0.03/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.12 % Command : run_vampire %s %d THM 0.12/0.34 % Computer : n009.cluster.edu 0.12/0.34 % Model : x86_64 x86_64 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.34 % Memory : 8042.1875MB 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.34 % CPULimit : 1440 0.12/0.34 % WCLimit : 180 0.12/0.34 % DateTime : Thu Jul 4 11:03:08 EDT 2024 0.12/0.34 % CPUTime : 0.12/0.36 This is a THF_ problem 0.12/0.36 Running higher-order theorem proving 0.21/0.39 Running /export/starexec/sandbox/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/tmp/tmp.2i9OyGfWTf/E---3.1_15619.p -m 16384 -t 180 0.21/0.42 % (15731)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on E---3.1_15619 for (1799ds/27Mi) 0.21/0.42 % (15730)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 E---3.1_15619 for (1799ds/4Mi) 0.21/0.42 % (15729)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on E---3.1_15619 for (1799ds/183Mi) 0.21/0.42 % (15733)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on E---3.1_15619 for (1799ds/2Mi) 0.21/0.42 % (15734)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on E---3.1_15619 for (1799ds/275Mi) 0.21/0.42 % (15732)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on E---3.1_15619 for (1799ds/2Mi) 0.21/0.42 % (15735)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on E---3.1_15619 for (1799ds/18Mi) 0.21/0.43 % (15732)Instruction limit reached! 0.21/0.43 % (15732)------------------------------ 0.21/0.43 % (15732)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.21/0.43 % (15733)Instruction limit reached! 0.21/0.43 % (15733)------------------------------ 0.21/0.43 % (15733)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.21/0.43 % (15732)Termination reason: Unknown 0.21/0.43 % (15732)Termination phase: shuffling 0.21/0.43 0.21/0.43 % (15732)Memory used [KB]: 1279 0.21/0.43 % (15732)Time elapsed: 0.004 s 0.21/0.43 % (15732)Instructions burned: 3 (million) 0.21/0.43 % (15732)------------------------------ 0.21/0.43 % (15732)------------------------------ 0.21/0.43 % (15733)Termination reason: Unknown 0.21/0.43 % (15733)Termination phase: shuffling 0.21/0.43 0.21/0.43 % (15733)Memory used [KB]: 1279 0.21/0.43 % (15733)Time elapsed: 0.004 s 0.21/0.43 % (15733)Instructions burned: 3 (million) 0.21/0.43 % (15733)------------------------------ 0.21/0.43 % (15733)------------------------------ 0.21/0.43 % (15730)Instruction limit reached! 0.21/0.43 % (15730)------------------------------ 0.21/0.43 % (15730)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.21/0.43 % (15730)Termination reason: Unknown 0.21/0.43 % (15730)Termination phase: shuffling 0.21/0.43 0.21/0.43 % (15730)Memory used [KB]: 1279 0.21/0.43 % (15730)Time elapsed: 0.005 s 0.21/0.43 % (15730)Instructions burned: 5 (million) 0.21/0.43 % (15730)------------------------------ 0.21/0.43 % (15730)------------------------------ 0.21/0.43 % (15735)Instruction limit reached! 0.21/0.43 % (15735)------------------------------ 0.21/0.43 % (15735)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.21/0.43 % (15735)Termination reason: Unknown 0.21/0.43 % (15735)Termination phase: shuffling 0.21/0.43 0.21/0.43 % (15735)Memory used [KB]: 1535 0.21/0.43 % (15735)Time elapsed: 0.012 s 0.21/0.43 % (15735)Instructions burned: 18 (million) 0.21/0.43 % (15735)------------------------------ 0.21/0.43 % (15735)------------------------------ 0.21/0.44 % (15731)Instruction limit reached! 0.21/0.44 % (15731)------------------------------ 0.21/0.44 % (15731)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.21/0.44 % (15731)Termination reason: Unknown 0.21/0.44 % (15731)Termination phase: Property scanning 0.21/0.44 0.21/0.44 % (15731)Memory used [KB]: 1535 0.21/0.44 % (15731)Time elapsed: 0.017 s 0.21/0.44 % (15731)Instructions burned: 28 (million) 0.21/0.44 % (15731)------------------------------ 0.21/0.44 % (15731)------------------------------ 0.21/0.44 % (15736)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on E---3.1_15619 for (1799ds/3Mi) 0.21/0.44 % (15737)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 E---3.1_15619 for (1799ds/37Mi) 0.21/0.44 % (15738)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on E---3.1_15619 for (1799ds/15Mi) 0.21/0.44 % (15736)Instruction limit reached! 0.21/0.44 % (15736)------------------------------ 0.21/0.44 % (15736)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.21/0.44 % (15736)Termination reason: Unknown 0.21/0.44 % (15736)Termination phase: shuffling 0.21/0.44 0.21/0.44 % (15736)Memory used [KB]: 1279 0.21/0.44 % (15736)Time elapsed: 0.004 s 0.21/0.44 % (15736)Instructions burned: 3 (million) 0.21/0.44 % (15736)------------------------------ 0.21/0.44 % (15736)------------------------------ 0.21/0.44 % (15734)Refutation not found, incomplete strategy 0.21/0.44 % (15734)------------------------------ 0.21/0.44 % (15734)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.21/0.44 % (15734)Termination reason: Refutation not found, incomplete strategy 0.21/0.44 0.21/0.44 0.21/0.44 % (15734)Memory used [KB]: 6140 0.21/0.44 % (15734)Time elapsed: 0.022 s 0.21/0.44 % (15734)Instructions burned: 36 (million) 0.21/0.44 % (15734)------------------------------ 0.21/0.44 % (15734)------------------------------ 0.25/0.45 % (15739)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on E---3.1_15619 for (1799ds/3Mi) 0.25/0.45 % (15738)Instruction limit reached! 0.25/0.45 % (15738)------------------------------ 0.25/0.45 % (15738)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.25/0.45 % (15738)Termination reason: Unknown 0.25/0.45 % (15738)Termination phase: shuffling 0.25/0.45 0.25/0.45 % (15738)Memory used [KB]: 1535 0.25/0.45 % (15738)Time elapsed: 0.011 s 0.25/0.45 % (15738)Instructions burned: 15 (million) 0.25/0.45 % (15738)------------------------------ 0.25/0.45 % (15738)------------------------------ 0.25/0.45 % (15739)Instruction limit reached! 0.25/0.45 % (15739)------------------------------ 0.25/0.45 % (15739)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.25/0.45 % (15739)Termination reason: Unknown 0.25/0.45 % (15739)Termination phase: shuffling 0.25/0.45 0.25/0.45 % (15739)Memory used [KB]: 1279 0.25/0.45 % (15739)Time elapsed: 0.004 s 0.25/0.45 % (15739)Instructions burned: 4 (million) 0.25/0.45 % (15739)------------------------------ 0.25/0.45 % (15739)------------------------------ 0.25/0.45 % (15740)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 E---3.1_15619 for (1799ds/1041Mi) 0.25/0.46 % (15741)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on E---3.1_15619 for (1799ds/7Mi) 0.25/0.46 % (15737)Instruction limit reached! 0.25/0.46 % (15737)------------------------------ 0.25/0.46 % (15737)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.25/0.46 % (15737)Termination reason: Unknown 0.25/0.46 % (15737)Termination phase: Property scanning 0.25/0.46 0.25/0.46 % (15737)Memory used [KB]: 1663 0.25/0.46 % (15737)Time elapsed: 0.020 s 0.25/0.46 % (15737)Instructions burned: 37 (million) 0.25/0.46 % (15737)------------------------------ 0.25/0.46 % (15737)------------------------------ 0.25/0.46 % (15742)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on E---3.1_15619 for (1799ds/16Mi) 0.25/0.46 % (15741)Instruction limit reached! 0.25/0.46 % (15741)------------------------------ 0.25/0.46 % (15741)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.25/0.46 % (15741)Termination reason: Unknown 0.25/0.46 % (15741)Termination phase: shuffling 0.25/0.46 0.25/0.46 % (15741)Memory used [KB]: 1407 0.25/0.46 % (15741)Time elapsed: 0.006 s 0.25/0.46 % (15741)Instructions burned: 7 (million) 0.25/0.46 % (15741)------------------------------ 0.25/0.46 % (15741)------------------------------ 0.25/0.47 % (15744)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 E---3.1_15619 for (1799ds/3Mi) 0.25/0.47 % (15743)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 E---3.1_15619 for (1799ds/3Mi) 0.25/0.47 % (15744)Instruction limit reached! 0.25/0.47 % (15744)------------------------------ 0.25/0.47 % (15744)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.25/0.47 % (15744)Termination reason: Unknown 0.25/0.47 % (15744)Termination phase: shuffling 0.25/0.47 0.25/0.47 % (15744)Memory used [KB]: 1279 0.25/0.47 % (15744)Time elapsed: 0.003 s 0.25/0.47 % (15744)Instructions burned: 3 (million) 0.25/0.47 % (15744)------------------------------ 0.25/0.47 % (15744)------------------------------ 0.25/0.47 % (15743)Instruction limit reached! 0.25/0.47 % (15743)------------------------------ 0.25/0.47 % (15743)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.25/0.47 % (15743)Termination reason: Unknown 0.25/0.47 % (15743)Termination phase: shuffling 0.25/0.47 0.25/0.47 % (15743)Memory used [KB]: 1279 0.25/0.47 % (15743)Time elapsed: 0.004 s 0.25/0.47 % (15743)Instructions burned: 3 (million) 0.25/0.47 % (15743)------------------------------ 0.25/0.47 % (15743)------------------------------ 0.25/0.47 % (15742)Instruction limit reached! 0.25/0.47 % (15742)------------------------------ 0.25/0.47 % (15742)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.25/0.47 % (15742)Termination reason: Unknown 0.25/0.47 % (15742)Termination phase: shuffling 0.25/0.47 0.25/0.47 % (15742)Memory used [KB]: 1535 0.25/0.47 % (15742)Time elapsed: 0.011 s 0.25/0.47 % (15742)Instructions burned: 16 (million) 0.25/0.47 % (15742)------------------------------ 0.25/0.47 % (15742)------------------------------ 0.25/0.48 % (15745)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on E---3.1_15619 for (1799ds/7Mi) 0.25/0.48 % (15747)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on E---3.1_15619 for (1799ds/4Mi) 0.25/0.48 % (15746)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on E---3.1_15619 for (1799ds/3Mi) 0.25/0.48 % (15745)Instruction limit reached! 0.25/0.48 % (15745)------------------------------ 0.25/0.48 % (15745)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.25/0.48 % (15745)Termination reason: Unknown 0.25/0.48 % (15745)Termination phase: shuffling 0.25/0.48 0.25/0.48 % (15745)Memory used [KB]: 1407 0.25/0.48 % (15745)Time elapsed: 0.006 s 0.25/0.48 % (15745)Instructions burned: 7 (million) 0.25/0.48 % (15745)------------------------------ 0.25/0.48 % (15745)------------------------------ 0.25/0.48 % (15747)Instruction limit reached! 0.25/0.48 % (15747)------------------------------ 0.25/0.48 % (15747)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.25/0.48 % (15747)Termination reason: Unknown 0.25/0.48 % (15747)Termination phase: shuffling 0.25/0.48 0.25/0.48 % (15747)Memory used [KB]: 1407 0.25/0.48 % (15747)Time elapsed: 0.003 s 0.25/0.48 % (15747)Instructions burned: 6 (million) 0.25/0.48 % (15747)------------------------------ 0.25/0.48 % (15747)------------------------------ 0.25/0.48 % (15746)Instruction limit reached! 0.25/0.48 % (15746)------------------------------ 0.25/0.48 % (15746)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.25/0.48 % (15746)Termination reason: Unknown 0.25/0.48 % (15746)Termination phase: shuffling 0.25/0.48 0.25/0.48 % (15746)Memory used [KB]: 1279 0.25/0.48 % (15746)Time elapsed: 0.004 s 0.25/0.48 % (15746)Instructions burned: 4 (million) 0.25/0.48 % (15746)------------------------------ 0.25/0.48 % (15746)------------------------------ 0.25/0.48 % (15749)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on E---3.1_15619 for (1799ds/710Mi) 0.25/0.49 % (15748)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on E---3.1_15619 for (1799ds/18Mi) 0.25/0.49 % (15751)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on E---3.1_15619 for (1799ds/902Mi) 0.25/0.50 % (15748)Instruction limit reached! 0.25/0.50 % (15748)------------------------------ 0.25/0.50 % (15748)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.25/0.50 % (15748)Termination reason: Unknown 0.25/0.50 % (15748)Termination phase: shuffling 0.25/0.50 0.25/0.50 % (15748)Memory used [KB]: 1535 0.25/0.50 % (15748)Time elapsed: 0.012 s 0.25/0.50 % (15748)Instructions burned: 18 (million) 0.25/0.50 % (15748)------------------------------ 0.25/0.50 % (15748)------------------------------ 0.25/0.50 % (15750)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on E---3.1_15619 for (1799ds/6Mi) 0.25/0.50 % (15729)Instruction limit reached! 0.25/0.50 % (15729)------------------------------ 0.25/0.50 % (15729)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.25/0.50 % (15729)Termination reason: Unknown 0.25/0.50 % (15729)Termination phase: Function definition elimination 0.25/0.50 0.25/0.50 % (15729)Memory used [KB]: 1918 0.25/0.50 % (15729)Time elapsed: 0.075 s 0.25/0.50 % (15729)Instructions burned: 183 (million) 0.25/0.50 % (15729)------------------------------ 0.25/0.50 % (15729)------------------------------ 0.25/0.50 % (15752)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 E---3.1_15619 for (1799ds/21Mi) 0.25/0.50 % (15750)Instruction limit reached! 