((in @ X8 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset))) => ((X2 = X8) | (X1 = X8))))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',upairset2E)). 41.00/5.57 thf(f635,plain,( 41.00/5.57 (singletoninpowunion = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y0)))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f455])). 41.00/5.57 thf(f455,plain,( 41.00/5.57 (singletoninpowunion = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ (setadjoin @ Y1 @ emptyset) @ (powerset @ (binunion @ Y2 @ Y0)))))))))))), 41.00/5.57 inference(fool_elimination,[],[f454])). 41.00/5.57 thf(f454,plain,( 41.00/5.57 (! [X0,X1,X2] : ((in @ X1 @ X0) => (in @ (setadjoin @ X1 @ emptyset) @ (powerset @ (binunion @ X0 @ X2)))) = singletoninpowunion)), 41.00/5.57 inference(rectify,[],[f142])). 41.00/5.57 thf(f142,axiom,( 41.00/5.57 (! [X3,X1,X4] : ((in @ X1 @ X3) => (in @ (setadjoin @ X1 @ emptyset) @ (powerset @ (binunion @ X3 @ X4)))) = singletoninpowunion)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',singletoninpowunion)). 41.00/5.57 thf(f683,plain,( 41.00/5.57 (singletoninpowerset = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ Y1))))))))), 41.00/5.57 inference(cnf_transformation,[],[f308])). 41.00/5.57 thf(f308,plain,( 41.00/5.57 (singletoninpowerset = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ (setadjoin @ Y0 @ emptyset) @ (powerset @ Y1))))))))), 41.00/5.57 inference(fool_elimination,[],[f307])). 41.00/5.57 thf(f307,plain,( 41.00/5.57 (! [X0,X1] : ((in @ X1 @ X0) => (in @ (setadjoin @ X1 @ emptyset) @ (powerset @ X0))) = singletoninpowerset)), 41.00/5.57 inference(rectify,[],[f141])). 41.00/5.57 thf(f141,axiom,( 41.00/5.57 (! [X3,X1] : ((in @ X1 @ X3) => (in @ (setadjoin @ X1 @ emptyset) @ (powerset @ X3))) = singletoninpowerset)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',singletoninpowerset)). 41.00/5.57 thf(f727,plain,( 41.00/5.57 (singletonsubset = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))))), 41.00/5.57 inference(cnf_transformation,[],[f385])). 41.00/5.57 thf(f385,plain,( 41.00/5.57 (singletonsubset = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ (setadjoin @ Y1 @ emptyset) @ Y0)))))))), 41.00/5.57 inference(fool_elimination,[],[f384])). 41.00/5.57 thf(f384,plain,( 41.00/5.57 (singletonsubset = ! [X0,X1] : ((in @ X0 @ X1) => (subset @ (setadjoin @ X0 @ emptyset) @ X1)))), 41.00/5.57 inference(rectify,[],[f140])). 41.00/5.57 thf(f140,axiom,( 41.00/5.57 (singletonsubset = ! [X1,X3] : ((in @ X1 @ X3) => (subset @ (setadjoin @ X1 @ emptyset) @ X3)))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',singletonsubset)). 41.00/5.57 thf(f619,plain,( 41.00/5.57 (kpairp = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y1 @ Y0)))))))), 41.00/5.57 inference(cnf_transformation,[],[f355])). 41.00/5.57 thf(f355,plain,( 41.00/5.57 (kpairp = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (kpair @ Y1 @ Y0)))))))), 41.00/5.57 inference(fool_elimination,[],[f354])). 41.00/5.57 thf(f354,plain,( 41.00/5.57 (! [X0,X1] : (iskpair @ (kpair @ X0 @ X1)) = kpairp)), 41.00/5.57 inference(rectify,[],[f139])). 41.00/5.57 thf(f139,axiom,( 41.00/5.57 (! [X1,X2] : (iskpair @ (kpair @ X1 @ X2)) = kpairp)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',kpairp)). 41.00/5.57 thf(f656,plain,( 41.00/5.57 (kpairiskpair = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))))), 41.00/5.57 inference(cnf_transformation,[],[f461])). 41.00/5.57 thf(f461,plain,( 41.00/5.57 (kpairiskpair = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (iskpair @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset))))))))), 41.00/5.57 inference(fool_elimination,[],[f460])). 41.00/5.57 thf(f460,plain,( 41.00/5.57 (! 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[X1,X2] : (iskpair @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset))) = kpairiskpair)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',kpairiskpair)). 41.00/5.57 thf(f612,plain,( 41.00/5.57 (setukpairIR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))))), 41.00/5.57 inference(cnf_transformation,[],[f517])). 41.00/5.57 thf(f517,plain,( 41.00/5.57 (setukpairIR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))))), 41.00/5.57 inference(fool_elimination,[],[f516])). 41.00/5.57 thf(f516,plain,( 41.00/5.57 (! [X0,X1] : (in @ X0 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset)))) = setukpairIR)), 41.00/5.57 inference(rectify,[],[f137])). 41.00/5.57 thf(f137,axiom,( 41.00/5.57 (! [X2,X1] : (in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)))) = setukpairIR)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',setukpairIR)). 41.00/5.57 thf(f720,plain,( 41.00/5.57 (setukpairIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))))), 41.00/5.57 inference(cnf_transformation,[],[f545])). 41.00/5.57 thf(f545,plain,( 41.00/5.57 (setukpairIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setunion @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)))))))))), 41.00/5.57 inference(fool_elimination,[],[f544])). 41.00/5.57 thf(f544,plain,( 41.00/5.57 (setukpairIL = ! [X0,X1] : (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ emptyset)))))), 41.00/5.57 inference(rectify,[],[f136])). 41.00/5.57 thf(f136,axiom,( 41.00/5.57 (setukpairIL = ! [X2,X1] : (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)))))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',setukpairIL)). 41.00/5.57 thf(f664,plain,( 41.00/5.57 (secondinupair = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))), 41.00/5.57 inference(cnf_transformation,[],[f509])). 41.00/5.57 thf(f509,plain,( 41.00/5.57 (secondinupair = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))), 41.00/5.57 inference(fool_elimination,[],[f508])). 41.00/5.57 thf(f508,plain,( 41.00/5.57 (! [X0,X1] : (in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = secondinupair)), 41.00/5.57 inference(rectify,[],[f135])). 41.00/5.57 thf(f135,axiom,( 41.00/5.57 (! [X1,X2] : (in @ X2 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset))) = secondinupair)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',secondinupair)). 41.00/5.57 thf(f606,plain,( 41.00/5.57 (symdiffIneg2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y0)) => ((~ (in @ Y2 @ Y1)) => (~ (in @ Y2 @ (symdiff @ Y0 @ Y1))))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f272])). 41.00/5.57 thf(f272,plain,( 41.00/5.57 (symdiffIneg2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y0)) => ((~ (in @ Y2 @ Y1)) => (~ (in @ Y2 @ (symdiff @ Y0 @ Y1))))))))))))), 41.00/5.57 inference(fool_elimination,[],[f271])). 41.00/5.57 thf(f271,plain,( 41.00/5.57 (! [X0,X1,X2] : (~(in @ X0 @ X2) => (~(in @ X0 @ X1) => ~(in @ X0 @ (symdiff @ X2 @ X1)))) = symdiffIneg2)), 41.00/5.57 inference(rectify,[],[f134])). 41.00/5.57 thf(f134,axiom,( 41.00/5.57 (! [X1,X4,X3] : (~(in @ X1 @ X3) => (~(in @ X1 @ X4) => ~(in @ X1 @ (symdiff @ X3 @ X4)))) = symdiffIneg2)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',symdiffIneg2)). 41.00/5.57 thf(f743,plain,( 41.00/5.57 (symdiffIneg1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (~ (in @ Y2 @ (symdiff @ Y0 @ Y1))))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f507])). 41.00/5.57 thf(f507,plain,( 41.00/5.57 (symdiffIneg1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ Y1) => (~ (in @ Y2 @ (symdiff @ Y0 @ Y1))))))))))))), 41.00/5.57 inference(fool_elimination,[],[f506])). 41.00/5.57 thf(f506,plain,( 41.00/5.57 (symdiffIneg1 = ! [X0,X1,X2] : ((in @ X0 @ X2) => ((in @ X0 @ X1) => ~(in @ X0 @ (symdiff @ X2 @ X1)))))), 41.00/5.57 inference(rectify,[],[f133])). 41.00/5.57 thf(f133,axiom,( 41.00/5.57 (symdiffIneg1 = ! [X1,X4,X3] : ((in @ X1 @ X3) => ((in @ X1 @ X4) => ~(in @ X1 @ (symdiff @ X3 @ X4)))))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',symdiffIneg1)). 41.00/5.57 thf(f759,plain,( 41.00/5.57 (symdiffI2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f393])). 41.00/5.57 thf(f393,plain,( 41.00/5.57 (symdiffI2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ Y1)) => ((in @ Y2 @ Y0) => (in @ Y2 @ (symdiff @ Y1 @ Y0)))))))))))), 41.00/5.57 inference(fool_elimination,[],[f392])). 41.00/5.57 thf(f392,plain,( 41.00/5.57 (! [X0,X1,X2] : (~(in @ X0 @ X1) => ((in @ X0 @ X2) => (in @ X0 @ (symdiff @ X1 @ X2)))) = symdiffI2)), 41.00/5.57 inference(rectify,[],[f132])). 41.00/5.57 thf(f132,axiom,( 41.00/5.57 (! [X1,X3,X4] : (~(in @ X1 @ X3) => ((in @ X1 @ X4) => (in @ X1 @ (symdiff @ X3 @ X4)))) = symdiffI2)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',symdiffI2)). 41.00/5.57 thf(f704,plain,( 41.00/5.57 (symdiffI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => (in @ Y2 @ (symdiff @ Y0 @ Y1)))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f422])). 41.00/5.57 thf(f422,plain,( 41.00/5.57 (symdiffI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => (in @ Y2 @ (symdiff @ Y0 @ Y1)))))))))))), 41.00/5.57 inference(fool_elimination,[],[f421])). 41.00/5.57 thf(f421,plain,( 41.00/5.57 (! [X0,X1,X2] : ((in @ X0 @ X2) => (~(in @ X0 @ X1) => (in @ X0 @ (symdiff @ X2 @ X1)))) = symdiffI1)), 41.00/5.57 inference(rectify,[],[f131])). 