0.25/0.50 % (15750)------------------------------ 0.25/0.50 % (15750)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.25/0.50 % (15750)Termination reason: Unknown 0.25/0.50 % (15750)Termination phase: shuffling 0.25/0.50 0.25/0.50 % (15750)Memory used [KB]: 1407 0.25/0.50 % (15750)Time elapsed: 0.006 s 0.25/0.50 % (15750)Instructions burned: 7 (million) 0.25/0.50 % (15750)------------------------------ 0.25/0.50 % (15750)------------------------------ 0.25/0.51 % (15752)Instruction limit reached! 0.25/0.51 % (15752)------------------------------ 0.25/0.51 % (15752)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.25/0.51 % (15752)Termination reason: Unknown 0.25/0.51 % (15752)Termination phase: Property scanning 0.25/0.51 0.25/0.51 % (15752)Memory used [KB]: 1535 0.25/0.51 % (15752)Time elapsed: 0.014 s 0.25/0.51 % (15752)Instructions burned: 22 (million) 0.25/0.51 % (15752)------------------------------ 0.25/0.51 % (15752)------------------------------ 0.25/0.51 % (15751)Refutation not found, incomplete strategy 0.25/0.51 % (15751)------------------------------ 0.25/0.51 % (15751)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.25/0.51 % (15751)Termination reason: Refutation not found, incomplete strategy 0.25/0.51 0.25/0.51 0.25/0.51 % (15751)Memory used [KB]: 6268 0.25/0.51 % (15751)Time elapsed: 0.022 s 0.25/0.51 % (15751)Instructions burned: 67 (million) 0.25/0.51 % (15751)------------------------------ 0.25/0.51 % (15751)------------------------------ 0.25/0.51 % (15753)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on E---3.1_15619 for (1798ds/5Mi) 0.25/0.51 % (15754)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 E---3.1_15619 for (1798ds/6Mi) 0.25/0.51 % (15753)Instruction limit reached! 0.25/0.51 % (15753)------------------------------ 0.25/0.51 % (15753)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.25/0.51 % (15753)Termination reason: Unknown 0.25/0.51 % (15753)Termination phase: shuffling 0.25/0.51 0.25/0.51 % (15753)Memory used [KB]: 1279 0.25/0.51 % (15753)Time elapsed: 0.005 s 0.25/0.51 % (15753)Instructions burned: 5 (million) 0.25/0.51 % (15753)------------------------------ 0.25/0.51 % (15753)------------------------------ 0.25/0.51 % (15755)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on E---3.1_15619 for (1798ds/377Mi) 0.25/0.52 % (15754)Instruction limit reached! 0.25/0.52 % (15754)------------------------------ 0.25/0.52 % (15754)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.25/0.52 % (15754)Termination reason: Unknown 0.25/0.52 % (15754)Termination phase: shuffling 0.25/0.52 0.25/0.52 % (15754)Memory used [KB]: 1279 0.25/0.52 % (15754)Time elapsed: 0.005 s 0.25/0.52 % (15754)Instructions burned: 6 (million) 0.25/0.52 % (15754)------------------------------ 0.25/0.52 % (15754)------------------------------ 0.25/0.52 % (15757)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 E---3.1_15619 for (1798ds/19Mi) 0.25/0.52 % (15756)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on E---3.1_15619 for (1798ds/779Mi) 0.25/0.53 % (15757)Instruction limit reached! 0.25/0.53 % (15757)------------------------------ 0.25/0.53 % (15757)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.25/0.53 % (15757)Termination reason: Unknown 0.25/0.53 % (15757)Termination phase: shuffling 0.25/0.53 0.25/0.53 % (15757)Memory used [KB]: 1535 0.25/0.53 % (15757)Time elapsed: 0.007 s 0.25/0.53 % (15757)Instructions burned: 19 (million) 0.25/0.53 % (15757)------------------------------ 0.25/0.53 % (15757)------------------------------ 0.25/0.53 % (15759)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on E---3.1_15619 for (1798ds/17Mi) 0.25/0.53 % (15758)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on E---3.1_15619 for (1798ds/879Mi) 0.25/0.53 % (15760)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on E---3.1_15619 for (1798ds/3Mi) 0.25/0.54 % (15760)Instruction limit reached! 0.25/0.54 % (15760)------------------------------ 0.25/0.54 % (15760)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.25/0.54 % (15760)Termination reason: Unknown 0.25/0.54 % (15760)Termination phase: shuffling 0.25/0.54 0.25/0.54 % (15760)Memory used [KB]: 1279 0.25/0.54 % (15760)Time elapsed: 0.003 s 0.25/0.54 % (15760)Instructions burned: 4 (million) 0.25/0.54 % (15760)------------------------------ 0.25/0.54 % (15760)------------------------------ 0.25/0.54 % (15759)Instruction limit reached! 0.25/0.54 % (15759)------------------------------ 0.25/0.54 % (15759)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.25/0.54 % (15759)Termination reason: Unknown 0.25/0.54 % (15759)Termination phase: shuffling 0.25/0.54 0.25/0.54 % (15759)Memory used [KB]: 1535 0.25/0.54 % (15759)Time elapsed: 0.011 s 0.25/0.54 % (15759)Instructions burned: 18 (million) 0.25/0.54 % (15759)------------------------------ 0.25/0.54 % (15759)------------------------------ 1.09/0.55 % (15762)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on E---3.1_15619 for (1798ds/127Mi) 1.09/0.55 % (15761)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on E---3.1_15619 for (1798ds/30Mi) 1.09/0.56 % (15761)Instruction limit reached! 1.09/0.56 % (15761)------------------------------ 1.09/0.56 % (15761)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.09/0.56 % (15761)Termination reason: Unknown 1.09/0.56 % (15761)Termination phase: Preprocessing 1 1.09/0.56 1.09/0.56 % (15761)Memory used [KB]: 1535 1.09/0.56 % (15761)Time elapsed: 0.011 s 1.09/0.56 % (15761)Instructions burned: 31 (million) 1.09/0.56 % (15761)------------------------------ 1.09/0.56 % (15761)------------------------------ 1.22/0.57 % (15763)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on E---3.1_15619 for (1798ds/100Mi) 1.22/0.58 % (15762)Instruction limit reached! 1.22/0.58 % (15762)------------------------------ 1.22/0.58 % (15762)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.22/0.58 % (15762)Termination reason: Unknown 1.22/0.58 % (15762)Termination phase: Function definition elimination 1.22/0.58 1.22/0.58 % (15762)Memory used [KB]: 1791 1.22/0.58 % (15762)Time elapsed: 0.033 s 1.22/0.58 % (15762)Instructions burned: 131 (million) 1.22/0.58 % (15762)------------------------------ 1.22/0.58 % (15762)------------------------------ 1.22/0.59 % (15764)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on E---3.1_15619 for (1798ds/3Mi) 1.22/0.59 % (15764)Instruction limit reached! 1.22/0.59 % (15764)------------------------------ 1.22/0.59 % (15764)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.22/0.59 % (15764)Termination reason: Unknown 1.22/0.59 % (15764)Termination phase: shuffling 1.22/0.59 1.22/0.59 % (15764)Memory used [KB]: 1279 1.22/0.59 % (15764)Time elapsed: 0.003 s 1.22/0.59 % (15764)Instructions burned: 4 (million) 1.22/0.59 % (15764)------------------------------ 1.22/0.59 % (15764)------------------------------ 1.22/0.60 % (15763)Instruction limit reached! 1.22/0.60 % (15763)------------------------------ 1.22/0.60 % (15763)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.22/0.60 % (15763)Termination reason: Unknown 1.22/0.60 % (15763)Termination phase: Function definition elimination 1.22/0.60 1.22/0.60 % (15763)Memory used [KB]: 1918 1.22/0.60 % (15763)Time elapsed: 0.027 s 1.22/0.60 % (15763)Instructions burned: 103 (million) 1.22/0.60 % (15763)------------------------------ 1.22/0.60 % (15763)------------------------------ 1.22/0.60 % (15765)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on E---3.1_15619 for (1798ds/20Mi) 1.22/0.61 % (15766)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 E---3.1_15619 for (1798ds/86Mi) 1.22/0.61 % (15765)Instruction limit reached! 1.22/0.61 % (15765)------------------------------ 1.22/0.61 % (15765)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.22/0.61 % (15765)Termination reason: Unknown 1.22/0.61 % (15765)Termination phase: Property scanning 1.22/0.61 1.22/0.61 % (15765)Memory used [KB]: 1535 1.22/0.61 % (15765)Time elapsed: 0.008 s 1.22/0.61 % (15765)Instructions burned: 20 (million) 1.22/0.61 % (15765)------------------------------ 1.22/0.61 % (15765)------------------------------ 1.22/0.61 % (15755)Instruction limit reached! 1.22/0.61 % (15755)------------------------------ 1.22/0.61 % (15755)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.22/0.61 % (15755)Termination reason: Unknown 1.22/0.61 % (15755)Termination phase: Property scanning 1.22/0.61 1.22/0.61 % (15755)Memory used [KB]: 1918 1.22/0.61 % (15755)Time elapsed: 0.100 s 1.22/0.61 % (15755)Instructions burned: 378 (million) 1.22/0.61 % (15755)------------------------------ 1.22/0.61 % (15755)------------------------------ 1.22/0.62 % (15767)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on E---3.1_15619 for (1797ds/107Mi) 1.22/0.62 % (15768)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on E---3.1_15619 for (1797ds/39Mi) 1.22/0.63 % (15768)Instruction limit reached! 1.22/0.63 % (15768)------------------------------ 1.22/0.63 % (15768)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.22/0.63 % (15768)Termination reason: Unknown 1.22/0.63 % (15768)Termination phase: Property scanning 1.22/0.63 1.22/0.63 % (15768)Memory used [KB]: 1663 1.22/0.63 % (15768)Time elapsed: 0.013 s 1.22/0.63 % (15768)Instructions burned: 39 (million) 1.22/0.63 % (15768)------------------------------ 1.22/0.63 % (15768)------------------------------ 1.22/0.63 % (15766)Instruction limit reached! 1.22/0.63 % (15766)------------------------------ 1.22/0.63 % (15766)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.22/0.63 % (15766)Termination reason: Unknown 1.22/0.63 % (15766)Termination phase: Function definition elimination 1.22/0.63 1.22/0.63 % (15766)Memory used [KB]: 1791 1.22/0.63 % (15766)Time elapsed: 0.030 s 1.22/0.63 % (15766)Instructions burned: 86 (million) 1.22/0.63 % (15766)------------------------------ 1.22/0.63 % (15766)------------------------------ 1.77/0.64 % (15769)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 E---3.1_15619 for (1797ds/448Mi) 1.77/0.64 % (15770)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on E---3.1_15619 for (1797ds/46Mi) 1.77/0.65 % (15767)Instruction limit reached! 1.77/0.65 % (15767)------------------------------ 1.77/0.65 % (15767)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.77/0.65 % (15767)Termination reason: Unknown 1.77/0.65 % (15767)Termination phase: Saturation 1.77/0.65 1.77/0.65 % (15767)Memory used [KB]: 6524 1.77/0.65 % (15767)Time elapsed: 0.033 s 1.77/0.65 % (15767)Instructions burned: 110 (million) 1.77/0.65 % (15767)------------------------------ 1.77/0.65 % (15767)------------------------------ 1.77/0.66 % (15772)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 E---3.1_15619 for (1797ds/98Mi) 1.77/0.66 % (15770)Instruction limit reached! 1.77/0.66 % (15770)------------------------------ 1.77/0.66 % (15770)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.77/0.66 % (15770)Termination reason: Unknown 1.77/0.66 % (15770)Termination phase: Property scanning 1.77/0.66 1.77/0.66 % (15770)Memory used [KB]: 1663 1.77/0.66 % (15770)Time elapsed: 0.016 s 1.77/0.66 % (15770)Instructions burned: 49 (million) 1.77/0.66 % (15770)------------------------------ 1.77/0.66 % (15770)------------------------------ 1.77/0.67 % (15773)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on E---3.1_15619 for (1797ds/507Mi) 1.96/0.68 % (15772)Instruction limit reached! 1.96/0.68 % (15772)------------------------------ 1.96/0.68 % (15772)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.96/0.68 % (15772)Termination reason: Unknown 1.96/0.68 % (15772)Termination phase: Function definition elimination 1.96/0.68 1.96/0.68 % (15772)Memory used [KB]: 1918 1.96/0.68 % (15772)Time elapsed: 0.026 s 1.96/0.68 % (15772)Instructions burned: 101 (million) 1.96/0.68 % (15772)------------------------------ 1.96/0.68 % (15772)------------------------------ 1.96/0.69 % (15774)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 E---3.1_15619 for (1797ds/149Mi) 1.96/0.73 % (15774)Instruction limit reached! 1.96/0.73 % (15774)------------------------------ 1.96/0.73 % (15774)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.96/0.73 % (15774)Termination reason: Unknown 1.96/0.73 % (15774)Termination phase: Function definition elimination 1.96/0.73 1.96/0.73 % (15774)Memory used [KB]: 1918 1.96/0.73 % (15774)Time elapsed: 0.037 s 1.96/0.73 % (15774)Instructions burned: 150 (million) 1.96/0.73 % (15774)------------------------------ 1.96/0.73 % (15774)------------------------------ 2.28/0.74 % (15775)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on E---3.1_15619 for (1796ds/39Mi) 2.28/0.74 % (15740)Instruction limit reached! 2.28/0.74 % (15740)------------------------------ 2.28/0.74 % (15740)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 2.28/0.74 % (15740)Termination reason: Unknown 2.28/0.74 % (15740)Termination phase: Property scanning 2.28/0.74 2.28/0.74 % (15740)Memory used [KB]: 2046 2.28/0.74 % (15740)Time elapsed: 0.286 s 2.28/0.74 % (15740)Instructions burned: 1043 (million) 2.28/0.74 % (15740)------------------------------ 2.28/0.74 % (15740)------------------------------ 2.28/0.75 % (15776)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on E---3.1_15619 for (1796ds/6Mi) 2.28/0.75 % (15775)Instruction limit reached! 2.28/0.75 % (15775)------------------------------ 2.28/0.75 % (15775)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 2.28/0.75 % (15775)Termination reason: Unknown 2.28/0.75 % (15775)Termination phase: Property scanning 2.28/0.75 2.28/0.75 % (15775)Memory used [KB]: 1663 2.28/0.75 % (15775)Time elapsed: 0.014 s 2.28/0.75 % (15775)Instructions burned: 41 (million) 2.28/0.75 % (15775)------------------------------ 2.28/0.75 % (15775)------------------------------ 2.28/0.75 % (15776)Instruction limit reached! 2.28/0.75 % (15776)------------------------------ 2.28/0.75 % (15776)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 2.28/0.75 % (15776)Termination reason: Unknown 2.28/0.75 % (15776)Termination phase: shuffling 2.28/0.75 2.28/0.75 % (15776)Memory used [KB]: 1407 2.28/0.75 % (15776)Time elapsed: 0.004 s 2.28/0.75 % (15776)Instructions burned: 7 (million) 2.28/0.75 % (15776)------------------------------ 2.28/0.75 % (15776)------------------------------ 2.28/0.75 % (15749)Instruction limit reached! 2.28/0.75 % (15749)------------------------------ 2.28/0.75 % (15749)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 2.28/0.75 % (15749)Termination reason: Unknown 2.28/0.75 % (15749)Termination phase: Saturation 2.28/0.75 2.28/0.75 % (15749)Memory used [KB]: 7419 2.28/0.75 % (15749)Time elapsed: 0.292 s 2.28/0.75 % (15749)Instructions burned: 712 (million) 2.28/0.75 % (15749)------------------------------ 2.28/0.75 % (15749)------------------------------ 2.41/0.76 % (15777)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on E---3.1_15619 for (1796ds/1087Mi) 2.41/0.76 % (15778)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on E---3.1_15619 for (1796ds/47Mi) 2.41/0.76 % (15779)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 E---3.1_15619 for (1796ds/44Mi) 2.41/0.77 % (15779)Instruction limit reached! 2.41/0.77 % (15779)------------------------------ 2.41/0.77 % (15779)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 2.41/0.77 % (15779)Termination reason: Unknown 2.41/0.77 % (15779)Termination phase: Property scanning 2.41/0.77 2.41/0.77 % (15779)Memory used [KB]: 1663 2.41/0.77 % (15779)Time elapsed: 0.015 s 2.41/0.77 % (15779)Instructions burned: 46 (million) 2.41/0.77 % (15779)------------------------------ 2.41/0.77 % (15779)------------------------------ 2.41/0.77 % (15778)Instruction limit reached! 2.41/0.77 % (15778)------------------------------ 2.41/0.77 % (15778)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 2.41/0.77 % (15778)Termination reason: Unknown 2.41/0.77 % (15778)Termination phase: Function definition elimination 2.41/0.77 2.41/0.77 % (15778)Memory used [KB]: 1663 2.41/0.77 % (15778)Time elapsed: 0.016 s 2.41/0.77 % (15778)Instructions burned: 50 (million) 2.41/0.77 % (15778)------------------------------ 2.41/0.77 % (15778)------------------------------ 2.41/0.78 % (15777)Refutation not found, incomplete strategy 2.41/0.78 % (15777)------------------------------ 2.41/0.78 % (15777)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 2.41/0.78 % (15777)Termination reason: Refutation not found, incomplete strategy 2.41/0.78 2.41/0.78 2.41/0.78 % (15777)Memory used [KB]: 6268 2.41/0.78 % (15777)Time elapsed: 0.023 s 2.41/0.78 % (15777)Instructions burned: 66 (million) 2.41/0.78 % (15777)------------------------------ 2.41/0.78 % (15777)------------------------------ 2.41/0.78 % (15780)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on E---3.1_15619 for (1796ds/432Mi) 2.41/0.78 % (15781)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on E---3.1_15619 for (1796ds/62Mi) 2.41/0.78 % (15756)Instruction limit reached! 2.41/0.78 % (15756)------------------------------ 2.41/0.78 % (15756)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 2.41/0.78 % (15756)Termination reason: Unknown 2.41/0.78 % (15756)Termination phase: Saturation 2.41/0.78 2.41/0.78 % (15756)Memory used [KB]: 7547 2.41/0.78 % (15756)Time elapsed: 0.262 s 2.41/0.78 % (15756)Instructions burned: 779 (million) 2.41/0.78 % (15756)------------------------------ 2.41/0.78 % (15756)------------------------------ 2.41/0.79 % (15773)Instruction limit reached! 2.41/0.79 % (15773)------------------------------ 2.41/0.79 % (15773)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 2.41/0.79 % (15773)Termination reason: Unknown 2.41/0.79 % (15773)Termination phase: Property scanning 2.41/0.79 2.41/0.79 % (15773)Memory used [KB]: 1918 2.41/0.79 % (15773)Time elapsed: 0.122 s 2.41/0.79 % (15773)Instructions burned: 508 (million) 2.41/0.79 % (15773)------------------------------ 2.41/0.79 % (15773)------------------------------ 2.41/0.79 % (15782)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on E---3.1_15619 for (1796ds/31Mi) 2.41/0.79 % (15769)Instruction limit reached! 2.41/0.79 % (15769)------------------------------ 2.41/0.79 % (15769)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 2.41/0.79 % (15769)Termination reason: Unknown 2.41/0.79 % (15769)Termination phase: Saturation 2.41/0.79 2.41/0.79 % (15769)Memory used [KB]: 7419 2.41/0.79 % (15783)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on E---3.1_15619 for (1796ds/96Mi) 2.41/0.79 % (15769)Time elapsed: 0.152 s 2.41/0.79 % (15769)Instructions burned: 448 (million) 2.41/0.79 % (15769)------------------------------ 2.41/0.79 % (15769)------------------------------ 2.41/0.80 % (15758)Refutation not found, non-redundant clauses discarded% (15758)------------------------------ 2.41/0.80 % (15758)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 2.41/0.80 % (15758)Termination reason: Refutation not found, non-redundant clauses discarded 2.41/0.80 2.41/0.80 % (15758)Memory used [KB]: 7547 2.41/0.80 % (15758)Time elapsed: 0.266 s 2.41/0.80 % (15758)Instructions burned: 870 (million) 2.41/0.80 % (15758)------------------------------ 2.41/0.80 % (15758)------------------------------ 2.41/0.80 % (15784)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on E---3.1_15619 for (1796ds/453Mi) 2.41/0.80 % (15782)Instruction limit reached! 2.41/0.80 % (15782)------------------------------ 2.41/0.80 % (15782)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 2.41/0.80 % (15782)Termination reason: Unknown 2.41/0.80 % (15782)Termination phase: Preprocessing 2 2.41/0.80 2.41/0.80 % (15782)Memory used [KB]: 1663 2.41/0.80 % (15782)Time elapsed: 0.011 s 2.41/0.80 % (15782)Instructions burned: 31 (million) 2.41/0.80 % (15782)------------------------------ 2.41/0.80 % (15782)------------------------------ 2.41/0.80 % (15781)Instruction limit reached! 2.41/0.80 % (15781)------------------------------ 2.41/0.80 % (15781)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 2.41/0.80 % (15781)Termination reason: Unknown 2.41/0.80 % (15781)Termination phase: Function definition elimination 2.41/0.80 2.41/0.80 % (15781)Memory used [KB]: 1918 2.41/0.80 % (15781)Time elapsed: 0.019 s 2.41/0.80 % (15781)Instructions burned: 66 (million) 2.41/0.80 % (15781)------------------------------ 2.41/0.80 % (15781)------------------------------ 2.41/0.80 % (15785)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on E---3.1_15619 for (1796ds/71Mi) 2.41/0.81 % (15786)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on E---3.1_15619 for (1796ds/83Mi) 2.41/0.81 % (15787)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on E---3.1_15619 for (1796ds/11Mi) 2.41/0.81 % (15788)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 E---3.1_15619 for (1796ds/41Mi) 2.41/0.81 % (15787)Instruction limit reached! 2.41/0.81 % (15787)------------------------------ 2.41/0.81 % (15787)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 2.41/0.81 % (15787)Termination reason: Unknown 2.41/0.81 % (15787)Termination phase: shuffling 2.41/0.81 2.41/0.81 % (15787)Memory used [KB]: 1535 2.41/0.81 % (15787)Time elapsed: 0.005 s 2.41/0.81 % (15787)Instructions burned: 11 (million) 2.41/0.81 % (15787)------------------------------ 2.41/0.81 % (15787)------------------------------ 2.41/0.82 % (15783)Instruction limit reached! 2.41/0.82 % (15783)------------------------------ 2.41/0.82 % (15783)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 2.41/0.82 % (15783)Termination reason: Unknown 2.41/0.82 % (15783)Termination phase: Function definition elimination 2.41/0.82 2.41/0.82 % (15783)Memory used [KB]: 1791 2.41/0.82 % (15783)Time elapsed: 0.026 s 2.41/0.82 % (15783)Instructions burned: 98 (million) 2.41/0.82 % (15783)------------------------------ 2.41/0.82 % (15783)------------------------------ 2.41/0.82 % (15789)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on E---3.1_15619 for (1796ds/6Mi) 2.41/0.82 % (15785)Instruction limit reached! 2.41/0.82 % (15785)------------------------------ 2.41/0.82 % (15785)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 2.41/0.82 % (15785)Termination reason: Unknown 2.41/0.82 % (15785)Termination phase: Function definition elimination 2.41/0.82 2.41/0.82 % (15785)Memory used [KB]: 1791 2.41/0.82 % (15785)Time elapsed: 0.021 s 2.41/0.82 % (15785)Instructions burned: 73 (million) 2.41/0.82 % (15785)------------------------------ 2.41/0.82 % (15785)------------------------------ 2.96/0.82 % (15788)Instruction limit reached! 2.96/0.82 % (15788)------------------------------ 2.96/0.82 % (15788)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 2.96/0.82 % (15788)Termination reason: Unknown 2.96/0.82 % (15788)Termination phase: Property scanning 2.96/0.82 2.96/0.82 % (15788)Memory used [KB]: 1663 2.96/0.82 % (15788)Time elapsed: 0.014 s 2.96/0.82 % (15788)Instructions burned: 44 (million) 2.96/0.82 % (15788)------------------------------ 2.96/0.82 % (15788)------------------------------ 2.96/0.82 % (15789)Instruction limit reached! 2.96/0.82 % (15789)------------------------------ 2.96/0.82 % (15789)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 2.96/0.82 % (15789)Termination reason: Unknown 2.96/0.82 % (15789)Termination phase: shuffling 2.96/0.82 2.96/0.82 % (15789)Memory used [KB]: 1407 2.96/0.82 % (15789)Time elapsed: 0.004 s 2.96/0.82 % (15789)Instructions burned: 8 (million) 2.96/0.82 % (15789)------------------------------ 2.96/0.82 % (15789)------------------------------ 2.96/0.83 % (15790)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on E---3.1_15619 for (1795ds/150Mi) 2.96/0.83 % (15791)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on E---3.1_15619 for (1795ds/343Mi) 2.96/0.83 % (15792)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on E---3.1_15619 for (1795ds/109Mi) 2.96/0.83 % (15793)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on E---3.1_15619 for (1795ds/253Mi) 2.96/0.83 % (15786)Instruction limit reached! 2.96/0.83 % (15786)------------------------------ 2.96/0.83 % (15786)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 2.96/0.83 % (15786)Termination reason: Unknown 2.96/0.83 % (15786)Termination phase: Saturation 2.96/0.83 2.96/0.83 % (15786)Memory used [KB]: 6396 2.96/0.83 % (15786)Time elapsed: 0.050 s 2.96/0.83 % (15786)Instructions burned: 83 (million) 2.96/0.83 % (15786)------------------------------ 2.96/0.83 % (15786)------------------------------ 2.96/0.84 % (15793)Refutation not found, incomplete strategy 2.96/0.84 % (15793)------------------------------ 2.96/0.84 % (15793)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 2.96/0.84 % (15793)Termination reason: Refutation not found, incomplete strategy 2.96/0.84 2.96/0.84 2.96/0.84 % (15793)Memory used [KB]: 6140 2.96/0.84 % (15793)Time elapsed: 0.013 s 2.96/0.84 % (15793)Instructions burned: 36 (million) 2.96/0.84 % (15793)------------------------------ 2.96/0.84 % (15793)------------------------------ 2.96/0.84 % (15794)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on E---3.1_15619 for (1795ds/140Mi) 2.96/0.85 % (15795)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on E---3.1_15619 for (1795ds/614Mi) 2.96/0.86 % (15794)Refutation not found, incomplete strategy 2.96/0.86 % (15794)------------------------------ 2.96/0.86 % (15794)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 2.96/0.86 % (15794)Termination reason: Refutation not found, incomplete strategy 2.96/0.86 2.96/0.86 2.96/0.86 % (15794)Memory used [KB]: 6140 2.96/0.86 % (15794)Time elapsed: 0.016 s 2.96/0.86 % (15794)Instructions burned: 42 (million) 2.96/0.86 % (15794)------------------------------ 2.96/0.86 % (15794)------------------------------ 2.96/0.86 % (15792)Instruction limit reached! 2.96/0.86 % (15792)------------------------------ 2.96/0.86 % (15792)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 2.96/0.86 % (15792)Termination reason: Unknown 2.96/0.86 % (15792)Termination phase: Function definition elimination 2.96/0.86 2.96/0.86 % (15792)Memory used [KB]: 1791 2.96/0.86 % (15792)Time elapsed: 0.029 s 2.96/0.86 % (15792)Instructions burned: 111 (million) 2.96/0.86 % (15792)------------------------------ 2.96/0.86 % (15792)------------------------------ 2.96/0.86 % (15790)Instruction limit reached! 