41.00/5.57 thf(f131,axiom,( 41.00/5.57 (! [X1,X4,X3] : ((in @ X1 @ X3) => (~(in @ X1 @ X4) => (in @ X1 @ (symdiff @ X3 @ X4)))) = symdiffI1)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',symdiffI1)). 41.00/5.57 thf(f739,plain,( 41.00/5.57 (symdiffE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => Y3)) => Y3))))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f282])). 41.00/5.57 thf(f282,plain,( 41.00/5.57 (symdiffE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (symdiff @ Y0 @ Y1)) => (!! @ $o @ (^[Y3 : $o]: (((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => Y3)) => (((~ (in @ Y2 @ Y0)) => ((in @ Y2 @ Y1) => Y3)) => Y3))))))))))))), 41.00/5.57 inference(fool_elimination,[],[f281])). 41.00/5.57 thf(f281,plain,( 41.00/5.57 (! [X0,X1,X2] : ((in @ X0 @ (symdiff @ X2 @ X1)) => ! [X3 : $o] : (((in @ X0 @ X2) => (~(in @ X0 @ X1) => X3)) => ((~(in @ X0 @ X2) => ((in @ X0 @ X1) => X3)) => X3))) = symdiffE)), 41.00/5.57 inference(rectify,[],[f130])). 41.00/5.57 thf(f130,axiom,( 41.00/5.57 (! [X1,X4,X3] : ((in @ X1 @ (symdiff @ X3 @ X4)) => ! [X0 : $o] : (((in @ X1 @ X3) => (~(in @ X1 @ X4) => X0)) => ((~(in @ X1 @ X3) => ((in @ X1 @ X4) => X0)) => X0))) = symdiffE)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',symdiffE)). 41.00/5.57 thf(f599,plain,( 41.00/5.57 (setminusSubset1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))))), 41.00/5.57 inference(cnf_transformation,[],[f324])). 41.00/5.57 thf(f324,plain,( 41.00/5.57 (setminusSubset1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((emptyset = (setminus @ Y1 @ Y0)) => (subset @ Y1 @ Y0)))))))), 41.00/5.57 inference(fool_elimination,[],[f323])). 41.00/5.57 thf(f323,plain,( 41.00/5.57 (! [X0,X1] : ((emptyset = (setminus @ X0 @ X1)) => (subset @ X0 @ X1)) = setminusSubset1)), 41.00/5.57 inference(rectify,[],[f129])). 41.00/5.57 thf(f129,axiom,( 41.00/5.57 (! [X3,X4] : ((emptyset = (setminus @ X3 @ X4)) => (subset @ X3 @ X4)) = setminusSubset1)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',setminusSubset1)). 41.00/5.57 thf(f629,plain,( 41.00/5.57 (setminusLsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))))), 41.00/5.57 inference(cnf_transformation,[],[f333])). 41.00/5.57 thf(f333,plain,( 41.00/5.57 (setminusLsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (setminus @ Y1 @ Y0) @ Y1))))))), 41.00/5.57 inference(fool_elimination,[],[f332])). 41.00/5.57 thf(f332,plain,( 41.00/5.57 (setminusLsub = ! [X0,X1] : (subset @ (setminus @ X0 @ X1) @ X0))), 41.00/5.57 inference(rectify,[],[f128])). 41.00/5.57 thf(f128,axiom,( 41.00/5.57 (setminusLsub = ! [X3,X4] : (subset @ (setminus @ X3 @ X4) @ X3))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',setminusLsub)). 41.00/5.57 thf(f731,plain,( 41.00/5.57 (setminusIRneg = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (~ (in @ Y1 @ (setminus @ Y2 @ Y0)))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f260])). 41.00/5.57 thf(f260,plain,( 41.00/5.57 (setminusIRneg = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (~ (in @ Y1 @ (setminus @ Y2 @ Y0)))))))))))), 41.00/5.57 inference(fool_elimination,[],[f259])). 41.00/5.57 thf(f259,plain,( 41.00/5.57 (setminusIRneg = ! [X0,X1,X2] : ((in @ X1 @ X2) => ~(in @ X1 @ (setminus @ X0 @ X2))))), 41.00/5.57 inference(rectify,[],[f127])). 41.00/5.57 thf(f127,axiom,( 41.00/5.57 (setminusIRneg = ! [X3,X1,X4] : ((in @ X1 @ X4) => ~(in @ X1 @ (setminus @ X3 @ X4))))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',setminusIRneg)). 41.00/5.57 thf(f745,plain,( 41.00/5.57 (setminusILneg = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f353])). 41.00/5.57 thf(f353,plain,( 41.00/5.57 (setminusILneg = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ (setminus @ Y1 @ Y2)))))))))))), 41.00/5.57 inference(fool_elimination,[],[f352])). 41.00/5.57 thf(f352,plain,( 41.00/5.57 (setminusILneg = ! [X0,X1,X2] : (~(in @ X2 @ X1) => ~(in @ X2 @ (setminus @ X1 @ X0))))), 41.00/5.57 inference(rectify,[],[f126])). 41.00/5.57 thf(f126,axiom,( 41.00/5.57 (setminusILneg = ! [X4,X3,X1] : (~(in @ X1 @ X3) => ~(in @ X1 @ (setminus @ X3 @ X4))))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',setminusILneg)). 41.00/5.57 thf(f780,plain,( 41.00/5.57 (setminusELneg = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y2 @ Y1))) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f207])). 41.00/5.57 thf(f207,plain,( 41.00/5.57 (setminusELneg = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y0 @ (setminus @ Y2 @ Y1))) => ((~ (in @ Y0 @ Y1)) => (~ (in @ Y0 @ Y2)))))))))))), 41.00/5.57 inference(fool_elimination,[],[f206])). 41.00/5.57 thf(f206,plain,( 41.00/5.57 (! [X0,X1,X2] : (~(in @ X2 @ (setminus @ X0 @ X1)) => (~(in @ X2 @ X1) => ~(in @ X2 @ X0))) = setminusELneg)), 41.00/5.57 inference(rectify,[],[f125])). 41.00/5.57 thf(f125,axiom,( 41.00/5.57 (! [X3,X4,X1] : (~(in @ X1 @ (setminus @ X3 @ X4)) => (~(in @ X1 @ X4) => ~(in @ X1 @ X3))) = setminusELneg)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',setminusELneg)). 41.00/5.57 thf(f665,plain,( 41.00/5.57 (setminusERneg = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y0 @ Y1))) => ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f310])). 41.00/5.57 thf(f310,plain,( 41.00/5.57 (setminusERneg = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (in @ Y2 @ (setminus @ Y0 @ Y1))) => ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))))))))), 41.00/5.57 inference(fool_elimination,[],[f309])). 41.00/5.57 thf(f309,plain,( 41.00/5.57 (! [X0,X1,X2] : (~(in @ X0 @ (setminus @ X2 @ X1)) => ((in @ X0 @ X2) => (in @ X0 @ X1))) = setminusERneg)), 41.00/5.57 inference(rectify,[],[f124])). 41.00/5.57 thf(f124,axiom,( 41.00/5.57 (! [X1,X4,X3] : (~(in @ X1 @ (setminus @ X3 @ X4)) => ((in @ X1 @ X3) => (in @ X1 @ X4))) = setminusERneg)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',setminusERneg)). 41.00/5.57 thf(f746,plain,( 41.00/5.57 (setminusSubset2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))))), 41.00/5.57 inference(cnf_transformation,[],[f473])). 41.00/5.57 thf(f473,plain,( 41.00/5.57 (setminusSubset2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => (emptyset = (setminus @ Y1 @ Y0))))))))), 41.00/5.57 inference(fool_elimination,[],[f472])). 41.00/5.57 thf(f472,plain,( 41.00/5.57 (! [X0,X1] : ((subset @ X0 @ X1) => (emptyset = (setminus @ X0 @ X1))) = setminusSubset2)), 41.00/5.57 inference(rectify,[],[f123])). 41.00/5.57 thf(f123,axiom,( 41.00/5.57 (! [X3,X4] : ((subset @ X3 @ X4) => (emptyset = (setminus @ X3 @ X4))) = setminusSubset2)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',setminusSubset2)). 41.00/5.57 thf(f737,plain,( 41.00/5.57 (setminusER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f312])). 41.00/5.57 thf(f312,plain,( 41.00/5.57 (setminusER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y1 @ Y2)) => (~ (in @ Y0 @ Y2))))))))))), 41.00/5.57 inference(fool_elimination,[],[f311])). 41.00/5.57 thf(f311,plain,( 41.00/5.57 (! [X0,X1,X2] : ((in @ X2 @ (setminus @ X1 @ X0)) => ~(in @ X2 @ X0)) = setminusER)), 41.00/5.57 inference(rectify,[],[f122])). 41.00/5.57 thf(f122,axiom,( 41.00/5.57 (! [X4,X3,X1] : ((in @ X1 @ (setminus @ X3 @ X4)) => ~(in @ X1 @ X4)) = setminusER)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',setminusER)). 41.00/5.57 thf(f718,plain,( 41.00/5.57 (setminusEL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))))), 41.00/5.57 inference(cnf_transformation,[],[f252])). 41.00/5.57 thf(f252,plain,( 41.00/5.57 (setminusEL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setminus @ Y1 @ Y0)) => (in @ Y2 @ Y1)))))))))), 41.00/5.57 inference(fool_elimination,[],[f251])). 41.00/5.57 thf(f251,plain,( 41.00/5.57 (! [X0,X1,X2] : ((in @ X0 @ (setminus @ X1 @ X2)) => (in @ X0 @ X1)) = setminusEL)), 41.00/5.57 inference(rectify,[],[f121])). 41.00/5.57 thf(f121,axiom,( 41.00/5.57 (! [X1,X3,X4] : ((in @ X1 @ (setminus @ X3 @ X4)) => (in @ X1 @ X3)) = setminusEL)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',setminusEL)). 41.00/5.57 thf(f652,plain,( 41.00/5.57 (setminusI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => (in @ Y2 @ (setminus @ Y0 @ Y1)))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f211])). 41.00/5.57 thf(f211,plain,( 41.00/5.57 (setminusI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => (in @ Y2 @ (setminus @ Y0 @ Y1)))))))))))), 41.00/5.57 inference(fool_elimination,[],[f210])). 41.00/5.57 thf(f210,plain,( 41.00/5.57 (setminusI = ! [X0,X1,X2] : ((in @ X0 @ X2) => (~(in @ X0 @ X1) => (in @ X0 @ (setminus @ X2 @ X1)))))), 41.00/5.57 inference(rectify,[],[f120])). 41.00/5.57 thf(f120,axiom,( 41.00/5.57 (setminusI = ! [X1,X4,X3] : ((in @ X1 @ X3) => (~(in @ X1 @ X4) => (in @ X1 @ (setminus @ X3 @ X4)))))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',setminusI)). 41.00/5.57 thf(f672,plain,( 41.00/5.57 (bs114d = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y0 @ Y1) @ (binintersect @ Y0 @ Y2)) = (binintersect @ Y0 @ (binunion @ Y1 @ Y2))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f453])). 41.00/5.57 thf(f453,plain,( 41.00/5.57 (bs114d = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((binunion @ (binintersect @ Y0 @ Y1) @ (binintersect @ Y0 @ Y2)) = (binintersect @ Y0 @ (binunion @ Y1 @ Y2))))))))))), 41.00/5.57 inference(fool_elimination,[],[f452])). 