2.96/0.86 % (15790)------------------------------ 2.96/0.86 % (15790)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 2.96/0.86 % (15790)Termination reason: Unknown 2.96/0.86 % (15790)Termination phase: Function definition elimination 2.96/0.86 2.96/0.86 % (15790)Memory used [KB]: 1791 2.96/0.86 % (15790)Time elapsed: 0.036 s 2.96/0.86 % (15790)Instructions burned: 150 (million) 2.96/0.86 % (15790)------------------------------ 2.96/0.86 % (15790)------------------------------ 3.14/0.87 % (15796)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on E---3.1_15619 for (1795ds/202Mi) 3.14/0.87 % (15797)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on E---3.1_15619 for (1795ds/339Mi) 3.14/0.87 % (15798)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on E---3.1_15619 for (1795ds/283Mi) 3.14/0.88 % (15796)Refutation not found, incomplete strategy 3.14/0.88 % (15796)------------------------------ 3.14/0.88 % (15796)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.14/0.88 % (15796)Termination reason: Refutation not found, incomplete strategy 3.14/0.88 3.14/0.88 3.14/0.88 % (15796)Memory used [KB]: 6140 3.14/0.88 % (15796)Time elapsed: 0.014 s 3.14/0.88 % (15796)Instructions burned: 40 (million) 3.14/0.88 % (15796)------------------------------ 3.14/0.88 % (15796)------------------------------ 3.14/0.88 % (15780)Instruction limit reached! 3.14/0.88 % (15780)------------------------------ 3.14/0.88 % (15780)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.14/0.88 % (15780)Termination reason: Unknown 3.14/0.88 % (15780)Termination phase: Property scanning 3.14/0.88 3.14/0.88 % (15780)Memory used [KB]: 1918 3.14/0.88 % (15780)Time elapsed: 0.099 s 3.14/0.88 % (15780)Instructions burned: 434 (million) 3.14/0.88 % (15780)------------------------------ 3.14/0.88 % (15780)------------------------------ 3.14/0.89 % (15800)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on E---3.1_15619 for (1795ds/298Mi) 3.14/0.89 % (15799)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on E---3.1_15619 for (1795ds/134Mi) 3.14/0.90 % (15784)Instruction limit reached! 3.14/0.90 % (15784)------------------------------ 3.14/0.90 % (15784)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.14/0.90 % (15784)Termination reason: Unknown 3.14/0.90 % (15784)Termination phase: Property scanning 3.14/0.90 3.14/0.90 % (15784)Memory used [KB]: 2046 3.14/0.90 % (15784)Time elapsed: 0.105 s 3.14/0.90 % (15784)Instructions burned: 456 (million) 3.14/0.90 % (15784)------------------------------ 3.14/0.90 % (15784)------------------------------ 3.14/0.91 % (15801)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on E---3.1_15619 for (1794ds/192Mi) 3.14/0.92 % (15799)Instruction limit reached! 3.14/0.92 % (15799)------------------------------ 3.14/0.92 % (15799)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.14/0.92 % (15799)Termination reason: Unknown 3.14/0.92 % (15799)Termination phase: Function definition elimination 3.14/0.92 3.14/0.92 % (15799)Memory used [KB]: 1791 3.14/0.92 % (15799)Time elapsed: 0.033 s 3.14/0.92 % (15799)Instructions burned: 135 (million) 3.14/0.92 % (15799)------------------------------ 3.14/0.92 % (15799)------------------------------ 3.14/0.93 % (15798)Instruction limit reached! 3.14/0.93 % (15798)------------------------------ 3.14/0.93 % (15798)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.14/0.93 % (15798)Termination reason: Unknown 3.14/0.93 % (15798)Termination phase: Property scanning 3.14/0.93 3.14/0.93 % (15798)Memory used [KB]: 2046 3.14/0.93 % (15798)Time elapsed: 0.058 s 3.14/0.93 % (15798)Instructions burned: 285 (million) 3.14/0.93 % (15798)------------------------------ 3.14/0.93 % (15798)------------------------------ 3.14/0.93 % (15802)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on E---3.1_15619 for (1794ds/258Mi) 3.14/0.93 % (15803)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 E---3.1_15619 for (1794ds/90Mi) 3.53/0.94 % (15797)Instruction limit reached! 3.53/0.94 % (15797)------------------------------ 3.53/0.94 % (15797)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.53/0.94 % (15797)Termination reason: Unknown 3.53/0.94 % (15797)Termination phase: Property scanning 3.53/0.94 3.53/0.94 % (15797)Memory used [KB]: 1918 3.53/0.94 % (15797)Time elapsed: 0.073 s 3.53/0.94 % (15797)Instructions burned: 339 (million) 3.53/0.94 % (15797)------------------------------ 3.53/0.94 % (15797)------------------------------ 3.53/0.94 % (15791)Instruction limit reached! 3.53/0.94 % (15791)------------------------------ 3.53/0.94 % (15791)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.53/0.94 % (15791)Termination reason: Unknown 3.53/0.94 % (15791)Termination phase: Saturation 3.53/0.94 3.53/0.94 % (15791)Memory used [KB]: 7164 3.53/0.94 % (15791)Time elapsed: 0.114 s 3.53/0.94 % (15791)Instructions burned: 345 (million) 3.53/0.94 % (15791)------------------------------ 3.53/0.94 % (15791)------------------------------ 3.53/0.95 % (15804)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 E---3.1_15619 for (1794ds/231Mi) 3.53/0.95 % (15800)Instruction limit reached! 3.53/0.95 % (15800)------------------------------ 3.53/0.95 % (15800)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.53/0.95 % (15800)Termination reason: Unknown 3.53/0.95 % (15800)Termination phase: Property scanning 3.53/0.95 3.53/0.95 % (15800)Memory used [KB]: 2046 3.53/0.95 % (15800)Time elapsed: 0.061 s 3.53/0.95 % (15800)Instructions burned: 301 (million) 3.53/0.95 % (15800)------------------------------ 3.53/0.95 % (15800)------------------------------ 3.53/0.95 % (15801)Instruction limit reached! 3.53/0.95 % (15801)------------------------------ 3.53/0.95 % (15801)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.53/0.95 % (15801)Termination reason: Unknown 3.53/0.95 % (15801)Termination phase: Function definition elimination 3.53/0.95 3.53/0.95 % (15801)Memory used [KB]: 1918 3.53/0.95 % (15801)Time elapsed: 0.041 s 3.53/0.95 % (15801)Instructions burned: 192 (million) 3.53/0.95 % (15801)------------------------------ 3.53/0.95 % (15801)------------------------------ 3.53/0.95 % (15805)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on E---3.1_15619 for (1794ds/458Mi) 3.53/0.96 % (15803)Instruction limit reached! 3.53/0.96 % (15803)------------------------------ 3.53/0.96 % (15803)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.53/0.96 % (15803)Termination reason: Unknown 3.53/0.96 % (15803)Termination phase: Function definition elimination 3.53/0.96 3.53/0.96 % (15803)Memory used [KB]: 1791 3.53/0.96 % (15803)Time elapsed: 0.022 s 3.53/0.96 % (15803)Instructions burned: 92 (million) 3.53/0.96 % (15803)------------------------------ 3.53/0.96 % (15803)------------------------------ 3.53/0.96 % (15806)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on E---3.1_15619 for (1794ds/31Mi) 3.53/0.96 % (15807)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 E---3.1_15619 for (1794ds/297Mi) 3.53/0.96 % (15808)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on E---3.1_15619 for (1794ds/987Mi) 3.53/0.97 % (15806)Instruction limit reached! 3.53/0.97 % (15806)------------------------------ 3.53/0.97 % (15806)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.53/0.97 % (15806)Termination reason: Unknown 3.53/0.97 % (15806)Termination phase: Clausification 3.53/0.97 3.53/0.97 % (15806)Memory used [KB]: 1663 3.53/0.97 % (15806)Time elapsed: 0.010 s 3.53/0.97 % (15806)Instructions burned: 33 (million) 3.53/0.97 % (15806)------------------------------ 3.53/0.97 % (15806)------------------------------ 3.89/0.97 % (15809)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 E---3.1_15619 for (1794ds/182Mi) 3.89/0.99 % (15802)Instruction limit reached! 3.89/0.99 % (15802)------------------------------ 3.89/0.99 % (15802)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.89/0.99 % (15802)Termination reason: Unknown 3.89/0.99 % (15802)Termination phase: Property scanning 3.89/0.99 3.89/0.99 % (15802)Memory used [KB]: 1918 3.89/0.99 % (15802)Time elapsed: 0.058 s 3.89/0.99 % (15802)Instructions burned: 259 (million) 3.89/0.99 % (15802)------------------------------ 3.89/0.99 % (15802)------------------------------ 3.89/0.99 % (15795)Instruction limit reached! 3.89/0.99 % (15795)------------------------------ 3.89/0.99 % (15795)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.89/0.99 % (15795)Termination reason: Unknown 3.89/0.99 % (15795)Termination phase: Property scanning 3.89/0.99 3.89/0.99 % (15795)Memory used [KB]: 1918 3.89/0.99 % (15795)Time elapsed: 0.142 s 3.89/0.99 % (15795)Instructions burned: 616 (million) 3.89/0.99 % (15795)------------------------------ 3.89/0.99 % (15795)------------------------------ 3.89/0.99 % (15804)Instruction limit reached! 3.89/0.99 % (15804)------------------------------ 3.89/0.99 % (15804)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.89/0.99 % (15804)Termination reason: Unknown 3.89/0.99 % (15804)Termination phase: Function definition elimination 3.89/0.99 3.89/0.99 % (15804)Memory used [KB]: 1918 3.89/0.99 % (15804)Time elapsed: 0.047 s 3.89/0.99 % (15804)Instructions burned: 231 (million) 3.89/0.99 % (15804)------------------------------ 3.89/0.99 % (15804)------------------------------ 3.89/0.99 % (15810)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 E---3.1_15619 for (1794ds/182Mi) 3.89/1.00 % (15811)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 E---3.1_15619 for (1794ds/154Mi) 3.89/1.00 % (15812)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on E---3.1_15619 for (1794ds/79Mi) 3.89/1.01 % (15809)Instruction limit reached! 3.89/1.01 % (15809)------------------------------ 3.89/1.01 % (15809)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.89/1.01 % (15809)Termination reason: Unknown 3.89/1.01 % (15809)Termination phase: Function definition elimination 3.89/1.01 3.89/1.01 % (15809)Memory used [KB]: 1918 3.89/1.01 % (15809)Time elapsed: 0.040 s 3.89/1.01 % (15809)Instructions burned: 187 (million) 3.89/1.01 % (15809)------------------------------ 3.89/1.01 % (15809)------------------------------ 3.89/1.02 % (15812)Instruction limit reached! 3.89/1.02 % (15812)------------------------------ 3.89/1.02 % (15812)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.89/1.02 % (15812)Termination reason: Unknown 3.89/1.02 % (15812)Termination phase: Function definition elimination 3.89/1.02 3.89/1.02 % (15812)Memory used [KB]: 1791 3.89/1.02 % (15812)Time elapsed: 0.020 s 3.89/1.02 % (15812)Instructions burned: 79 (million) 3.89/1.02 % (15812)------------------------------ 3.89/1.02 % (15812)------------------------------ 3.89/1.02 % (15813)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on E---3.1_15619 for (1793ds/216Mi) 3.89/1.03 % (15814)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on E---3.1_15619 for (1793ds/114Mi) 4.23/1.03 % (15811)Instruction limit reached! 4.23/1.03 % (15811)------------------------------ 4.23/1.03 % (15811)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 4.23/1.03 % (15811)Termination reason: Unknown 4.23/1.03 % (15811)Termination phase: Function definition elimination 4.23/1.03 4.23/1.03 % (15811)Memory used [KB]: 1918 4.23/1.03 % (15811)Time elapsed: 0.034 s 4.23/1.03 % (15811)Instructions burned: 159 (million) 4.23/1.03 % (15811)------------------------------ 4.23/1.03 % (15811)------------------------------ 4.23/1.04 % (15815)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on E---3.1_15619 for (1793ds/922Mi) 4.23/1.05 % (15805)Instruction limit reached! 4.23/1.05 % (15805)------------------------------ 4.23/1.05 % (15805)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 4.23/1.05 % (15805)Termination reason: Unknown 4.23/1.05 % (15805)Termination phase: Property scanning 4.23/1.05 4.23/1.05 % (15805)Memory used [KB]: 2046 4.23/1.05 % (15805)Time elapsed: 0.098 s 4.23/1.05 % (15805)Instructions burned: 459 (million) 4.23/1.05 % (15805)------------------------------ 4.23/1.05 % (15805)------------------------------ 4.23/1.05 % (15807)Instruction limit reached! 4.23/1.05 % (15807)------------------------------ 4.23/1.05 % (15807)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 4.23/1.05 % (15807)Termination reason: Unknown 4.23/1.05 % (15807)Termination phase: Saturation 4.23/1.05 4.23/1.05 % (15807)Memory used [KB]: 7164 4.23/1.05 % (15807)Time elapsed: 0.093 s 4.23/1.05 % (15807)Instructions burned: 299 (million) 4.23/1.05 % (15807)------------------------------ 4.23/1.05 % (15807)------------------------------ 4.23/1.05 % (15810)Instruction limit reached! 4.23/1.05 % (15810)------------------------------ 4.23/1.05 % (15810)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 4.23/1.05 % (15810)Termination reason: Unknown 4.23/1.05 % (15810)Termination phase: Saturation 4.23/1.05 4.23/1.05 % (15810)Memory used [KB]: 6652 4.23/1.05 % (15810)Time elapsed: 0.059 s 4.23/1.05 % (15810)Instructions burned: 183 (million) 4.23/1.05 % (15810)------------------------------ 4.23/1.05 % (15810)------------------------------ 4.23/1.05 % (15814)Instruction limit reached! 