41.00/5.57 thf(f452,plain,( 41.00/5.57 (! [X0,X1,X2] : ((binunion @ (binintersect @ X2 @ X1) @ (binintersect @ X2 @ X0)) = (binintersect @ X2 @ (binunion @ X1 @ X0))) = bs114d)), 41.00/5.57 inference(rectify,[],[f119])). 41.00/5.57 thf(f119,axiom,( 41.00/5.57 (! [X5,X4,X3] : ((binintersect @ X3 @ (binunion @ X4 @ X5)) = (binunion @ (binintersect @ X3 @ X4) @ (binintersect @ X3 @ X5))) = bs114d)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',bs114d)). 41.00/5.57 thf(f708,plain,( 41.00/5.57 (binintersectSubset1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y0) => (subset @ Y0 @ Y1)))))))), 41.00/5.57 inference(cnf_transformation,[],[f412])). 41.00/5.57 thf(f412,plain,( 41.00/5.57 (binintersectSubset1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y0) => (subset @ Y0 @ Y1)))))))), 41.00/5.57 inference(fool_elimination,[],[f411])). 41.00/5.57 thf(f411,plain,( 41.00/5.57 (! [X0,X1] : (((binintersect @ X1 @ X0) = X1) => (subset @ X1 @ X0)) = binintersectSubset1)), 41.00/5.57 inference(rectify,[],[f118])). 41.00/5.57 thf(f118,axiom,( 41.00/5.57 (! [X4,X3] : (((binintersect @ X3 @ X4) = X3) => (subset @ X3 @ X4)) = binintersectSubset1)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',binintersectSubset1)). 41.00/5.57 thf(f688,plain,( 41.00/5.57 (binintersectSubset4 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y0 @ Y1) = Y1)))))))), 41.00/5.57 inference(cnf_transformation,[],[f239])). 41.00/5.57 thf(f239,plain,( 41.00/5.57 (binintersectSubset4 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y0 @ Y1) = Y1)))))))), 41.00/5.57 inference(fool_elimination,[],[f238])). 41.00/5.57 thf(f238,plain,( 41.00/5.57 (binintersectSubset4 = ! [X0,X1] : ((subset @ X0 @ X1) => ((binintersect @ X1 @ X0) = X0)))), 41.00/5.57 inference(rectify,[],[f117])). 41.00/5.57 thf(f117,axiom,( 41.00/5.57 (binintersectSubset4 = ! [X4,X3] : ((subset @ X4 @ X3) => ((binintersect @ X3 @ X4) = X4)))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',binintersectSubset4)). 41.00/5.57 thf(f650,plain,( 41.00/5.57 (binintersectRsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))))), 41.00/5.57 inference(cnf_transformation,[],[f428])). 41.00/5.57 thf(f428,plain,( 41.00/5.57 (binintersectRsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y0 @ Y1) @ Y1))))))), 41.00/5.57 inference(fool_elimination,[],[f427])). 41.00/5.57 thf(f427,plain,( 41.00/5.57 (! [X0,X1] : (subset @ (binintersect @ X1 @ X0) @ X0) = binintersectRsub)), 41.00/5.57 inference(rectify,[],[f116])). 41.00/5.57 thf(f116,axiom,( 41.00/5.57 (! [X4,X3] : (subset @ (binintersect @ X3 @ X4) @ X4) = binintersectRsub)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',binintersectRsub)). 41.00/5.57 thf(f738,plain,( 41.00/5.57 (disjointsetsI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y1 @ Y0))))))))), 41.00/5.57 inference(cnf_transformation,[],[f426])). 41.00/5.57 thf(f426,plain,( 41.00/5.57 (disjointsetsI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y2 @ Y1))))) => (emptyset = (binintersect @ Y1 @ Y0))))))))), 41.00/5.57 inference(fool_elimination,[],[f425])). 41.00/5.57 thf(f425,plain,( 41.00/5.57 (! [X0,X1] : (~? [X2] : ((in @ X2 @ X0) & (in @ X2 @ X1)) => (emptyset = (binintersect @ X0 @ X1))) = disjointsetsI1)), 41.00/5.57 inference(rectify,[],[f115])). 41.00/5.57 thf(f115,axiom,( 41.00/5.57 (! [X3,X4] : (~? [X1] : ((in @ X1 @ X3) & (in @ X1 @ X4)) => (emptyset = (binintersect @ X3 @ X4))) = disjointsetsI1)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',disjointsetsI1)). 41.00/5.57 thf(f713,plain,( 41.00/5.57 (binintersectER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1)))))))))), 41.00/5.57 inference(cnf_transformation,[],[f533])). 41.00/5.57 thf(f533,plain,( 41.00/5.57 (binintersectER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1)))))))))), 41.00/5.57 inference(fool_elimination,[],[f532])). 41.00/5.57 thf(f532,plain,( 41.00/5.57 (binintersectER = ! [X0,X1,X2] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X1)))), 41.00/5.57 inference(rectify,[],[f114])). 41.00/5.57 thf(f114,axiom,( 41.00/5.57 (binintersectER = ! [X3,X4,X1] : ((in @ X1 @ (binintersect @ X3 @ X4)) => (in @ X1 @ X4)))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',binintersectER)). 41.00/5.57 thf(f602,plain,( 41.00/5.57 (binintersectSubset3 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))))), 41.00/5.57 inference(cnf_transformation,[],[f314])). 41.00/5.57 thf(f314,plain,( 41.00/5.57 (binintersectSubset3 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((binintersect @ Y0 @ Y1) = Y1) => (subset @ Y1 @ Y0)))))))), 41.00/5.57 inference(fool_elimination,[],[f313])). 41.00/5.57 thf(f313,plain,( 41.00/5.57 (! [X0,X1] : (((binintersect @ X1 @ X0) = X0) => (subset @ X0 @ X1)) = binintersectSubset3)), 41.00/5.57 inference(rectify,[],[f113])). 41.00/5.57 thf(f113,axiom,( 41.00/5.57 (! [X4,X3] : (((binintersect @ X3 @ X4) = X4) => (subset @ X4 @ X3)) = binintersectSubset3)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',binintersectSubset3)). 41.00/5.57 thf(f789,plain,( 41.00/5.57 (binintersectSubset2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))))), 41.00/5.57 inference(cnf_transformation,[],[f318])). 41.00/5.57 thf(f318,plain,( 41.00/5.57 (binintersectSubset2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ Y0) => ((binintersect @ Y1 @ Y0) = Y1)))))))), 41.00/5.57 inference(fool_elimination,[],[f317])). 41.00/5.57 thf(f317,plain,( 41.00/5.57 (binintersectSubset2 = ! [X0,X1] : ((subset @ X0 @ X1) => ((binintersect @ X0 @ X1) = X0)))), 41.00/5.57 inference(rectify,[],[f112])). 41.00/5.57 thf(f112,axiom,( 41.00/5.57 (binintersectSubset2 = ! [X3,X4] : ((subset @ X3 @ X4) => ((binintersect @ X3 @ X4) = X3)))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',binintersectSubset2)). 41.00/5.57 thf(f791,plain,( 41.00/5.57 (binintersectLsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))))), 41.00/5.57 inference(cnf_transformation,[],[f379])). 41.00/5.57 thf(f379,plain,( 41.00/5.57 (binintersectLsub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ (binintersect @ Y1 @ Y0) @ Y1))))))), 41.00/5.57 inference(fool_elimination,[],[f378])). 41.00/5.57 thf(f378,plain,( 41.00/5.57 (binintersectLsub = ! [X0,X1] : (subset @ (binintersect @ X0 @ X1) @ X0))), 41.00/5.57 inference(rectify,[],[f111])). 41.00/5.57 thf(f111,axiom,( 41.00/5.57 (binintersectLsub = ! [X3,X4] : (subset @ (binintersect @ X3 @ X4) @ X3))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',binintersectLsub)). 41.00/5.57 thf(f794,plain,( 41.00/5.57 (binintersectEL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))))), 41.00/5.57 inference(cnf_transformation,[],[f409])). 41.00/5.57 thf(f409,plain,( 41.00/5.57 (binintersectEL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (binintersect @ Y0 @ Y2)) => (in @ Y1 @ Y0)))))))))), 41.00/5.57 inference(fool_elimination,[],[f408])). 41.00/5.57 thf(f408,plain,( 41.00/5.57 (! [X0,X1,X2] : ((in @ X1 @ (binintersect @ X2 @ X0)) => (in @ X1 @ X2)) = binintersectEL)), 41.00/5.57 inference(rectify,[],[f110])). 41.00/5.57 thf(f110,axiom,( 41.00/5.57 (! 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[X3,X4] : ((subset @ X3 @ X4) => ((subset @ X4 @ X3) => (X3 = X4))))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',setextsub)). 41.00/5.57 thf(f628,plain,( 41.00/5.57 (subset2powerset = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))))), 41.00/5.57 inference(cnf_transformation,[],[f268])). 41.00/5.57 thf(f268,plain,( 41.00/5.57 (subset2powerset = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1) => (in @ Y0 @ (powerset @ Y1))))))))), 41.00/5.57 inference(fool_elimination,[],[f267])). 41.00/5.57 thf(f267,plain,( 41.00/5.57 (subset2powerset = ! [X0,X1] : ((subset @ X1 @ X0) => (in @ X1 @ (powerset @ X0))))), 41.00/5.57 inference(rectify,[],[f92])). 41.00/5.57 thf(f92,axiom,( 41.00/5.57 (subset2powerset = ! [X4,X3] : ((subset @ X3 @ X4) => (in @ X3 @ (powerset @ X4))))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',subset2powerset)). 41.00/5.57 thf(f620,plain,( 41.00/5.57 (setadjoinSub2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f381])). 41.00/5.57 thf(f381,plain,( 41.00/5.57 (setadjoinSub2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ Y2) => (subset @ Y1 @ (setadjoin @ Y0 @ Y2))))))))))), 41.00/5.57 inference(fool_elimination,[],[f380])). 41.00/5.57 thf(f380,plain,( 41.00/5.57 (setadjoinSub2 = ! [X0,X1,X2] : ((subset @ X1 @ X0) => (subset @ X1 @ (setadjoin @ X2 @ X0))))), 41.00/5.57 inference(rectify,[],[f91])). 41.00/5.57 thf(f91,axiom,( 41.00/5.57 (setadjoinSub2 = ! [X4,X3,X1] : ((subset @ X3 @ X4) => (subset @ X3 @ (setadjoin @ X1 @ X4))))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',setadjoinSub2)). 41.00/5.57 thf(f728,plain,( 41.00/5.57 (setadjoinSub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (setadjoin @ Y1 @ Y0)))))))), 41.00/5.57 inference(cnf_transformation,[],[f495])). 41.00/5.57 thf(f495,plain,( 41.00/5.57 (setadjoinSub = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (subset @ Y0 @ (setadjoin @ Y1 @ Y0)))))))), 41.00/5.57 inference(fool_elimination,[],[f494])). 