4.23/1.05 % (15814)------------------------------ 4.23/1.05 % (15814)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 4.23/1.06 % (15814)Termination reason: Unknown 4.23/1.06 % (15814)Termination phase: Function definition elimination 4.23/1.06 4.23/1.06 % (15814)Memory used [KB]: 1791 4.23/1.06 % (15814)Time elapsed: 0.027 s 4.23/1.06 % (15814)Instructions burned: 119 (million) 4.23/1.06 % (15814)------------------------------ 4.23/1.06 % (15814)------------------------------ 4.23/1.06 % (15816)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 E---3.1_15619 for (1793ds/182Mi) 4.23/1.06 % (15818)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on E---3.1_15619 for (1793ds/50Mi) 4.23/1.06 % (15819)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on E---3.1_15619 for (1793ds/368Mi) 4.79/1.07 % (15817)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 E---3.1_15619 for (1793ds/164Mi) 4.79/1.07 % (15818)Instruction limit reached! 4.79/1.07 % (15818)------------------------------ 4.79/1.07 % (15818)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 4.79/1.07 % (15818)Termination reason: Unknown 4.79/1.07 % (15818)Termination phase: Function definition elimination 4.79/1.07 4.79/1.07 % (15818)Memory used [KB]: 1663 4.79/1.07 % (15818)Time elapsed: 0.014 s 4.79/1.07 % (15818)Instructions burned: 52 (million) 4.79/1.07 % (15818)------------------------------ 4.79/1.07 % (15818)------------------------------ 4.79/1.08 % (15820)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 E---3.1_15619 for (1793ds/1021Mi) 4.79/1.09 % (15813)Instruction limit reached! 4.79/1.09 % (15813)------------------------------ 4.79/1.09 % (15813)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 4.79/1.09 % (15813)Termination reason: Unknown 4.79/1.09 % (15813)Termination phase: Saturation 4.79/1.09 4.79/1.09 % (15813)Memory used [KB]: 7036 4.79/1.09 % (15813)Time elapsed: 0.066 s 4.79/1.09 % (15813)Instructions burned: 218 (million) 4.79/1.09 % (15813)------------------------------ 4.79/1.09 % (15813)------------------------------ 4.79/1.09 % (15816)Instruction limit reached! 4.79/1.09 % (15816)------------------------------ 4.79/1.09 % (15816)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 4.79/1.09 % (15816)Termination reason: Unknown 4.79/1.09 % (15816)Termination phase: Function definition elimination 4.79/1.09 4.79/1.09 % (15816)Memory used [KB]: 1918 4.79/1.09 % (15816)Time elapsed: 0.038 s 4.79/1.09 % (15816)Instructions burned: 182 (million) 4.79/1.09 % (15816)------------------------------ 4.79/1.09 % (15816)------------------------------ 4.79/1.10 % (15821)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on E---3.1_15619 for (1793ds/267Mi) 4.79/1.10 % (15822)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 E---3.1_15619 for (1793ds/204Mi) 4.79/1.12 % (15817)Instruction limit reached! 4.79/1.12 % (15817)------------------------------ 4.79/1.12 % (15817)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 4.79/1.12 % (15817)Termination reason: Unknown 4.79/1.12 % (15817)Termination phase: Saturation 4.79/1.12 4.79/1.12 % (15817)Memory used [KB]: 2046 4.79/1.12 % (15817)Time elapsed: 0.072 s 4.79/1.12 % (15817)Instructions burned: 166 (million) 4.79/1.12 % (15817)------------------------------ 4.79/1.12 % (15817)------------------------------ 4.79/1.13 % (15823)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on E---3.1_15619 for (1792ds/26Mi) 5.11/1.14 % (15823)Instruction limit reached! 5.11/1.14 % (15823)------------------------------ 5.11/1.14 % (15823)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 5.11/1.14 % (15823)Termination reason: Unknown 5.11/1.14 % (15823)Termination phase: Property scanning 5.11/1.14 5.11/1.14 % (15823)Memory used [KB]: 1663 5.11/1.14 % (15823)Time elapsed: 0.009 s 5.11/1.14 % (15823)Instructions burned: 29 (million) 5.11/1.14 % (15823)------------------------------ 5.11/1.14 % (15823)------------------------------ 5.11/1.14 % (15819)Instruction limit reached! 5.11/1.14 % (15819)------------------------------ 5.11/1.14 % (15819)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 5.11/1.14 % (15819)Termination reason: Unknown 5.11/1.14 % (15819)Termination phase: Property scanning 5.11/1.14 5.11/1.14 % (15819)Memory used [KB]: 1918 5.11/1.14 % (15819)Time elapsed: 0.077 s 5.11/1.14 % (15819)Instructions burned: 370 (million) 5.11/1.14 % (15819)------------------------------ 5.11/1.14 % (15819)------------------------------ 5.11/1.15 % (15822)Instruction limit reached! 5.11/1.15 % (15822)------------------------------ 5.11/1.15 % (15822)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 5.11/1.15 % (15822)Termination reason: Unknown 5.11/1.15 % (15822)Termination phase: Function definition elimination 5.11/1.15 5.11/1.15 % (15822)Memory used [KB]: 1918 5.11/1.15 % (15822)Time elapsed: 0.044 s 5.11/1.15 % (15822)Instructions burned: 206 (million) 5.11/1.15 % (15822)------------------------------ 5.11/1.15 % (15822)------------------------------ 5.11/1.15 % (15824)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on E---3.1_15619 for (1792ds/53Mi) 5.11/1.15 % (15825)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on E---3.1_15619 for (1792ds/4436Mi) 5.11/1.15 % (15821)Instruction limit reached! 5.11/1.15 % (15821)------------------------------ 5.11/1.15 % (15821)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 5.11/1.15 % (15821)Termination reason: Unknown 5.11/1.15 % (15821)Termination phase: Function definition elimination 5.11/1.15 5.11/1.15 % (15821)Memory used [KB]: 1918 5.11/1.15 % (15821)Time elapsed: 0.054 s 5.11/1.15 % (15821)Instructions burned: 269 (million) 5.11/1.15 % (15821)------------------------------ 5.11/1.15 % (15821)------------------------------ 5.11/1.15 % (15826)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on E---3.1_15619 for (1792ds/1539Mi) 5.11/1.16 % (15827)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on E---3.1_15619 for (1792ds/408Mi) 5.11/1.16 % (15824)Instruction limit reached! 5.11/1.16 % (15824)------------------------------ 5.11/1.16 % (15824)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 5.11/1.16 % (15824)Termination reason: Unknown 5.11/1.16 % (15824)Termination phase: Function definition elimination 5.11/1.16 5.11/1.16 % (15824)Memory used [KB]: 1918 5.11/1.16 % (15824)Time elapsed: 0.015 s 5.11/1.16 % (15824)Instructions burned: 57 (million) 5.11/1.16 % (15824)------------------------------ 5.11/1.16 % (15824)------------------------------ 5.11/1.17 % (15825)Refutation not found, incomplete strategy 5.11/1.17 % (15825)------------------------------ 5.11/1.17 % (15825)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 5.11/1.17 % (15825)Termination reason: Refutation not found, incomplete strategy 5.11/1.17 5.11/1.17 5.11/1.17 % (15825)Memory used [KB]: 6268 5.11/1.17 % (15825)Time elapsed: 0.021 s 5.11/1.17 % (15825)Instructions burned: 67 (million) 5.11/1.17 % (15825)------------------------------ 5.11/1.17 % (15825)------------------------------ 5.11/1.17 % (15828)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on E---3.1_15619 for (1792ds/5205Mi) 5.38/1.18 % (15829)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on E---3.1_15619 for (1792ds/1913Mi) 5.38/1.18 % (15808)Instruction limit reached! 5.38/1.18 % (15808)------------------------------ 5.38/1.18 % (15808)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 5.38/1.18 % (15808)Termination reason: Unknown 5.38/1.18 % (15808)Termination phase: Property scanning 5.38/1.18 5.38/1.18 % (15808)Memory used [KB]: 2046 5.38/1.18 % (15808)Time elapsed: 0.216 s 5.38/1.18 % (15808)Instructions burned: 988 (million) 5.38/1.18 % (15808)------------------------------ 5.38/1.18 % (15808)------------------------------ 5.38/1.19 % (15830)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 E---3.1_15619 for (1792ds/4350Mi) 5.46/1.25 % (15815)Instruction limit reached! 5.46/1.25 % (15815)------------------------------ 5.46/1.25 % (15815)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 5.46/1.25 % (15815)Termination reason: Unknown 5.46/1.25 % (15815)Termination phase: Property scanning 5.46/1.25 5.46/1.25 % (15815)Memory used [KB]: 1918 5.46/1.25 % (15815)Time elapsed: 0.205 s 5.46/1.25 % (15815)Instructions burned: 922 (million) 5.46/1.25 % (15815)------------------------------ 5.46/1.25 % (15815)------------------------------ 5.46/1.26 % (15831)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on E---3.1_15619 for (1791ds/68Mi) 5.48/1.27 % (15827)Instruction limit reached! 5.48/1.27 % (15827)------------------------------ 5.48/1.27 % (15827)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 5.48/1.27 % (15827)Termination reason: Unknown 5.48/1.27 % (15827)Termination phase: Saturation 5.48/1.27 5.48/1.27 % (15827)Memory used [KB]: 7291 5.48/1.27 % (15827)Time elapsed: 0.115 s 5.48/1.27 % (15827)Instructions burned: 408 (million) 5.48/1.27 % (15827)------------------------------ 5.48/1.27 % (15827)------------------------------ 5.48/1.27 % (15831)Instruction limit reached! 5.48/1.27 % (15831)------------------------------ 5.48/1.27 % (15831)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 5.48/1.27 % (15831)Termination reason: Unknown 5.48/1.27 % (15831)Termination phase: Function definition elimination 5.48/1.27 5.48/1.27 % (15831)Memory used [KB]: 1791 5.48/1.27 % (15831)Time elapsed: 0.019 s 5.48/1.27 % (15831)Instructions burned: 70 (million) 5.48/1.27 % (15831)------------------------------ 5.48/1.27 % (15831)------------------------------ 5.48/1.28 % (15832)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 E---3.1_15619 for (1791ds/358Mi) 5.48/1.28 % (15833)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on E---3.1_15619 for (1791ds/31Mi) 5.48/1.29 % (15833)Instruction limit reached! 5.48/1.29 % (15833)------------------------------ 5.48/1.29 % (15833)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 5.48/1.29 % (15833)Termination reason: Unknown 5.48/1.29 % (15833)Termination phase: Preprocessing 3 5.48/1.29 5.48/1.29 % (15833)Memory used [KB]: 1663 5.48/1.29 % (15833)Time elapsed: 0.010 s 5.48/1.29 % (15833)Instructions burned: 32 (million) 5.48/1.29 % (15833)------------------------------ 5.48/1.29 % (15833)------------------------------ 5.48/1.30 % (15834)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on E---3.1_15619 for (1791ds/279Mi) 5.48/1.31 % (15820)Instruction limit reached! 5.48/1.31 % (15820)------------------------------ 5.48/1.31 % (15820)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 5.48/1.31 % (15820)Termination reason: Unknown 5.48/1.31 % (15820)Termination phase: Property scanning 5.48/1.31 5.48/1.31 % (15820)Memory used [KB]: 2046 5.48/1.31 % (15820)Time elapsed: 0.233 s 5.48/1.31 % (15820)Instructions burned: 1023 (million) 5.48/1.31 % (15820)------------------------------ 5.48/1.31 % (15820)------------------------------ 5.88/1.32 % (15835)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on E---3.1_15619 for (1790ds/258Mi) 5.88/1.37 % (15832)Instruction limit reached! 5.88/1.37 % (15832)------------------------------ 5.88/1.37 % (15832)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 5.88/1.37 % (15832)Termination reason: Unknown 5.88/1.37 % (15832)Termination phase: Saturation 5.88/1.37 5.88/1.37 % (15832)Memory used [KB]: 6524 5.88/1.37 % (15832)Time elapsed: 0.088 s 5.88/1.37 % (15832)Instructions burned: 358 (million) 5.88/1.37 % (15832)------------------------------ 5.88/1.37 % (15832)------------------------------ 5.88/1.38 % (15836)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on E---3.1_15619 for (1790ds/26Mi) 5.88/1.38 % (15836)Instruction limit reached! 5.88/1.38 % (15836)------------------------------ 5.88/1.38 % (15836)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 5.88/1.38 % (15836)Termination reason: Unknown 5.88/1.38 % (15836)Termination phase: Property scanning 5.88/1.38 5.88/1.38 % (15836)Memory used [KB]: 1663 5.88/1.38 % (15836)Time elapsed: 0.008 s 5.88/1.38 % (15836)Instructions burned: 26 (million) 5.88/1.38 % (15836)------------------------------ 5.88/1.38 % (15836)------------------------------ 5.88/1.38 % (15834)Instruction limit reached! 5.88/1.38 % (15834)------------------------------ 5.88/1.38 % (15834)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 5.88/1.38 % (15834)Termination reason: Unknown 5.88/1.38 % (15834)Termination phase: Saturation 5.88/1.38 5.88/1.38 % (15834)Memory used [KB]: 7036 5.88/1.38 % (15834)Time elapsed: 0.084 s 5.88/1.38 % (15834)Instructions burned: 280 (million) 5.88/1.38 % (15834)------------------------------ 5.88/1.38 % (15834)------------------------------ 5.88/1.39 % (15837)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on E---3.1_15619 for (1790ds/995Mi) 5.88/1.39 % (15838)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on E---3.1_15619 for (1790ds/373Mi) 5.88/1.40 % (15835)Instruction limit reached! 