41.00/5.57 thf(f494,plain,( 41.00/5.57 (! [X0,X1] : (subset @ X1 @ (setadjoin @ X0 @ X1)) = setadjoinSub)), 41.00/5.57 inference(rectify,[],[f90])). 41.00/5.57 thf(f90,axiom,( 41.00/5.57 (! [X1,X3] : (subset @ X3 @ (setadjoin @ X1 @ X3)) = setadjoinSub)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',setadjoinSub)). 41.00/5.57 thf(f721,plain,( 41.00/5.57 (subsetTrans = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f335])). 41.00/5.57 thf(f335,plain,( 41.00/5.57 (subsetTrans = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y2) => ((subset @ Y2 @ Y1) => (subset @ Y0 @ Y1))))))))))), 41.00/5.57 inference(fool_elimination,[],[f334])). 41.00/5.57 thf(f334,plain,( 41.00/5.57 (subsetTrans = ! [X0,X1,X2] : ((subset @ X2 @ X0) => ((subset @ X0 @ X1) => (subset @ X2 @ X1))))), 41.00/5.57 inference(rectify,[],[f89])). 41.00/5.57 thf(f89,axiom,( 41.00/5.57 (subsetTrans = ! [X4,X5,X3] : ((subset @ X3 @ X4) => ((subset @ X4 @ X5) => (subset @ X3 @ X5))))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',subsetTrans)). 41.00/5.57 thf(f735,plain,( 41.00/5.57 (subsetRefl = (!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))))), 41.00/5.57 inference(cnf_transformation,[],[f441])). 41.00/5.57 thf(f441,plain,( 41.00/5.57 (subsetRefl = (!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0))))), 41.00/5.57 inference(fool_elimination,[],[f440])). 41.00/5.57 thf(f440,plain,( 41.00/5.57 (! [X0] : (subset @ X0 @ X0) = subsetRefl)), 41.00/5.57 inference(rectify,[],[f88])). 41.00/5.57 thf(f88,axiom,( 41.00/5.57 (! [X3] : (subset @ X3 @ X3) = subsetRefl)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',subsetRefl)). 41.00/5.57 thf(f707,plain,( 41.00/5.57 (notequalI2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = Y0)))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f247])). 41.00/5.57 thf(f247,plain,( 41.00/5.57 (notequalI2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((~ (in @ Y1 @ Y0)) => (~ (Y2 = Y0)))))))))))), 41.00/5.57 inference(fool_elimination,[],[f246])). 41.00/5.57 thf(f246,plain,( 41.00/5.57 (notequalI2 = ! [X0,X1,X2] : ((in @ X1 @ X0) => (~(in @ X1 @ X2) => (X0 != X2))))), 41.00/5.57 inference(rectify,[],[f87])). 41.00/5.57 thf(f87,axiom,( 41.00/5.57 (notequalI2 = ! [X3,X1,X4] : ((in @ X1 @ X3) => (~(in @ X1 @ X4) => (X3 != X4))))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',notequalI2)). 41.00/5.57 thf(f749,plain,( 41.00/5.57 (notequalI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))))), 41.00/5.57 inference(cnf_transformation,[],[f235])). 41.00/5.57 thf(f235,plain,( 41.00/5.57 (notequalI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (subset @ Y0 @ Y1)) => (~ (Y1 = Y0))))))))), 41.00/5.57 inference(fool_elimination,[],[f234])). 41.00/5.57 thf(f234,plain,( 41.00/5.57 (notequalI1 = ! [X0,X1] : (~(subset @ X1 @ X0) => (X0 != X1)))), 41.00/5.57 inference(rectify,[],[f86])). 41.00/5.57 thf(f86,axiom,( 41.00/5.57 (notequalI1 = ! [X4,X3] : (~(subset @ X3 @ X4) => (X3 != X4)))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',notequalI1)). 41.00/5.57 thf(f774,plain,( 41.00/5.57 (notsubsetI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => (~ (subset @ Y0 @ Y1)))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f363])). 41.00/5.57 thf(f363,plain,( 41.00/5.57 (notsubsetI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((~ (in @ Y2 @ Y1)) => (~ (subset @ Y0 @ Y1)))))))))))), 41.00/5.57 inference(fool_elimination,[],[f362])). 41.00/5.57 thf(f362,plain,( 41.00/5.57 (notsubsetI = ! [X0,X1,X2] : ((in @ X0 @ X2) => (~(in @ X0 @ X1) => ~(subset @ X2 @ X1))))), 41.00/5.57 inference(rectify,[],[f85])). 41.00/5.57 thf(f85,axiom,( 41.00/5.57 (notsubsetI = ! [X1,X4,X3] : ((in @ X1 @ X3) => (~(in @ X1 @ X4) => ~(subset @ X3 @ X4))))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',notsubsetI)). 41.00/5.57 thf(f666,plain,( 41.00/5.57 (subsetE2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y0) => ((~ (in @ Y1 @ Y0)) => (~ (in @ Y1 @ Y2)))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f481])). 41.00/5.57 thf(f481,plain,( 41.00/5.57 (subsetE2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y0) => ((~ (in @ Y1 @ Y0)) => (~ (in @ Y1 @ Y2)))))))))))), 41.00/5.57 inference(fool_elimination,[],[f480])). 41.00/5.57 thf(f480,plain,( 41.00/5.57 (subsetE2 = ! [X0,X1,X2] : ((subset @ X0 @ X2) => (~(in @ X1 @ X2) => ~(in @ X1 @ X0))))), 41.00/5.57 inference(rectify,[],[f84])). 41.00/5.57 thf(f84,axiom,( 41.00/5.57 (subsetE2 = ! [X3,X1,X4] : ((subset @ X3 @ X4) => (~(in @ X1 @ X4) => ~(in @ X1 @ X3))))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',subsetE2)). 41.00/5.57 thf(f613,plain,( 41.00/5.57 (subsetE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y0) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f543])). 41.00/5.57 thf(f543,plain,( 41.00/5.57 (subsetE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ Y0) => ((in @ Y1 @ Y2) => (in @ Y1 @ Y0))))))))))), 41.00/5.57 inference(fool_elimination,[],[f542])). 41.00/5.57 thf(f542,plain,( 41.00/5.57 (! [X0,X1,X2] : ((subset @ X0 @ X2) => ((in @ X1 @ X0) => (in @ X1 @ X2))) = subsetE)), 41.00/5.57 inference(rectify,[],[f83])). 41.00/5.57 thf(f83,axiom,( 41.00/5.57 (! [X3,X1,X4] : ((subset @ X3 @ X4) => ((in @ X1 @ X3) => (in @ X1 @ X4))) = subsetE)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',subsetE)). 41.00/5.57 thf(f655,plain,( 41.00/5.57 (emptysetsubset = (!! @ $i @ (^[Y0 : $i]: (subset @ emptyset @ Y0))))), 41.00/5.57 inference(cnf_transformation,[],[f583])). 41.00/5.57 thf(f583,plain,( 41.00/5.57 (emptysetsubset = (!! @ $i @ (^[Y0 : $i]: (subset @ emptyset @ Y0))))), 41.00/5.57 inference(fool_elimination,[],[f582])). 41.00/5.57 thf(f582,plain,( 41.00/5.57 (! [X0] : (subset @ emptyset @ X0) = emptysetsubset)), 41.00/5.57 inference(rectify,[],[f82])). 41.00/5.57 thf(f82,axiom,( 41.00/5.57 (! 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[X1] : ((in @ X1 @ X3) => (in @ X1 @ X4)) => (subset @ X3 @ X4)))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',subsetI2)). 41.00/5.57 thf(f761,plain,( 41.00/5.57 (eqimpsubset1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))))), 41.00/5.57 inference(cnf_transformation,[],[f523])). 41.00/5.57 thf(f523,plain,( 41.00/5.57 (eqimpsubset1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (subset @ Y0 @ Y1)))))))), 41.00/5.57 inference(fool_elimination,[],[f522])). 41.00/5.57 thf(f522,plain,( 41.00/5.57 (eqimpsubset1 = ! [X0,X1] : ((X0 = X1) => (subset @ X1 @ X0)))), 41.00/5.57 inference(rectify,[],[f80])). 41.00/5.57 thf(f80,axiom,( 41.00/5.57 (eqimpsubset1 = ! 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[X1] : ((in @ X1 @ X3) => (in @ X1 @ X4)) => (subset @ X3 @ X4)))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',subsetI1)). 41.00/5.57 thf(f681,plain,( 41.00/5.57 (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 @ Y5) = (Y2 @ Y4))))))))) => ((dsetconstr @ Y1 @ (^[Y4 : $i]: (Y2 @ Y4))) = (dsetconstr @ Y0 @ (^[Y4 : $i]: (Y3 @ Y4)))))))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f316])). 41.00/5.57 thf(f316,plain,( 41.00/5.57 (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 @ Y5) = (Y2 @ Y4))))))))) => ((dsetconstr @ Y1 @ (^[Y4 : $i]: (Y2 @ Y4))) = (dsetconstr @ Y0 @ (^[Y4 : $i]: (Y3 @ Y4)))))))))))))))), 41.00/5.57 inference(fool_elimination,[],[f315])). 41.00/5.57 thf(f315,plain,( 41.00/5.57 (! [X0,X1] : ((X0 = X1) => ! [X2 : $i > $o,X3 : $i > $o] : (! [X4] : ((in @ X4 @ X0) => ! [X5] : ((in @ X5 @ X1) => ((X4 = X5) => ((X2 @ X5) <=> (X3 @ X4))))) => ((dsetconstr @ X0 @ (^[X6 : $i] : (X3 @ X6))) = (dsetconstr @ X1 @ (^[X7 : $i] : (X2 @ X7)))))) = dsetconstr__Cong)), 41.00/5.57 inference(rectify,[],[f77])). 41.00/5.57 thf(f77,axiom,( 41.00/5.57 (! [X3,X4] : ((X3 = X4) => ! [X9 : $i > $o,X0 : $i > $o] : (! [X1] : ((in @ X1 @ X3) => ! [X2] : ((in @ X2 @ X4) => ((X1 = X2) => ((X9 @ X2) <=> (X0 @ X1))))) => ((dsetconstr @ X3 @ (^[X1 : $i] : (X0 @ X1))) = (dsetconstr @ X4 @ (^[X1 : $i] : (X9 @ X1)))))) = dsetconstr__Cong)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',dsetconstr__Cong)). 41.00/5.57 thf(f810,plain,( 41.00/5.57 (descr__Cong = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => (((^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) => (Y3 = Y4)))))))) @ (^[Y2 : $i]: (Y0 @ Y2))) => (((^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) => (Y3 = Y4)))))))) @ (^[Y2 : $i]: (Y1 @ Y2))) => ((descr @ (^[Y2 : $i]: (Y0 @ Y2))) = (descr @ (^[Y2 : $i]: (Y1 @ Y2))))))))))))), 41.00/5.57 inference(definition_unfolding,[],[f692,f694,f694])). 41.00/5.57 thf(f694,plain,( 41.00/5.57 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))), 41.00/5.57 inference(cnf_transformation,[],[f499])). 41.00/5.57 thf(f499,plain,( 41.00/5.57 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))), 41.00/5.57 inference(fool_elimination,[],[f498])). 41.00/5.57 thf(f498,plain,( 41.00/5.57 (exu = (^[X0 : $i > $o] : (? [X1] : (! [X2] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))))), 41.00/5.57 inference(rectify,[],[f1])). 