5.88/1.40 % (15835)------------------------------ 5.88/1.40 % (15835)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 5.88/1.40 % (15835)Termination reason: Unknown 5.88/1.40 % (15835)Termination phase: Saturation 5.88/1.40 5.88/1.40 % (15835)Memory used [KB]: 7164 5.88/1.40 % (15835)Time elapsed: 0.081 s 5.88/1.40 % (15835)Instructions burned: 259 (million) 5.88/1.40 % (15835)------------------------------ 5.88/1.40 % (15835)------------------------------ 5.88/1.41 % (15839)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on E---3.1_15619 for (1789ds/253Mi) 6.17/1.46 % (15839)Instruction limit reached! 6.17/1.46 % (15839)------------------------------ 6.17/1.46 % (15839)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 6.17/1.46 % (15839)Termination reason: Unknown 6.17/1.46 % (15839)Termination phase: Function definition elimination 6.17/1.46 6.17/1.46 % (15839)Memory used [KB]: 1918 6.17/1.46 % (15839)Time elapsed: 0.052 s 6.17/1.46 % (15839)Instructions burned: 254 (million) 6.17/1.46 % (15839)------------------------------ 6.17/1.46 % (15839)------------------------------ 6.17/1.47 % (15838)Instruction limit reached! 6.17/1.47 % (15838)------------------------------ 6.17/1.47 % (15838)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 6.17/1.47 % (15838)Termination reason: Unknown 6.17/1.47 % (15838)Termination phase: Property scanning 6.17/1.47 6.17/1.47 % (15838)Memory used [KB]: 1918 6.17/1.47 % (15838)Time elapsed: 0.079 s 6.17/1.47 % (15838)Instructions burned: 376 (million) 6.17/1.47 % (15838)------------------------------ 6.17/1.47 % (15838)------------------------------ 6.17/1.47 % (15840)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on E---3.1_15619 for (1789ds/832Mi) 6.32/1.48 % (15841)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 E---3.1_15619 for (1789ds/668Mi) 6.32/1.49 % (15840)Refutation not found, incomplete strategy 6.32/1.49 % (15840)------------------------------ 6.32/1.49 % (15840)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 6.32/1.49 % (15840)Termination reason: Refutation not found, incomplete strategy 6.32/1.49 6.32/1.49 6.32/1.49 % (15840)Memory used [KB]: 6396 6.32/1.49 % (15840)Time elapsed: 0.020 s 6.32/1.49 % (15840)Instructions burned: 65 (million) 6.32/1.49 % (15840)------------------------------ 6.32/1.49 % (15840)------------------------------ 6.32/1.50 % (15842)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on E---3.1_15619 for (1789ds/40Mi) 6.32/1.50 % (15826)Instruction limit reached! 6.32/1.50 % (15826)------------------------------ 6.32/1.50 % (15826)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 6.32/1.50 % (15826)Termination reason: Unknown 6.32/1.50 % (15826)Termination phase: Property scanning 6.32/1.50 6.32/1.50 % (15826)Memory used [KB]: 1918 6.32/1.50 % (15826)Time elapsed: 0.351 s 6.32/1.50 % (15826)Instructions burned: 1541 (million) 6.32/1.50 % (15826)------------------------------ 6.32/1.50 % (15826)------------------------------ 6.32/1.51 % (15842)Instruction limit reached! 6.32/1.51 % (15842)------------------------------ 6.32/1.51 % (15842)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 6.32/1.51 % (15842)Termination reason: Unknown 6.32/1.51 % (15842)Termination phase: Property scanning 6.32/1.51 6.32/1.51 % (15842)Memory used [KB]: 1663 6.32/1.51 % (15842)Time elapsed: 0.012 s 6.32/1.51 % (15842)Instructions burned: 43 (million) 6.32/1.51 % (15842)------------------------------ 6.32/1.51 % (15842)------------------------------ 6.32/1.51 % (15843)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 E---3.1_15619 for (1788ds/294Mi) 6.32/1.52 % (15844)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 E---3.1_15619 for (1788ds/187Mi) 6.72/1.56 % (15844)Instruction limit reached! 6.72/1.56 % (15844)------------------------------ 6.72/1.56 % (15844)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 6.72/1.56 % (15844)Termination reason: Unknown 6.72/1.56 % (15844)Termination phase: Function definition elimination 6.72/1.56 6.72/1.56 % (15844)Memory used [KB]: 1918 6.72/1.56 % (15844)Time elapsed: 0.040 s 6.72/1.56 % (15844)Instructions burned: 188 (million) 6.72/1.56 % (15844)------------------------------ 6.72/1.56 % (15844)------------------------------ 6.72/1.57 % (15845)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on E---3.1_15619 for (1788ds/371Mi) 6.72/1.60 % (15843)Instruction limit reached! 6.72/1.60 % (15843)------------------------------ 6.72/1.60 % (15843)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 6.72/1.60 % (15843)Termination reason: Unknown 6.72/1.60 % (15843)Termination phase: Saturation 6.72/1.60 6.72/1.60 % (15843)Memory used [KB]: 6780 6.72/1.60 % (15843)Time elapsed: 0.086 s 6.72/1.60 % (15843)Instructions burned: 296 (million) 6.72/1.60 % (15843)------------------------------ 6.72/1.60 % (15843)------------------------------ 6.72/1.61 % (15846)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on E---3.1_15619 for (1788ds/1827Mi) 6.72/1.62 % (15837)Instruction limit reached! 6.72/1.62 % (15837)------------------------------ 6.72/1.62 % (15837)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 6.72/1.62 % (15837)Termination reason: Unknown 6.72/1.62 % (15837)Termination phase: Property scanning 6.72/1.62 6.72/1.62 % (15837)Memory used [KB]: 2046 6.72/1.62 % (15837)Time elapsed: 0.230 s 6.72/1.62 % (15837)Instructions burned: 996 (million) 6.72/1.62 % (15837)------------------------------ 6.72/1.62 % (15837)------------------------------ 6.72/1.62 % (15841)Instruction limit reached! 6.72/1.62 % (15841)------------------------------ 6.72/1.62 % (15841)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 6.72/1.62 % (15841)Termination reason: Unknown 6.72/1.62 % (15841)Termination phase: Property scanning 6.72/1.62 6.72/1.62 % (15841)Memory used [KB]: 2046 6.72/1.62 % (15841)Time elapsed: 0.147 s 6.72/1.62 % (15841)Instructions burned: 669 (million) 6.72/1.62 % (15841)------------------------------ 6.72/1.62 % (15841)------------------------------ 6.72/1.63 % (15847)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 E---3.1_15619 for (1787ds/70Mi) 8.68/1.63 % (15848)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on E---3.1_15619 for (1787ds/316Mi) 8.68/1.64 % (15847)Instruction limit reached! 8.68/1.64 % (15847)------------------------------ 8.68/1.64 % (15847)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 8.68/1.64 % (15847)Termination reason: Unknown 8.68/1.64 % (15847)Termination phase: Function definition elimination 8.68/1.64 8.68/1.64 % (15847)Memory used [KB]: 1918 8.68/1.64 % (15847)Time elapsed: 0.018 s 8.68/1.64 % (15847)Instructions burned: 71 (million) 8.68/1.64 % (15847)------------------------------ 8.68/1.64 % (15847)------------------------------ 8.68/1.65 % (15849)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 E---3.1_15619 for (1787ds/932Mi) 8.90/1.68 % (15845)Instruction limit reached! 8.90/1.68 % (15845)------------------------------ 8.90/1.68 % (15845)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 8.90/1.68 % (15845)Termination reason: Unknown 8.90/1.68 % (15845)Termination phase: Saturation 8.90/1.68 8.90/1.68 % (15845)Memory used [KB]: 7164 8.90/1.68 % (15845)Time elapsed: 0.113 s 8.90/1.68 % (15845)Instructions burned: 373 (million) 8.90/1.68 % (15845)------------------------------ 8.90/1.68 % (15845)------------------------------ 8.90/1.69 % (15850)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on E---3.1_15619 for (1787ds/4714Mi) 8.90/1.70 % (15848)Instruction limit reached! 8.90/1.70 % (15848)------------------------------ 8.90/1.70 % (15848)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 8.90/1.70 % (15848)Termination reason: Unknown 8.90/1.70 % (15848)Termination phase: Property scanning 8.90/1.70 8.90/1.70 % (15848)Memory used [KB]: 2046 8.90/1.70 % (15848)Time elapsed: 0.065 s 8.90/1.70 % (15848)Instructions burned: 316 (million) 8.90/1.70 % (15848)------------------------------ 8.90/1.70 % (15848)------------------------------ 8.90/1.70 % (15851)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 E---3.1_15619 for (1787ds/8250Mi) 9.42/1.79 % (15829)Instruction limit reached! 9.42/1.79 % (15829)------------------------------ 9.42/1.79 % (15829)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 9.42/1.79 % (15829)Termination reason: Unknown 9.42/1.79 % (15829)Termination phase: Saturation 9.42/1.79 9.42/1.79 % (15829)Memory used [KB]: 3965 9.42/1.79 % (15829)Time elapsed: 0.618 s 9.42/1.79 % (15829)Instructions burned: 1915 (million) 9.42/1.79 % (15829)------------------------------ 9.42/1.79 % (15829)------------------------------ 9.42/1.80 % (15852)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on E---3.1_15619 for (1786ds/770Mi) 9.42/1.82 % (15852)Refutation not found, incomplete strategy 9.42/1.82 % (15852)------------------------------ 9.42/1.82 % (15852)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 9.42/1.82 % (15852)Termination reason: Refutation not found, incomplete strategy 9.42/1.82 9.42/1.82 9.42/1.82 % (15852)Memory used [KB]: 6268 9.42/1.82 % (15852)Time elapsed: 0.014 s 9.42/1.82 % (15852)Instructions burned: 41 (million) 9.42/1.82 % (15852)------------------------------ 9.42/1.82 % (15852)------------------------------ 9.61/1.83 % (15853)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on E---3.1_15619 for (1785ds/794Mi) 9.67/1.86 % (15849)Instruction limit reached! 9.67/1.86 % (15849)------------------------------ 9.67/1.86 % (15849)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 9.67/1.86 % (15849)Termination reason: Unknown 9.67/1.86 % (15849)Termination phase: Property scanning 9.67/1.86 9.67/1.86 % (15849)Memory used [KB]: 2046 9.67/1.86 % (15849)Time elapsed: 0.205 s 9.67/1.86 % (15849)Instructions burned: 934 (million) 9.67/1.86 % (15849)------------------------------ 9.67/1.86 % (15849)------------------------------ 9.67/1.87 % (15854)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on E---3.1_15619 for (1785ds/464Mi) 10.11/1.97 % (15854)Instruction limit reached! 10.11/1.97 % (15854)------------------------------ 10.11/1.97 % (15854)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 10.11/1.97 % (15854)Termination reason: Unknown 10.11/1.97 % (15854)Termination phase: Property scanning 10.11/1.97 10.11/1.97 % (15854)Memory used [KB]: 1918 10.11/1.97 % (15854)Time elapsed: 0.103 s 10.11/1.97 % (15854)Instructions burned: 464 (million) 10.11/1.97 % (15854)------------------------------ 10.11/1.97 % (15854)------------------------------ 10.36/1.98 % (15855)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on E---3.1_15619 for (1784ds/1376Mi) 10.36/2.00 % (15853)Instruction limit reached! 10.36/2.00 % (15853)------------------------------ 10.36/2.00 % (15853)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 10.36/2.00 % (15853)Termination reason: Unknown 10.36/2.00 % (15853)Termination phase: Property scanning 10.36/2.00 10.36/2.00 % (15853)Memory used [KB]: 2046 10.36/2.00 % (15853)Time elapsed: 0.176 s 10.36/2.00 % (15853)Instructions burned: 796 (million) 10.36/2.00 % (15853)------------------------------ 10.36/2.00 % (15853)------------------------------ 10.36/2.01 % (15856)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on E---3.1_15619 for (1784ds/906Mi) 12.35/2.17 % (15846)Instruction limit reached! 12.35/2.17 % (15846)------------------------------ 12.35/2.17 % (15846)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 12.35/2.17 % (15846)Termination reason: Unknown 12.35/2.17 % (15846)Termination phase: Saturation 12.35/2.17 12.35/2.17 % (15846)Memory used [KB]: 9850 12.35/2.17 % (15846)Time elapsed: 0.569 s 12.35/2.17 % (15846)Instructions burned: 1828 (million) 12.35/2.17 % (15846)------------------------------ 12.35/2.17 % (15846)------------------------------ 12.35/2.18 % (15857)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 E---3.1_15619 for (1782ds/434Mi) 12.35/2.21 % (15856)Instruction limit reached! 12.35/2.21 % (15856)------------------------------ 12.35/2.21 % (15856)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 12.35/2.21 % (15856)Termination reason: Unknown 12.35/2.21 % (15856)Termination phase: Property scanning 12.35/2.21 12.35/2.21 % (15856)Memory used [KB]: 1918 12.35/2.21 % (15856)Time elapsed: 0.203 s 12.35/2.21 % (15856)Instructions burned: 907 (million) 12.35/2.21 % (15856)------------------------------ 12.35/2.21 % (15856)------------------------------ 12.35/2.22 % (15858)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on E---3.1_15619 for (1781ds/865Mi) 13.07/2.28 % (15855)Instruction limit reached! 