41.00/5.57 thf(f1,axiom,( 41.00/5.57 (exu = (^[X0 : $i > $o] : (? [X1] : (! [X2] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1)))))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',exu)). 41.00/5.57 thf(f692,plain,( 41.00/5.57 (descr__Cong = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((exu @ (^[Y2 : $i]: (Y0 @ Y2))) => ((exu @ (^[Y2 : $i]: (Y1 @ Y2))) => ((descr @ (^[Y2 : $i]: (Y0 @ Y2))) = (descr @ (^[Y2 : $i]: (Y1 @ Y2))))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f322])). 41.00/5.57 thf(f322,plain,( 41.00/5.57 (descr__Cong = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y3) = (Y1 @ Y2))))))) => ((exu @ (^[Y2 : $i]: (Y0 @ Y2))) => ((exu @ (^[Y2 : $i]: (Y1 @ Y2))) => ((descr @ (^[Y2 : $i]: (Y0 @ Y2))) = (descr @ (^[Y2 : $i]: (Y1 @ Y2))))))))))))), 41.00/5.57 inference(fool_elimination,[],[f321])). 41.00/5.57 thf(f321,plain,( 41.00/5.57 (! [X0 : $i > $o,X1 : $i > $o] : (! [X2,X3] : ((X2 = X3) => ((X1 @ X2) <=> (X0 @ X3))) => ((exu @ (^[X4 : $i] : (X1 @ X4))) => ((exu @ (^[X5 : $i] : (X0 @ X5))) => ((descr @ (^[X6 : $i] : (X1 @ X6))) = (descr @ (^[X7 : $i] : (X0 @ X7))))))) = descr__Cong)), 41.00/5.57 inference(rectify,[],[f76])). 41.00/5.57 thf(f76,axiom,( 41.00/5.57 (! [X9 : $i > $o,X0 : $i > $o] : (! [X1,X2] : ((X1 = X2) => ((X0 @ X1) <=> (X9 @ X2))) => ((exu @ (^[X1 : $i] : (X0 @ X1))) => ((exu @ (^[X1 : $i] : (X9 @ X1))) => ((descr @ (^[X1 : $i] : (X0 @ X1))) = (descr @ (^[X1 : $i] : (X9 @ X1))))))) = descr__Cong)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',descr__Cong)). 41.00/5.57 thf(f809,plain,( 41.00/5.57 (exuEu = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))))))) @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))))), 41.00/5.57 inference(definition_unfolding,[],[f623,f694])). 41.00/5.57 thf(f623,plain,( 41.00/5.57 (exuEu = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f284])). 41.00/5.57 thf(f284,plain,( 41.00/5.57 (exuEu = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))))), 41.00/5.57 inference(fool_elimination,[],[f283])). 41.00/5.57 thf(f283,plain,( 41.00/5.57 (! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ! [X2,X3] : ((X0 @ X2) => ((X0 @ X3) => (X2 = X3)))) = exuEu)), 41.00/5.57 inference(rectify,[],[f75])). 41.00/5.57 thf(f75,axiom,( 41.00/5.57 (! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ! [X1,X2] : ((X0 @ X1) => ((X0 @ X2) => (X1 = X2)))) = exuEu)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',exuEu)). 41.00/5.57 thf(f661,plain,( 41.00/5.57 (omega__Cong = (omega = omega))), 41.00/5.57 inference(cnf_transformation,[],[f410])). 41.00/5.57 thf(f410,plain,( 41.00/5.57 (omega__Cong = (omega = omega))), 41.00/5.57 inference(fool_elimination,[],[f74])). 41.00/5.57 thf(f74,axiom,( 41.00/5.57 (omega__Cong = (omega = omega))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',omega__Cong)). 41.00/5.57 thf(f668,plain,( 41.00/5.57 (setunion__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))))), 41.00/5.57 inference(cnf_transformation,[],[f349])). 41.00/5.57 thf(f349,plain,( 41.00/5.57 (setunion__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((setunion @ Y0) = (setunion @ Y1))))))))), 41.00/5.57 inference(fool_elimination,[],[f348])). 41.00/5.57 thf(f348,plain,( 41.00/5.57 (setunion__Cong = ! [X0,X1] : ((X0 = X1) => ((setunion @ X1) = (setunion @ X0))))), 41.00/5.57 inference(rectify,[],[f73])). 41.00/5.57 thf(f73,axiom,( 41.00/5.57 (setunion__Cong = ! [X4,X3] : ((X3 = X4) => ((setunion @ X3) = (setunion @ X4))))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',setunion__Cong)). 41.00/5.57 thf(f771,plain,( 41.00/5.57 (powerset__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))))), 41.00/5.57 inference(cnf_transformation,[],[f345])). 41.00/5.57 thf(f345,plain,( 41.00/5.57 (powerset__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => ((powerset @ Y0) = (powerset @ Y1))))))))), 41.00/5.57 inference(fool_elimination,[],[f344])). 41.00/5.57 thf(f344,plain,( 41.00/5.57 (! [X0,X1] : ((X0 = X1) => ((powerset @ X1) = (powerset @ X0))) = powerset__Cong)), 41.00/5.57 inference(rectify,[],[f72])). 41.00/5.57 thf(f72,axiom,( 41.00/5.57 (! [X4,X3] : ((X3 = X4) => ((powerset @ X3) = (powerset @ X4))) = powerset__Cong)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',powerset__Cong)). 41.00/5.57 thf(f768,plain,( 41.00/5.57 (setadjoin__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f371])). 41.00/5.57 thf(f371,plain,( 41.00/5.57 (setadjoin__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((setadjoin @ Y0 @ Y3) = (setadjoin @ Y1 @ Y2)))))))))))))), 41.00/5.57 inference(fool_elimination,[],[f370])). 41.00/5.57 thf(f370,plain,( 41.00/5.57 (! [X0,X1] : ((X0 = X1) => ! [X2,X3] : ((X2 = X3) => ((setadjoin @ X1 @ X2) = (setadjoin @ X0 @ X3)))) = setadjoin__Cong)), 41.00/5.57 inference(rectify,[],[f71])). 41.00/5.57 thf(f71,axiom,( 41.00/5.57 (! [X2,X1] : ((X1 = X2) => ! [X8,X10] : ((X8 = X10) => ((setadjoin @ X1 @ X8) = (setadjoin @ X2 @ X10)))) = setadjoin__Cong)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',setadjoin__Cong)). 41.00/5.57 thf(f687,plain,( 41.00/5.57 (emptyset__Cong = (emptyset = emptyset))), 41.00/5.57 inference(cnf_transformation,[],[f435])). 41.00/5.57 thf(f435,plain,( 41.00/5.57 (emptyset__Cong = (emptyset = emptyset))), 41.00/5.57 inference(fool_elimination,[],[f70])). 41.00/5.57 thf(f70,axiom,( 41.00/5.57 (emptyset__Cong = (emptyset = emptyset))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',emptyset__Cong)). 41.00/5.57 thf(f808,plain,( 41.00/5.57 (exu__Cong = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ Y3))))))) => (((^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) => (Y3 = Y4)))))))) @ (^[Y2 : $i]: (Y0 @ Y2))) = ((^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) => (Y3 = Y4)))))))) @ (^[Y2 : $i]: (Y1 @ Y2))))))))))), 41.00/5.57 inference(definition_unfolding,[],[f765,f694,f694])). 41.00/5.57 thf(f765,plain,( 41.00/5.57 (exu__Cong = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ Y3))))))) => ((exu @ (^[Y2 : $i]: (Y0 @ Y2))) = (exu @ (^[Y2 : $i]: (Y1 @ Y2))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f521])). 41.00/5.57 thf(f521,plain,( 41.00/5.57 (exu__Cong = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((Y0 @ Y2) = (Y1 @ Y3))))))) => ((exu @ (^[Y2 : $i]: (Y0 @ Y2))) = (exu @ (^[Y2 : $i]: (Y1 @ Y2))))))))))), 41.00/5.57 inference(fool_elimination,[],[f520])). 41.00/5.57 thf(f520,plain,( 41.00/5.57 (! [X0 : $i > $o,X1 : $i > $o] : (! [X2,X3] : ((X2 = X3) => ((X1 @ X3) <=> (X0 @ X2))) => ((exu @ (^[X4 : $i] : (X1 @ X4))) <=> (exu @ (^[X5 : $i] : (X0 @ X5))))) = exu__Cong)), 41.00/5.57 inference(rectify,[],[f69])). 41.00/5.57 thf(f69,axiom,( 41.00/5.57 (! [X9 : $i > $o,X0 : $i > $o] : (! [X2,X1] : ((X1 = X2) => ((X0 @ X1) <=> (X9 @ X2))) => ((exu @ (^[X1 : $i] : (X0 @ X1))) <=> (exu @ (^[X1 : $i] : (X9 @ X1))))) = exu__Cong)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',exu__Cong)). 41.00/5.57 thf(f807,plain,( 41.00/5.57 (exuE3u = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))))))) @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))))), 41.00/5.57 inference(definition_unfolding,[],[f657,f694])). 41.00/5.57 thf(f657,plain,( 41.00/5.57 (exuE3u = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f213])). 41.00/5.57 thf(f213,plain,( 41.00/5.57 (exuE3u = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => ((Y0 @ Y1) => (Y2 = Y1)))))))))))), 41.00/5.57 inference(fool_elimination,[],[f212])). 41.00/5.57 thf(f212,plain,( 41.00/5.57 (exuE3u = ! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ! [X2,X3] : ((X0 @ X2) => ((X0 @ X3) => (X2 = X3)))))), 41.00/5.57 inference(rectify,[],[f68])). 41.00/5.57 thf(f68,axiom,( 41.00/5.57 (exuE3u = ! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ! [X1,X2] : ((X0 @ X1) => ((X0 @ X2) => (X1 = X2)))))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',exuE3u)). 41.00/5.57 thf(f667,plain,( 41.00/5.57 (in__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f593])). 41.00/5.57 thf(f593,plain,( 41.00/5.57 (in__Cong = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y0) = (in @ Y2 @ Y1)))))))))))))), 41.00/5.57 inference(fool_elimination,[],[f592])). 41.00/5.57 thf(f592,plain,( 41.00/5.57 (in__Cong = ! [X0,X1] : ((X0 = X1) => ! [X2,X3] : ((X2 = X3) => ((in @ X2 @ X1) <=> (in @ X3 @ X0)))))), 41.00/5.57 inference(rectify,[],[f67])). 41.00/5.57 thf(f67,axiom,( 41.00/5.57 (in__Cong = ! [X3,X4] : ((X3 = X4) => ! [X2,X1] : ((X1 = X2) => ((in @ X2 @ X4) <=> (in @ X1 @ X3)))))), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',in__Cong)). 41.00/5.57 thf(f633,plain,( 41.00/5.57 (inCongP = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))))), 41.00/5.57 inference(cnf_transformation,[],[f525])). 41.00/5.57 thf(f525,plain,( 41.00/5.57 (inCongP = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((Y1 = Y0) => (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y3 = Y2) => ((in @ Y3 @ Y1) => (in @ Y2 @ Y0)))))))))))))), 41.00/5.57 inference(fool_elimination,[],[f524])). 41.00/5.57 thf(f524,plain,( 41.00/5.57 (! [X0,X1] : ((X0 = X1) => ! [X2,X3] : ((X2 = X3) => ((in @ X2 @ X0) => (in @ X3 @ X1)))) = inCongP)), 41.00/5.57 inference(rectify,[],[f66])). 