13.07/2.28 % (15855)------------------------------ 13.07/2.28 % (15855)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 13.07/2.28 % (15855)Termination reason: Unknown 13.07/2.28 % (15855)Termination phase: Property scanning 13.07/2.28 13.07/2.28 % (15855)Memory used [KB]: 2046 13.07/2.28 % (15855)Time elapsed: 0.307 s 13.07/2.28 % (15855)Instructions burned: 1377 (million) 13.07/2.28 % (15855)------------------------------ 13.07/2.28 % (15855)------------------------------ 13.07/2.29 % (15859)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on E---3.1_15619 for (1781ds/593Mi) 13.07/2.33 % (15857)Instruction limit reached! 13.07/2.33 % (15857)------------------------------ 13.07/2.33 % (15857)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 13.07/2.33 % (15857)Termination reason: Unknown 13.07/2.33 % (15857)Termination phase: Saturation 13.07/2.33 13.07/2.33 % (15857)Memory used [KB]: 7675 13.07/2.33 % (15857)Time elapsed: 0.148 s 13.07/2.33 % (15857)Instructions burned: 434 (million) 13.07/2.33 % (15857)------------------------------ 13.07/2.33 % (15857)------------------------------ 13.07/2.34 % (15860)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on E---3.1_15619 for (1780ds/443Mi) 13.76/2.42 % (15859)Instruction limit reached! 13.76/2.42 % (15859)------------------------------ 13.76/2.42 % (15859)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 13.76/2.42 % (15859)Termination reason: Unknown 13.76/2.42 % (15859)Termination phase: Property scanning 13.76/2.42 13.76/2.42 % (15859)Memory used [KB]: 2046 13.76/2.42 % (15859)Time elapsed: 0.131 s 13.76/2.42 % (15859)Instructions burned: 593 (million) 13.76/2.42 % (15859)------------------------------ 13.76/2.42 % (15859)------------------------------ 13.76/2.42 % (15828)Instruction limit reached! 13.76/2.42 % (15828)------------------------------ 13.76/2.42 % (15828)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 13.76/2.42 % (15828)Termination reason: Unknown 13.76/2.42 % (15828)Termination phase: Saturation 13.76/2.42 13.76/2.42 % (15828)Memory used [KB]: 6908 13.76/2.42 % (15828)Time elapsed: 1.231 s 13.76/2.42 % (15828)Instructions burned: 5206 (million) 13.76/2.42 % (15828)------------------------------ 13.76/2.42 % (15828)------------------------------ 13.76/2.43 % (15861)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on E---3.1_15619 for (1779ds/594Mi) 13.76/2.43 % (15862)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on E---3.1_15619 for (1779ds/327Mi) 14.02/2.45 % (15860)Instruction limit reached! 14.02/2.45 % (15860)------------------------------ 14.02/2.45 % (15860)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 14.02/2.45 % (15860)Termination reason: Unknown 14.02/2.45 % (15860)Termination phase: Saturation 14.02/2.45 14.02/2.45 % (15860)Memory used [KB]: 6524 14.02/2.45 % (15860)Time elapsed: 0.109 s 14.02/2.45 % (15860)Instructions burned: 444 (million) 14.02/2.45 % (15860)------------------------------ 14.02/2.45 % (15860)------------------------------ 14.02/2.46 % (15863)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on E---3.1_15619 for (1779ds/5411Mi) 14.02/2.47 % (15863)Refutation not found, incomplete strategy 14.02/2.47 % (15863)------------------------------ 14.02/2.47 % (15863)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 14.02/2.47 % (15863)Termination reason: Refutation not found, incomplete strategy 14.02/2.47 14.02/2.47 14.02/2.47 % (15863)Memory used [KB]: 6140 14.02/2.47 % (15863)Time elapsed: 0.011 s 14.02/2.47 % (15863)Instructions burned: 35 (million) 14.02/2.47 % (15863)------------------------------ 14.02/2.47 % (15863)------------------------------ 14.02/2.47 % (15858)Instruction limit reached! 14.02/2.47 % (15858)------------------------------ 14.02/2.47 % (15858)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 14.02/2.47 % (15858)Termination reason: Unknown 14.02/2.47 % (15858)Termination phase: Saturation 14.02/2.47 14.02/2.47 % (15858)Memory used [KB]: 11001 14.02/2.47 % (15858)Time elapsed: 0.251 s 14.02/2.47 % (15858)Instructions burned: 866 (million) 14.02/2.47 % (15858)------------------------------ 14.02/2.47 % (15858)------------------------------ 14.02/2.47 % (15864)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 E---3.1_15619 for (1779ds/1762Mi) 14.02/2.48 % (15865)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on E---3.1_15619 for (1779ds/96Mi) 14.02/2.48 % (15830)Instruction limit reached! 14.02/2.48 % (15830)------------------------------ 14.02/2.48 % (15830)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 14.02/2.48 % (15830)Termination reason: Unknown 14.02/2.48 % (15830)Termination phase: Saturation 14.02/2.48 14.02/2.48 % (15830)Memory used [KB]: 15735 14.02/2.48 % (15830)Time elapsed: 1.293 s 14.02/2.48 % (15830)Instructions burned: 4352 (million) 14.02/2.48 % (15830)------------------------------ 14.02/2.48 % (15830)------------------------------ 14.02/2.49 % (15866)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 E---3.1_15619 for (1779ds/503Mi) 14.02/2.50 % (15865)Instruction limit reached! 14.02/2.50 % (15865)------------------------------ 14.02/2.50 % (15865)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 14.02/2.50 % (15865)Termination reason: Unknown 14.02/2.50 % (15865)Termination phase: Function definition elimination 14.02/2.50 14.02/2.50 % (15865)Memory used [KB]: 1918 14.02/2.50 % (15865)Time elapsed: 0.023 s 14.02/2.50 % (15865)Instructions burned: 99 (million) 14.02/2.50 % (15865)------------------------------ 14.02/2.50 % (15865)------------------------------ 14.02/2.51 % (15867)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 E---3.1_15619 for (1779ds/90Mi) 14.02/2.53 % (15867)Instruction limit reached! 14.02/2.53 % (15867)------------------------------ 14.02/2.53 % (15867)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 14.02/2.53 % (15867)Termination reason: Unknown 14.02/2.53 % (15867)Termination phase: Function definition elimination 14.64/2.53 14.64/2.53 % (15867)Memory used [KB]: 1791 14.64/2.53 % (15867)Time elapsed: 0.022 s 14.64/2.53 % (15867)Instructions burned: 91 (million) 14.64/2.53 % (15867)------------------------------ 14.64/2.53 % (15867)------------------------------ 14.64/2.54 % (15868)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on E---3.1_15619 for (1778ds/593Mi) 14.64/2.54 % (15862)Instruction limit reached! 14.64/2.54 % (15862)------------------------------ 14.64/2.54 % (15862)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 14.64/2.54 % (15862)Termination reason: Unknown 14.64/2.54 % (15862)Termination phase: Saturation 14.64/2.54 14.64/2.54 % (15862)Memory used [KB]: 7291 14.64/2.54 % (15862)Time elapsed: 0.110 s 14.64/2.54 % (15862)Instructions burned: 328 (million) 14.64/2.54 % (15862)------------------------------ 14.64/2.54 % (15862)------------------------------ 14.64/2.55 % (15869)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on E---3.1_15619 for (1778ds/1512Mi) 14.64/2.57 % (15869)Refutation not found, incomplete strategy 14.64/2.57 % (15869)------------------------------ 14.64/2.57 % (15869)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 14.64/2.57 % (15869)Termination reason: Refutation not found, incomplete strategy 14.64/2.57 14.64/2.57 14.64/2.57 % (15869)Memory used [KB]: 6524 14.64/2.57 % (15869)Time elapsed: 0.022 s 14.64/2.57 % (15869)Instructions burned: 69 (million) 14.64/2.57 % (15869)------------------------------ 14.64/2.57 % (15869)------------------------------ 14.64/2.58 % (15870)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on E---3.1_15619 for (1778ds/569Mi) 14.93/2.61 % (15861)Instruction limit reached! 14.93/2.61 % (15861)------------------------------ 14.93/2.61 % (15861)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 14.93/2.61 % (15861)Termination reason: Unknown 14.93/2.61 % (15861)Termination phase: Saturation 14.93/2.61 14.93/2.61 % (15861)Memory used [KB]: 7164 14.93/2.61 % (15861)Time elapsed: 0.178 s 14.93/2.61 % (15861)Instructions burned: 594 (million) 14.93/2.61 % (15861)------------------------------ 14.93/2.61 % (15861)------------------------------ 14.93/2.62 % (15871)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 E---3.1_15619 for (1778ds/501Mi) 15.24/2.65 % (15866)Instruction limit reached! 15.24/2.65 % (15866)------------------------------ 15.24/2.65 % (15866)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 15.24/2.65 % (15866)Termination reason: Unknown 15.24/2.65 % (15866)Termination phase: Saturation 15.24/2.65 15.24/2.65 % (15866)Memory used [KB]: 8443 15.24/2.65 % (15866)Time elapsed: 0.164 s 15.24/2.65 % (15866)Instructions burned: 505 (million) 15.24/2.65 % (15866)------------------------------ 15.24/2.65 % (15866)------------------------------ 15.24/2.66 % (15872)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 E---3.1_15619 for (1777ds/562Mi) 15.45/2.67 % (15868)Instruction limit reached! 15.45/2.67 % (15868)------------------------------ 15.45/2.67 % (15868)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 15.45/2.67 % (15868)Termination reason: Unknown 15.45/2.67 % (15868)Termination phase: Property scanning 15.45/2.67 15.45/2.67 % (15868)Memory used [KB]: 1918 15.45/2.67 % (15868)Time elapsed: 0.130 s 15.45/2.67 % (15868)Instructions burned: 593 (million) 15.45/2.67 % (15868)------------------------------ 15.45/2.67 % (15868)------------------------------ 15.45/2.68 % (15873)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on E---3.1_15619 for (1777ds/406Mi) 15.45/2.70 % (15870)Instruction limit reached! 15.45/2.70 % (15870)------------------------------ 15.45/2.70 % (15870)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 15.45/2.70 % (15870)Termination reason: Unknown 15.45/2.70 % (15870)Termination phase: Property scanning 15.45/2.70 15.45/2.70 % (15870)Memory used [KB]: 2046 15.45/2.70 % (15870)Time elapsed: 0.124 s 15.45/2.70 % (15870)Instructions burned: 571 (million) 15.45/2.70 % (15870)------------------------------ 15.45/2.70 % (15870)------------------------------ 15.45/2.71 % (15874)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on E---3.1_15619 for (1776ds/582Mi) 15.45/2.72 % (15871)Instruction limit reached! 15.45/2.72 % (15871)------------------------------ 15.45/2.72 % (15871)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 15.45/2.72 % (15871)Termination reason: Unknown 15.45/2.72 % (15871)Termination phase: Property scanning 15.45/2.72 15.45/2.72 % (15871)Memory used [KB]: 1918 15.45/2.72 % (15871)Time elapsed: 0.107 s 15.45/2.72 % (15871)Instructions burned: 501 (million) 15.45/2.72 % (15871)------------------------------ 15.45/2.72 % (15871)------------------------------ 16.32/2.73 % (15875)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on E---3.1_15619 for (1776ds/456Mi) 16.54/2.81 % (15873)Instruction limit reached! 16.54/2.81 % (15873)------------------------------ 16.54/2.81 % (15873)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 16.54/2.81 % (15873)Termination reason: Unknown 16.54/2.81 % (15873)Termination phase: Saturation 16.54/2.81 16.54/2.81 % (15873)Memory used [KB]: 7419 16.54/2.81 % (15873)Time elapsed: 0.158 s 16.54/2.81 % (15873)Instructions burned: 408 (million) 16.54/2.81 % (15873)------------------------------ 16.54/2.81 % (15873)------------------------------ 16.54/2.81 % (15850)Instruction limit reached! 16.54/2.81 % (15850)------------------------------ 16.54/2.81 % (15850)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 16.54/2.81 % (15850)Termination reason: Unknown 16.54/2.81 % (15850)Termination phase: Saturation 16.54/2.81 16.54/2.81 % (15850)Memory used [KB]: 2430 16.54/2.81 % (15850)Time elapsed: 1.127 s 16.54/2.81 % (15850)Instructions burned: 4714 (million) 16.54/2.81 % (15850)------------------------------ 16.54/2.81 % (15850)------------------------------ 16.54/2.82 % (15876)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on E---3.1_15619 for (1775ds/393Mi) 16.54/2.82 % (15877)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on E---3.1_15619 for (1775ds/1335Mi) 16.54/2.83 % (15872)Instruction limit reached! 16.54/2.83 % (15872)------------------------------ 16.54/2.83 % (15872)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 16.54/2.83 % (15872)Termination reason: Unknown 16.54/2.83 % (15872)Termination phase: Saturation 16.54/2.83 16.54/2.83 % (15872)Memory used [KB]: 7547 16.54/2.83 % (15872)Time elapsed: 0.196 s 16.54/2.83 % (15872)Instructions burned: 562 (million) 16.54/2.83 % (15872)------------------------------ 16.54/2.83 % (15872)------------------------------ 16.54/2.84 % (15875)Instruction limit reached! 16.54/2.84 % (15875)------------------------------ 16.54/2.84 % (15875)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 16.54/2.84 % (15875)Termination reason: Unknown 16.54/2.84 % (15875)Termination phase: Property scanning 16.54/2.84 16.54/2.84 % (15875)Memory used [KB]: 1918 16.54/2.84 % (15875)Time elapsed: 0.107 s 16.54/2.84 % (15875)Instructions burned: 456 (million) 16.54/2.84 % (15875)------------------------------ 16.54/2.84 % (15875)------------------------------ 17.11/2.84 % (15878)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on E---3.1_15619 for (1775ds/3373Mi) 17.11/2.85 % (15879)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on E---3.1_15619 for (1775ds/474Mi) 17.11/2.86 % (15874)Instruction limit reached! 