41.00/5.57 thf(f66,axiom,( 41.00/5.57 (! [X3,X4] : ((X3 = X4) => ! [X1,X2] : ((X1 = X2) => ((in @ X1 @ X3) => (in @ X2 @ X4)))) = inCongP)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',inCongP)). 41.00/5.57 thf(f806,plain,( 41.00/5.57 (exuI2 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))))))) @ (^[Y1 : $i]: (Y0 @ Y1)))))))), 41.00/5.57 inference(definition_unfolding,[],[f695,f694])). 41.00/5.57 thf(f695,plain,( 41.00/5.57 (exuI2 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1)))))))), 41.00/5.57 inference(cnf_transformation,[],[f591])). 41.00/5.57 thf(f591,plain,( 41.00/5.57 (exuI2 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = (Y1 = Y2)))))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1)))))))), 41.00/5.57 inference(fool_elimination,[],[f590])). 41.00/5.57 thf(f590,plain,( 41.00/5.57 (! [X0 : $i > $o] : (? [X1] : ! [X2] : ((X0 @ X2) <=> (X1 = X2)) => (exu @ (^[X3 : $i] : (X0 @ X3)))) = exuI2)), 41.00/5.57 inference(rectify,[],[f65])). 41.00/5.57 thf(f65,axiom,( 41.00/5.57 (! [X0 : $i > $o] : (? [X1] : ! [X2] : ((X0 @ X2) <=> (X1 = X2)) => (exu @ (^[X1 : $i] : (X0 @ X1)))) = exuI2)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',exuI2)). 41.00/5.57 thf(f805,plain,( 41.00/5.57 (exuI3 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))))))) @ (^[Y1 : $i]: (Y0 @ Y1))))))))), 41.00/5.57 inference(definition_unfolding,[],[f611,f694])). 41.00/5.57 thf(f611,plain,( 41.00/5.57 (exuI3 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))) => ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1) => ((Y0 @ Y2) => (Y2 = Y1))))))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1))))))))), 41.00/5.57 inference(cnf_transformation,[],[f367])). 41.00/5.57 thf(f367,plain,( 41.00/5.57 (exuI3 = (!! @ ($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))))))))), 41.00/5.57 inference(fool_elimination,[],[f366])). 41.00/5.57 thf(f366,plain,( 41.00/5.57 (! 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[X2,X1] : ((X0 @ X1) => ((X0 @ X2) => (X1 = X2))) => (exu @ (^[X1 : $i] : (X0 @ X1))))) = exuI3)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',exuI3)). 41.00/5.57 thf(f804,plain,( 41.00/5.57 (exuI1 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))))))) @ (^[Y1 : $i]: (Y0 @ Y1)))))))), 41.00/5.57 inference(definition_unfolding,[],[f722,f694])). 41.00/5.57 thf(f722,plain,( 41.00/5.57 (exuI1 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1)))))))), 41.00/5.57 inference(cnf_transformation,[],[f227])). 41.00/5.57 thf(f227,plain,( 41.00/5.57 (exuI1 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2))))))) => (exu @ (^[Y1 : $i]: (Y0 @ Y1)))))))), 41.00/5.57 inference(fool_elimination,[],[f226])). 41.00/5.57 thf(f226,plain,( 41.00/5.57 (exuI1 = ! 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[X1] : ((in @ X1 @ X3) & (X0 @ X1))) = quantDeMorgan2)), 41.00/5.57 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',quantDeMorgan2)). 41.00/5.57 thf(f600,plain,( 41.00/5.58 (quantDeMorgan1 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))))), 41.00/5.58 inference(cnf_transformation,[],[f203])). 41.00/5.58 thf(f203,plain,( 41.00/5.58 (quantDeMorgan1 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (Y0 @ Y2))))) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) & (~ (Y0 @ Y2)))))))))))), 41.00/5.58 inference(fool_elimination,[],[f202])). 41.00/5.58 thf(f202,plain,( 41.00/5.58 (! [X0,X1 : $i > $o] : (~! [X2] : ((in @ X2 @ X0) => (X1 @ X2)) => ? 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[X3] : (in @ emptyset @ (powerset @ X3)) = emptyInPowerset)), 41.00/5.58 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',emptyInPowerset)). 41.00/5.58 thf(f648,plain,( 41.00/5.58 (emptyinPowerset = (!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))))), 41.00/5.58 inference(cnf_transformation,[],[f491])). 41.00/5.58 thf(f491,plain,( 41.00/5.58 (emptyinPowerset = (!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))))), 41.00/5.58 inference(fool_elimination,[],[f490])). 41.00/5.58 thf(f490,plain,( 41.00/5.58 (emptyinPowerset = ! [X0] : (in @ emptyset @ (powerset @ X0)))), 41.00/5.58 inference(rectify,[],[f38])). 41.00/5.58 thf(f38,axiom,( 41.00/5.58 (emptyinPowerset = ! [X3] : (in @ emptyset @ (powerset @ X3)))), 41.00/5.58 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',emptyinPowerset)). 41.00/5.58 thf(f649,plain,( 41.00/5.58 (powersetI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))))), 41.00/5.58 inference(cnf_transformation,[],[f573])). 41.00/5.58 thf(f573,plain,( 41.00/5.58 (powersetI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (in @ Y0 @ (powerset @ Y1))))))))), 41.00/5.58 inference(fool_elimination,[],[f572])). 41.00/5.58 thf(f572,plain,( 41.00/5.58 (powersetI = ! [X0,X1] : (! [X2] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0))))), 41.00/5.58 inference(rectify,[],[f37])). 41.00/5.58 thf(f37,axiom,( 41.00/5.58 (powersetI = ! [X3,X4] : (! [X1] : ((in @ X1 @ X4) => (in @ X1 @ X3)) => (in @ X4 @ (powerset @ X3))))), 41.00/5.58 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',powersetI)). 41.00/5.58 thf(f680,plain,( 41.00/5.58 (setoftrueEq = (!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))))), 41.00/5.58 inference(cnf_transformation,[],[f383])). 41.00/5.58 thf(f383,plain,( 41.00/5.58 (setoftrueEq = (!! @ $i @ (^[Y0 : $i]: ((dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))) = Y0))))), 41.00/5.58 inference(fool_elimination,[],[f382])). 41.00/5.58 thf(f382,plain,( 41.00/5.58 (! [X0] : ((dsetconstr @ X0 @ (^[X1 : $i] : ($true))) = X0) = setoftrueEq)), 41.00/5.58 inference(rectify,[],[f36])). 41.00/5.58 thf(f36,axiom,( 41.00/5.58 (! [X3] : ((dsetconstr @ X3 @ (^[X1 : $i] : ($true))) = X3) = setoftrueEq)), 41.00/5.58 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',setoftrueEq)). 41.00/5.58 thf(f624,plain,( 41.00/5.58 (setadjoinOr = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((Y1 = Y0) | (in @ Y1 @ Y2))))))))))), 41.00/5.58 inference(cnf_transformation,[],[f217])). 41.00/5.58 thf(f217,plain,( 41.00/5.58 (setadjoinOr = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ Y2)) => ((Y1 = Y0) | (in @ Y1 @ Y2))))))))))), 41.00/5.58 inference(fool_elimination,[],[f216])). 41.00/5.58 thf(f216,plain,( 41.00/5.58 (setadjoinOr = ! [X0,X1,X2] : ((in @ X1 @ (setadjoin @ X2 @ X0)) => ((in @ X1 @ X0) | (X1 = X2))))), 41.00/5.58 inference(rectify,[],[f35])). 41.00/5.58 thf(f35,axiom,( 41.00/5.58 (setadjoinOr = ! [X3,X2,X1] : ((in @ X2 @ (setadjoin @ X1 @ X3)) => ((in @ X2 @ X3) | (X1 = X2))))), 41.00/5.58 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',setadjoinOr)). 41.00/5.58 thf(f662,plain,( 41.00/5.58 (setadjoinE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((Y2 = Y1) => Y3) => (((in @ Y2 @ Y0) => Y3) => Y3))))))))))))), 41.00/5.58 inference(cnf_transformation,[],[f231])). 41.00/5.58 thf(f231,plain,( 41.00/5.58 (setadjoinE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y1 @ Y0)) => (!! @ $o @ (^[Y3 : $o]: (((Y2 = Y1) => Y3) => (((in @ Y2 @ Y0) => Y3) => Y3))))))))))))), 41.00/5.58 inference(fool_elimination,[],[f230])). 41.00/5.58 thf(f230,plain,( 41.00/5.58 (setadjoinE = ! [X0,X1,X2] : ((in @ X0 @ (setadjoin @ X1 @ X2)) => ! [X3 : $o] : (((X0 = X1) => X3) => (((in @ X0 @ X2) => X3) => X3))))), 41.00/5.58 inference(rectify,[],[f34])). 41.00/5.58 thf(f34,axiom,( 41.00/5.58 (setadjoinE = ! [X2,X1,X3] : ((in @ X2 @ (setadjoin @ X1 @ X3)) => ! [X0 : $o] : (((X1 = X2) => X0) => (((in @ X2 @ X3) => X0) => X0))))), 41.00/5.58 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',setadjoinE)). 41.00/5.58 thf(f630,plain,( 41.00/5.58 (setadjoinIR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (setadjoin @ Y0 @ Y2))))))))))), 41.00/5.58 inference(cnf_transformation,[],[f535])). 41.00/5.58 thf(f535,plain,( 41.00/5.58 (setadjoinIR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (setadjoin @ Y0 @ Y2))))))))))), 41.00/5.58 inference(fool_elimination,[],[f534])). 41.00/5.58 thf(f534,plain,( 41.00/5.58 (setadjoinIR = ! [X0,X1,X2] : ((in @ X1 @ X0) => (in @ X1 @ (setadjoin @ X2 @ X0))))), 41.00/5.58 inference(rectify,[],[f33])). 41.00/5.58 thf(f33,axiom,( 41.00/5.58 (setadjoinIR = ! [X3,X2,X1] : ((in @ X2 @ X3) => (in @ X2 @ (setadjoin @ X1 @ X3))))), 41.00/5.58 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',setadjoinIR)). 41.00/5.58 thf(f783,plain,( 41.00/5.58 (emptyinunitempty = (in @ emptyset @ (setadjoin @ emptyset @ emptyset)))), 41.00/5.58 inference(cnf_transformation,[],[f248])). 41.00/5.58 thf(f248,plain,( 41.00/5.58 (emptyinunitempty = (in @ emptyset @ (setadjoin @ emptyset @ emptyset)))), 41.00/5.58 inference(fool_elimination,[],[f32])). 41.00/5.58 thf(f32,axiom,( 41.00/5.58 (emptyinunitempty = (in @ emptyset @ (setadjoin @ emptyset @ emptyset)))), 41.00/5.58 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',emptyinunitempty)). 41.00/5.58 thf(f742,plain,( 41.00/5.58 (setadjoinIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))))), 41.00/5.58 inference(cnf_transformation,[],[f250])). 41.00/5.58 thf(f250,plain,( 41.00/5.58 (setadjoinIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y1 @ (setadjoin @ Y1 @ Y0)))))))), 41.00/5.58 inference(fool_elimination,[],[f249])). 41.00/5.58 thf(f249,plain,( 41.00/5.58 (! [X0,X1] : (in @ X0 @ (setadjoin @ X0 @ X1)) = setadjoinIL)), 41.00/5.58 inference(rectify,[],[f31])). 41.00/5.58 thf(f31,axiom,( 41.00/5.58 (! [X1,X2] : (in @ X1 @ (setadjoin @ X1 @ X2)) = setadjoinIL)), 41.00/5.58 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',setadjoinIL)). 41.00/5.58 thf(f801,plain,( 41.00/5.58 (nonemptyI1 = (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => ((^[Y1 : $i]: (~ (emptyset = Y1))) @ Y0)))))), 41.00/5.58 inference(definition_unfolding,[],[f744,f622])). 41.00/5.58 thf(f744,plain,( 41.00/5.58 (nonemptyI1 = (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (nonempty @ Y0)))))), 41.00/5.58 inference(cnf_transformation,[],[f209])). 41.00/5.58 thf(f209,plain,( 41.00/5.58 (nonemptyI1 = (!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0))) => (nonempty @ Y0)))))), 41.00/5.58 inference(fool_elimination,[],[f208])). 41.00/5.58 thf(f208,plain,( 41.00/5.58 (! [X0] : (? [X1] : (in @ X1 @ X0) => (nonempty @ X0)) = nonemptyI1)), 41.00/5.58 inference(rectify,[],[f30])). 41.00/5.58 thf(f30,axiom,( 41.00/5.58 (! [X3] : (? [X1] : (in @ X1 @ X3) => (nonempty @ X3)) = nonemptyI1)), 41.00/5.58 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',nonemptyI1)). 41.00/5.58 thf(f800,plain,( 41.00/5.58 (nonemptyI = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => ((^[Y3 : $i]: (~ (emptyset = Y3))) @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))))))))))))), 41.00/5.58 inference(definition_unfolding,[],[f773,f622])). 41.00/5.58 thf(f773,plain,( 41.00/5.58 (nonemptyI = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (nonempty @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))))))))))))), 41.00/5.58 inference(cnf_transformation,[],[f401])). 41.00/5.58 thf(f401,plain,( 41.00/5.58 (nonemptyI = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (nonempty @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))))))))))))), 41.00/5.58 inference(fool_elimination,[],[f400])). 41.00/5.58 thf(f400,plain,( 41.00/5.58 (nonemptyI = ! [X0,X1 : $i > $o,X2] : ((in @ X0 @ X2) => ((X1 @ X0) => (nonempty @ (dsetconstr @ X2 @ (^[X3 : $i] : (X1 @ X3)))))))), 41.00/5.58 inference(rectify,[],[f29])). 41.00/5.58 thf(f29,axiom,( 41.00/5.58 (nonemptyI = ! [X1,X0 : $i > $o,X3] : ((in @ X1 @ X3) => ((X0 @ X1) => (nonempty @ (dsetconstr @ X3 @ (^[X2 : $i] : (X0 @ X2)))))))), 41.00/5.58 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',nonemptyI)). 41.00/5.58 thf(f799,plain,( 41.00/5.58 (nonemptyE1 = (!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (~ (emptyset = Y1))) @ Y0) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))))), 41.00/5.58 inference(definition_unfolding,[],[f758,f622])). 41.00/5.58 thf(f758,plain,( 41.00/5.58 (nonemptyE1 = (!! @ $i @ (^[Y0 : $i]: ((nonempty @ Y0) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))))), 41.00/5.58 inference(cnf_transformation,[],[f377])). 41.00/5.58 thf(f377,plain,( 41.00/5.58 (nonemptyE1 = (!! @ $i @ (^[Y0 : $i]: ((nonempty @ Y0) => (?? @ $i @ (^[Y1 : $i]: (in @ Y1 @ Y0)))))))), 41.00/5.58 inference(fool_elimination,[],[f376])). 41.00/5.58 thf(f376,plain,( 41.00/5.58 (! [X0] : ((nonempty @ X0) => ? [X1] : (in @ X1 @ X0)) = nonemptyE1)), 41.00/5.58 inference(rectify,[],[f28])). 41.00/5.58 thf(f28,axiom,( 41.00/5.58 (! [X3] : ((nonempty @ X3) => ? [X1] : (in @ X1 @ X3)) = nonemptyE1)), 41.00/5.58 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',nonemptyE1)). 41.00/5.58 thf(f764,plain,( 41.00/5.58 (setbeta = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))) = (Y1 @ Y2))))))))))), 41.00/5.58 inference(cnf_transformation,[],[f493])). 41.00/5.58 thf(f493,plain,( 41.00/5.58 (setbeta = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((in @ Y2 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))) = (Y1 @ Y2))))))))))), 41.00/5.58 inference(fool_elimination,[],[f492])). 41.00/5.58 thf(f492,plain,( 41.00/5.58 (setbeta = ! [X0,X1 : $i > $o,X2] : ((in @ X0 @ X2) => ((in @ X0 @ (dsetconstr @ X2 @ (^[X3 : $i] : (X1 @ X3)))) <=> (X1 @ X0))))), 41.00/5.58 inference(rectify,[],[f26])). 41.00/5.58 thf(f26,axiom,( 41.00/5.58 (setbeta = ! [X1,X0 : $i > $o,X3] : ((in @ X1 @ X3) => ((in @ X1 @ (dsetconstr @ X3 @ (^[X2 : $i] : (X0 @ X2)))) <=> (X0 @ X1))))), 41.00/5.58 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',setbeta)). 41.00/5.58 thf(f734,plain,( 41.00/5.58 (noeltsimpempty = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))))), 41.00/5.58 inference(cnf_transformation,[],[f443])). 41.00/5.58 thf(f443,plain,( 41.00/5.58 (noeltsimpempty = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))))), 41.00/5.58 inference(fool_elimination,[],[f442])). 41.00/5.58 thf(f442,plain,( 41.00/5.58 (! [X0] : (! [X1] : ~(in @ X1 @ X0) => (emptyset = X0)) = noeltsimpempty)), 41.00/5.58 inference(rectify,[],[f25])). 41.00/5.58 thf(f25,axiom,( 41.00/5.58 (! [X3] : (! [X1] : ~(in @ X1 @ X3) => (emptyset = X3)) = noeltsimpempty)), 41.00/5.58 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',noeltsimpempty)). 41.00/5.58 thf(f726,plain,( 41.00/5.58 (emptyI = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))))), 41.00/5.58 inference(cnf_transformation,[],[f483])). 41.00/5.58 thf(f483,plain,( 41.00/5.58 (emptyI = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (~ (in @ Y1 @ Y0)))) => (emptyset = Y0)))))), 41.00/5.58 inference(fool_elimination,[],[f482])). 41.00/5.58 thf(f482,plain,( 41.00/5.58 (! [X0] : (! [X1] : ~(in @ X1 @ X0) => (emptyset = X0)) = emptyI)), 41.00/5.58 inference(rectify,[],[f24])). 41.00/5.58 thf(f24,axiom,( 41.00/5.58 (! [X3] : (! [X1] : ~(in @ X1 @ X3) => (emptyset = X3)) = emptyI)), 41.00/5.58 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',emptyI)). 41.00/5.58 thf(f654,plain,( 41.00/5.58 (setext = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))))), 41.00/5.58 inference(cnf_transformation,[],[f341])). 41.00/5.58 thf(f341,plain,( 41.00/5.58 (setext = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ Y2 @ Y0)))) => (Y1 = Y0))))))))), 41.00/5.58 inference(fool_elimination,[],[f340])). 41.00/5.58 thf(f340,plain,( 41.00/5.58 (! [X0,X1] : (! [X2] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (! [X3] : ((in @ X3 @ X0) => (in @ X3 @ X1)) => (X0 = X1))) = setext)), 41.00/5.58 inference(rectify,[],[f23])). 41.00/5.58 thf(f23,axiom,( 41.00/5.58 (! [X4,X3] : (! [X1] : ((in @ X1 @ X3) => (in @ X1 @ X4)) => (! [X1] : ((in @ X1 @ X4) => (in @ X1 @ X3)) => (X3 = X4))) = setext)), 41.00/5.58 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',setext)). 41.00/5.58 thf(f798,plain,( 41.00/5.58 (exuE3e = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))))))) @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))), 41.00/5.58 inference(definition_unfolding,[],[f767,f694])). 41.00/5.58 thf(f767,plain,( 41.00/5.58 (exuE3e = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))), 41.00/5.58 inference(cnf_transformation,[],[f418])). 41.00/5.58 thf(f418,plain,( 41.00/5.58 (exuE3e = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))), 41.00/5.58 inference(fool_elimination,[],[f417])). 41.00/5.58 thf(f417,plain,( 41.00/5.58 (exuE3e = ! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ? [X2] : (X0 @ X2)))), 41.00/5.58 inference(rectify,[],[f22])). 41.00/5.58 thf(f22,axiom,( 41.00/5.58 (exuE3e = ! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ? [X1] : (X0 @ X1)))), 41.00/5.58 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',exuE3e)). 41.00/5.58 thf(f782,plain,( 41.00/5.58 (notinemptyset = (!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))))), 41.00/5.58 inference(cnf_transformation,[],[f511])). 41.00/5.58 thf(f511,plain,( 41.00/5.58 (notinemptyset = (!! @ $i @ (^[Y0 : $i]: (~ (in @ Y0 @ emptyset)))))), 41.00/5.58 inference(fool_elimination,[],[f510])). 41.00/5.58 thf(f510,plain,( 41.00/5.58 (notinemptyset = ! [X0] : ~(in @ X0 @ emptyset))), 41.00/5.58 inference(rectify,[],[f21])). 41.00/5.58 thf(f21,axiom,( 41.00/5.58 (notinemptyset = ! [X1] : ~(in @ X1 @ emptyset))), 41.00/5.58 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',notinemptyset)). 41.00/5.58 thf(f730,plain,( 41.00/5.58 (emptysetimpfalse = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))))), 41.00/5.58 inference(cnf_transformation,[],[f389])). 41.00/5.58 thf(f389,plain,( 41.00/5.58 (emptysetimpfalse = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => $false))))), 41.00/5.58 inference(fool_elimination,[],[f388])). 41.00/5.58 thf(f388,plain,( 41.00/5.58 (! [X0] : ((in @ X0 @ emptyset) => $false) = emptysetimpfalse)), 41.00/5.58 inference(rectify,[],[f20])). 41.00/5.58 thf(f20,axiom,( 41.00/5.58 (! [X1] : ((in @ X1 @ emptyset) => $false) = emptysetimpfalse)), 41.00/5.58 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',emptysetimpfalse)). 41.00/5.58 thf(f700,plain,( 41.00/5.58 (emptysetE = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))))), 41.00/5.58 inference(cnf_transformation,[],[f339])). 41.00/5.58 thf(f339,plain,( 41.00/5.58 (emptysetE = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ emptyset) => (!! @ $o @ (^[Y1 : $o]: (Y1)))))))), 41.00/5.58 inference(fool_elimination,[],[f338])). 41.00/5.58 thf(f338,plain,( 41.00/5.58 (emptysetE = ! [X0] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1))), 41.00/5.58 inference(rectify,[],[f19])). 41.00/5.58 thf(f19,axiom,( 41.00/5.58 (emptysetE = ! [X1] : ((in @ X1 @ emptyset) => ! [X0 : $o] : X0))), 41.00/5.58 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',emptysetE)). 41.00/5.58 thf(f747,plain,( 41.00/5.58 (prop2setE = (!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))))), 41.00/5.58 inference(cnf_transformation,[],[f254])). 41.00/5.58 thf(f254,plain,( 41.00/5.58 (prop2setE = (!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ Y0 @ (prop2set @ Y1)) => Y1))))))), 41.00/5.58 inference(fool_elimination,[],[f253])). 41.00/5.58 thf(f253,plain,( 41.00/5.58 (prop2setE = ! [X0 : $o,X1] : ((in @ X1 @ (prop2set @ X0)) => X0))), 41.00/5.58 inference(rectify,[],[f18])). 41.00/5.58 thf(f18,axiom,( 41.00/5.58 (prop2setE = ! [X0 : $o,X1] : ((in @ X1 @ (prop2set @ X0)) => X0))), 41.00/5.58 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',prop2setE)). 41.00/5.58 thf(f797,plain,( 41.00/5.58 (exuE1 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))))))) @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))))), 41.00/5.58 inference(definition_unfolding,[],[f770,f694])). 41.00/5.58 thf(f770,plain,( 41.00/5.58 (exuE1 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))))), 41.00/5.58 inference(cnf_transformation,[],[f306])). 41.00/5.58 thf(f306,plain,( 41.00/5.58 (exuE1 = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))))))))))), 41.00/5.58 inference(fool_elimination,[],[f305])). 41.00/5.58 thf(f305,plain,( 41.00/5.58 (exuE1 = ! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ? [X2] : (! [X3] : ((X0 @ X3) => (X2 = X3)) & (X0 @ X2))))), 41.00/5.58 inference(rectify,[],[f17])). 41.00/5.58 thf(f17,axiom,( 41.00/5.58 (exuE1 = ! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ? [X1] : (! [X2] : ((X0 @ X2) => (X1 = X2)) & (X0 @ X1))))), 41.00/5.58 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',exuE1)). 41.00/5.58 thf(f690,plain,( 41.00/5.58 (dsetconstrER = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3)))) => (Y1 @ Y0)))))))))), 41.00/5.58 inference(cnf_transformation,[],[f407])). 41.00/5.58 thf(f407,plain,( 41.00/5.58 (dsetconstrER = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y1 @ Y3)))) => (Y1 @ Y0)))))))))), 41.00/5.58 inference(fool_elimination,[],[f406])). 41.00/5.58 thf(f406,plain,( 41.00/5.58 (! [X0,X1 : $i > $o,X2] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X2)) = dsetconstrER)), 41.00/5.58 inference(rectify,[],[f16])). 41.00/5.58 thf(f16,axiom,( 41.00/5.58 (! [X3,X0 : $i > $o,X1] : ((in @ X1 @ (dsetconstr @ X3 @ (^[X2 : $i] : (X0 @ X2)))) => (X0 @ X1)) = dsetconstrER)), 41.00/5.58 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',dsetconstrER)). 41.00/5.58 thf(f608,plain,( 41.00/5.58 (dsetconstrEL = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))) => (in @ Y2 @ Y0)))))))))), 41.00/5.58 inference(cnf_transformation,[],[f549])). 41.00/5.58 thf(f549,plain,( 41.00/5.58 (dsetconstrEL = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))) => (in @ Y2 @ Y0)))))))))), 41.00/5.58 inference(fool_elimination,[],[f548])). 41.00/5.58 thf(f548,plain,( 41.00/5.58 (! [X0,X1 : $i > $o,X2] : ((in @ X0 @ (dsetconstr @ X2 @ (^[X3 : $i] : (X1 @ X3)))) => (in @ X0 @ X2)) = dsetconstrEL)), 41.00/5.58 inference(rectify,[],[f15])). 41.00/5.58 thf(f15,axiom,( 41.00/5.58 (! [X1,X0 : $i > $o,X3] : ((in @ X1 @ (dsetconstr @ X3 @ (^[X2 : $i] : (X0 @ X2)))) => (in @ X1 @ X3)) = dsetconstrEL)), 41.00/5.58 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',dsetconstrEL)). 41.00/5.58 thf(f670,plain,( 41.00/5.58 (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)))))))))))))), 41.00/5.58 inference(cnf_transformation,[],[f395])). 41.00/5.58 thf(f395,plain,( 41.00/5.58 (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)))))))))))))), 41.00/5.58 inference(fool_elimination,[],[f394])). 41.00/5.58 thf(f394,plain,( 41.00/5.58 (! [X0,X1 : $i > $o,X2] : ((in @ X2 @ X0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))))) = dsetconstrI)), 41.00/5.58 inference(rectify,[],[f14])). 41.00/5.58 thf(f14,axiom,( 41.00/5.58 (! [X3,X0 : $i > $o,X1] : ((in @ X1 @ X3) => ((X0 @ X1) => (in @ X1 @ (dsetconstr @ X3 @ (^[X2 : $i] : (X0 @ X2)))))) = dsetconstrI)), 41.00/5.58 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',dsetconstrI)). 41.00/5.58 thf(f796,plain,( 41.00/5.58 (descrp = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) => (Y2 = Y3)))))))) @ (^[Y1 : $i]: (Y0 @ Y1))) => (Y0 @ (descr @ (^[Y1 : $i]: (Y0 @ Y1))))))))), 41.00/5.58 inference(definition_unfolding,[],[f659,f694])). 41.00/5.58 thf(f659,plain,( 41.00/5.58 (descrp = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (Y0 @ (descr @ (^[Y1 : $i]: (Y0 @ Y1))))))))), 41.00/5.58 inference(cnf_transformation,[],[f553])). 41.00/5.58 thf(f553,plain,( 41.00/5.58 (descrp = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((exu @ (^[Y1 : $i]: (Y0 @ Y1))) => (Y0 @ (descr @ (^[Y1 : $i]: (Y0 @ Y1))))))))), 41.00/5.58 inference(fool_elimination,[],[f552])). 41.00/5.58 thf(f552,plain,( 41.00/5.58 (! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => (X0 @ (descr @ (^[X2 : $i] : (X0 @ X2))))) = descrp)), 41.00/5.58 inference(rectify,[],[f13])). 41.00/5.58 thf(f13,axiom,( 41.00/5.58 (! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => (X0 @ (descr @ (^[X1 : $i] : (X0 @ X1))))) = descrp)), 41.00/5.58 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',descrp)). 41.00/5.58 thf(f644,plain,( 41.00/5.58 (wellorderingAx = (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))))), 41.00/5.58 inference(cnf_transformation,[],[f437])). 41.00/5.58 thf(f437,plain,( 41.00/5.58 (wellorderingAx = (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))))) & (!! @ $i @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: (in @ Y3 @ Y2))) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ Y3 @ Y0))))) => (?? @ $i @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (in @ Y5 @ Y2))))) & (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ Y4 @ Y5) | (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y5) => (in @ Y6 @ Y3))))))))) & (in @ Y4 @ Y2)) & (in @ Y3 @ Y1)))))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y2 @ Y0) & (in @ Y3 @ Y0)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y3 @ Y4) = (in @ Y2 @ Y4))))) => (Y3 = Y2)))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((in @ Y3 @ Y1) & (in @ Y2 @ Y1)) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (in @ Y4 @ Y3)))) | (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => (in @ Y4 @ Y2))))))))))))))))), 41.00/5.58 inference(fool_elimination,[],[f436])). 41.00/5.58 thf(f436,plain,( 41.00/5.58 (wellorderingAx = ! 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[X5] : ((in @ X5 @ X4) => ((in @ X2 @ X5) <=> (in @ X1 @ X5))) => (X1 = X2))) & ! [X5] : ((! [X1] : ((in @ X1 @ X5) => (in @ X1 @ X3)) & ? [X1] : (in @ X1 @ X5)) => ? [X1,X6] : ((in @ X6 @ X4) & (in @ X1 @ X5) & ! [X7] : ((in @ X7 @ X4) => (! [X2] : ((in @ X2 @ X7) => (in @ X2 @ X6)) | (in @ X1 @ X7))) & ~? [X2] : ((in @ X2 @ X5) & (in @ X2 @ X6)))) & ! [X5] : ((in @ X5 @ X4) => ! 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@ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y1 @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (in @ (ap @ Y1 @ Y0 @ Y2 @ Y3) @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 41.00/5.58 inference(fool_elimination,[],[f244])). 41.00/5.58 thf(f244,plain,( 41.00/5.58 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => ! [X0,X1,X2] : ((func @ X1 @ X2 @ X0) => ! [X3] : ((in @ X3 @ X1) => (in @ (ap @ X1 @ X2 @ X0 @ X3) @ X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 41.00/5.58 inference(rectify,[],[f200])). 41.00/5.58 thf(f200,negated_conjecture,( 41.00/5.58 ~(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 => ! [X13,X3,X4] : ((func @ X3 @ X4 @ X13) => ! [X1] : ((in @ X1 @ X3) => (in @ (ap @ X3 @ X4 @ X13 @ X1) @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 41.00/5.58 inference(negated_conjecture,[],[f199])). 41.00/5.58 thf(f199,conjecture,( 41.00/5.58 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 => ! [X13,X3,X4] : ((func @ X3 @ X4 @ X13) => ! [X1] : ((in @ X1 @ X3) => (in @ (ap @ X3 @ X4 @ X13 @ X1) @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 41.00/5.58 file('/export/starexec/sandbox2/tmp/tmp.ximOiPZlHt/Vampire---4.8_16456',app)). 41.00/5.58 % SZS output end Proof for Vampire---4 41.00/5.58 % (16714)------------------------------ 41.00/5.58 % (16714)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 41.00/5.58 % (16714)Termination reason: Refutation 41.00/5.58 41.00/5.58 % (16714)Memory used [KB]: 199314 41.00/5.58 % (16714)Time elapsed: 1.071 s 41.00/5.58 % (16714)Instructions burned: 785 (million) 41.00/5.58 % (16714)------------------------------ 41.00/5.58 % (16714)------------------------------ 41.00/5.58 % (16563)Success in time 5.228 s 41.00/5.58 % Vampire---4.8 exiting 41.00/5.58 EOF