17.11/2.86 % (15874)------------------------------ 17.11/2.86 % (15874)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 17.11/2.86 % (15874)Termination reason: Unknown 17.11/2.86 % (15874)Termination phase: Property scanning 17.11/2.86 17.11/2.86 % (15874)Memory used [KB]: 1918 17.11/2.86 % (15874)Time elapsed: 0.149 s 17.11/2.86 % (15874)Instructions burned: 585 (million) 17.11/2.86 % (15874)------------------------------ 17.11/2.86 % (15874)------------------------------ 17.11/2.87 % (15880)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 E---3.1_15619 for (1775ds/157Mi) 17.11/2.88 % (15864)Instruction limit reached! 17.11/2.88 % (15864)------------------------------ 17.11/2.88 % (15864)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 17.11/2.88 % (15864)Termination reason: Unknown 17.11/2.88 % (15864)Termination phase: Saturation 17.11/2.88 17.11/2.88 % (15864)Memory used [KB]: 6652 17.11/2.88 % (15864)Time elapsed: 0.403 s 17.11/2.88 % (15864)Instructions burned: 1762 (million) 17.11/2.88 % (15864)------------------------------ 17.11/2.88 % (15864)------------------------------ 17.21/2.89 % (15881)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 E---3.1_15619 for (1775ds/590Mi) 17.21/2.90 % (15876)Instruction limit reached! 17.21/2.90 % (15876)------------------------------ 17.21/2.90 % (15876)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 17.21/2.90 % (15876)Termination reason: Unknown 17.21/2.90 % (15876)Termination phase: Property scanning 17.21/2.90 17.21/2.90 % (15876)Memory used [KB]: 2046 17.21/2.90 % (15876)Time elapsed: 0.084 s 17.21/2.90 % (15876)Instructions burned: 393 (million) 17.21/2.90 % (15876)------------------------------ 17.21/2.90 % (15876)------------------------------ 17.21/2.90 % (15880)Instruction limit reached! 17.21/2.90 % (15880)------------------------------ 17.21/2.90 % (15880)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 17.21/2.90 % (15880)Termination reason: Unknown 17.21/2.90 % (15880)Termination phase: Function definition elimination 17.21/2.90 17.21/2.90 % (15880)Memory used [KB]: 1918 17.21/2.90 % (15880)Time elapsed: 0.035 s 17.21/2.90 % (15880)Instructions burned: 161 (million) 17.21/2.90 % (15880)------------------------------ 17.21/2.90 % (15880)------------------------------ 17.21/2.91 % (15882)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on E---3.1_15619 for (1774ds/104Mi) 17.21/2.91 % (15883)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on E---3.1_15619 for (1774ds/414Mi) 17.21/2.93 % (15882)Instruction limit reached! 17.21/2.93 % (15882)------------------------------ 17.21/2.93 % (15882)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 17.21/2.93 % (15882)Termination reason: Unknown 17.21/2.93 % (15882)Termination phase: Function definition elimination 17.21/2.93 17.21/2.93 % (15882)Memory used [KB]: 1791 17.21/2.93 % (15882)Time elapsed: 0.024 s 17.21/2.93 % (15882)Instructions burned: 104 (million) 17.21/2.93 % (15882)------------------------------ 17.21/2.93 % (15882)------------------------------ 17.43/2.94 % (15884)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 E---3.1_15619 for (1774ds/715Mi) 17.45/2.95 % (15879)Instruction limit reached! 17.45/2.95 % (15879)------------------------------ 17.45/2.95 % (15879)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 17.45/2.95 % (15879)Termination reason: Unknown 17.45/2.95 % (15879)Termination phase: Property scanning 17.45/2.95 17.45/2.95 % (15879)Memory used [KB]: 2046 17.45/2.95 % (15879)Time elapsed: 0.104 s 17.45/2.95 % (15879)Instructions burned: 474 (million) 17.45/2.95 % (15879)------------------------------ 17.45/2.95 % (15879)------------------------------ 17.45/2.96 % (15885)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 E---3.1_15619 for (1774ds/961Mi) 17.45/3.00 % (15883)Instruction limit reached! 17.45/3.00 % (15883)------------------------------ 17.45/3.00 % (15883)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 17.45/3.00 % (15883)Termination reason: Unknown 17.45/3.00 % (15883)Termination phase: Property scanning 17.45/3.00 17.45/3.00 % (15883)Memory used [KB]: 2046 17.45/3.00 % (15883)Time elapsed: 0.087 s 17.45/3.00 % (15883)Instructions burned: 415 (million) 17.45/3.00 % (15883)------------------------------ 17.45/3.00 % (15883)------------------------------ 17.45/3.01 % (15886)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on E---3.1_15619 for (1774ds/1213Mi) 17.71/3.02 % (15881)Instruction limit reached! 17.71/3.02 % (15881)------------------------------ 17.71/3.02 % (15881)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 17.71/3.02 % (15881)Termination reason: Unknown 17.71/3.02 % (15881)Termination phase: Property scanning 17.71/3.02 17.71/3.02 % (15881)Memory used [KB]: 1918 17.71/3.02 % (15881)Time elapsed: 0.131 s 17.71/3.02 % (15881)Instructions burned: 593 (million) 17.71/3.02 % (15881)------------------------------ 17.71/3.02 % (15881)------------------------------ 17.71/3.02 % (15887)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on E---3.1_15619 for (1773ds/1979Mi) 17.91/3.10 % (15884)Instruction limit reached! 17.91/3.10 % (15884)------------------------------ 17.91/3.10 % (15884)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 17.91/3.10 % (15884)Termination reason: Unknown 17.91/3.10 % (15884)Termination phase: Property scanning 17.91/3.10 17.91/3.10 % (15884)Memory used [KB]: 1918 17.91/3.10 % (15884)Time elapsed: 0.156 s 17.91/3.10 % (15884)Instructions burned: 717 (million) 17.91/3.10 % (15884)------------------------------ 17.91/3.10 % (15884)------------------------------ 17.91/3.11 % (15888)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 E---3.1_15619 for (1773ds/481Mi) 18.15/3.18 % (15885)Instruction limit reached! 18.15/3.18 % (15885)------------------------------ 18.15/3.18 % (15885)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 18.15/3.18 % (15885)Termination reason: Unknown 18.15/3.18 % (15885)Termination phase: Property scanning 18.15/3.18 18.15/3.18 % (15885)Memory used [KB]: 1918 18.15/3.18 % (15885)Time elapsed: 0.216 s 18.15/3.18 % (15885)Instructions burned: 963 (million) 18.15/3.18 % (15885)------------------------------ 18.15/3.18 % (15885)------------------------------ 18.41/3.19 % (15889)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 E---3.1_15619 for (1772ds/783Mi) 18.41/3.21 % (15888)Instruction limit reached! 18.41/3.21 % (15888)------------------------------ 18.41/3.21 % (15888)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 18.41/3.21 % (15888)Termination reason: Unknown 18.41/3.21 % (15888)Termination phase: Property scanning 18.41/3.21 18.41/3.21 % (15888)Memory used [KB]: 2046 18.41/3.21 % (15888)Time elapsed: 0.104 s 18.41/3.21 % (15888)Instructions burned: 481 (million) 18.41/3.21 % (15888)------------------------------ 18.41/3.21 % (15888)------------------------------ 18.41/3.22 % (15890)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 E---3.1_15619 for (1771ds/432Mi) 18.58/3.25 % (15877)Refutation not found, non-redundant clauses discarded% (15877)------------------------------ 18.58/3.25 % (15877)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 18.58/3.25 % (15877)Termination reason: Refutation not found, non-redundant clauses discarded 18.58/3.25 18.58/3.25 % (15877)Memory used [KB]: 8443 18.58/3.25 % (15877)Time elapsed: 0.425 s 18.58/3.25 % (15877)Instructions burned: 1307 (million) 18.58/3.25 % (15877)------------------------------ 18.58/3.25 % (15877)------------------------------ 18.58/3.25 % (15891)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 E---3.1_15619 for (1771ds/1670Mi) 20.52/3.36 % (15890)Instruction limit reached! 20.52/3.36 % (15890)------------------------------ 20.52/3.36 % (15890)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 20.52/3.36 % (15890)Termination reason: Unknown 20.52/3.36 % (15890)Termination phase: Saturation 20.52/3.36 20.52/3.36 % (15890)Memory used [KB]: 7675 20.52/3.36 % (15890)Time elapsed: 0.144 s 20.52/3.36 % (15890)Instructions burned: 434 (million) 20.52/3.36 % (15890)------------------------------ 20.52/3.36 % (15890)------------------------------ 20.84/3.37 % (15892)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on E---3.1_15619 for (1770ds/90Mi) 20.84/3.39 % (15886)Instruction limit reached! 20.84/3.39 % (15886)------------------------------ 20.84/3.39 % (15886)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 20.84/3.39 % (15886)Termination reason: Unknown 20.84/3.39 % (15886)Termination phase: Saturation 20.84/3.39 20.84/3.39 % (15886)Memory used [KB]: 8699 20.84/3.39 % (15886)Time elapsed: 0.383 s 20.84/3.39 % (15886)Instructions burned: 1214 (million) 20.84/3.39 % (15886)------------------------------ 20.84/3.39 % (15886)------------------------------ 20.84/3.39 % (15892)Instruction limit reached! 20.84/3.39 % (15892)------------------------------ 20.84/3.39 % (15892)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 20.84/3.39 % (15892)Termination reason: Unknown 20.84/3.39 % (15892)Termination phase: Function definition elimination 20.84/3.39 20.84/3.39 % (15892)Memory used [KB]: 1791 20.84/3.39 % (15892)Time elapsed: 0.023 s 20.84/3.39 % (15892)Instructions burned: 92 (million) 20.84/3.39 % (15892)------------------------------ 20.84/3.39 % (15892)------------------------------ 20.84/3.40 % (15893)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on E---3.1_15619 for (1770ds/346Mi) 20.84/3.40 % (15894)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 E---3.1_15619 for (1770ds/401Mi) 21.27/3.46 % (15889)Instruction limit reached! 21.27/3.46 % (15889)------------------------------ 21.27/3.46 % (15889)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 21.27/3.46 % (15889)Termination reason: Unknown 21.27/3.46 % (15889)Termination phase: Saturation 21.27/3.46 21.27/3.46 % (15889)Memory used [KB]: 8827 21.27/3.46 % (15889)Time elapsed: 0.278 s 21.27/3.46 % (15889)Instructions burned: 785 (million) 21.27/3.46 % (15889)------------------------------ 21.27/3.46 % (15889)------------------------------ 21.27/3.47 % (15893)Instruction limit reached! 21.27/3.47 % (15893)------------------------------ 21.27/3.47 % (15893)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 21.27/3.47 % (15893)Termination reason: Unknown 21.27/3.47 % (15893)Termination phase: Property scanning 21.27/3.47 21.27/3.47 % (15893)Memory used [KB]: 1918 21.27/3.47 % (15893)Time elapsed: 0.071 s 21.27/3.47 % (15893)Instructions burned: 346 (million) 21.27/3.47 % (15893)------------------------------ 21.27/3.47 % (15893)------------------------------ 21.49/3.47 % (15895)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on E---3.1_15619 for (1769ds/6454Mi) 21.49/3.47 % (15896)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on E---3.1_15619 for (1769ds/283Mi) 21.49/3.48 % (15887)Instruction limit reached! 21.49/3.48 % (15887)------------------------------ 21.49/3.48 % (15887)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 21.49/3.48 % (15887)Termination reason: Unknown 21.49/3.48 % (15887)Termination phase: Saturation 21.49/3.48 21.49/3.48 % (15887)Memory used [KB]: 6908 21.49/3.48 % (15887)Time elapsed: 0.461 s 21.49/3.48 % (15887)Instructions burned: 1979 (million) 21.49/3.48 % (15887)------------------------------ 21.49/3.48 % (15887)------------------------------ 21.49/3.49 % (15894)Instruction limit reached! 21.49/3.49 % (15894)------------------------------ 21.49/3.49 % (15894)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 21.49/3.49 % (15894)Termination reason: Unknown 21.49/3.49 % (15894)Termination phase: Property scanning 21.49/3.49 21.49/3.49 % (15894)Memory used [KB]: 2046 21.49/3.49 % (15894)Time elapsed: 0.094 s 21.49/3.49 % (15894)Instructions burned: 403 (million) 21.49/3.49 % (15894)------------------------------ 21.49/3.49 % (15894)------------------------------ 21.49/3.49 % (15897)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on E---3.1_15619 for (1769ds/865Mi) 21.49/3.50 % (15898)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on E---3.1_15619 for (1769ds/4528Mi) 21.49/3.51 % (15898)Refutation not found, incomplete strategy 21.49/3.51 % (15898)------------------------------ 21.49/3.51 % (15898)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 21.49/3.51 % (15898)Termination reason: Refutation not found, incomplete strategy 21.49/3.51 21.49/3.51 21.49/3.51 % (15898)Memory used [KB]: 1663 21.49/3.51 % (15898)Time elapsed: 0.011 s 21.49/3.51 % (15898)Instructions burned: 35 (million) 21.49/3.51 % (15898)------------------------------ 21.49/3.51 % (15898)------------------------------ 21.49/3.52 % (15899)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on E---3.1_15619 for (1768ds/1001Mi) 21.78/3.53 % (15896)Instruction limit reached! 21.78/3.53 % (15896)------------------------------ 21.78/3.53 % (15896)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 21.78/3.53 % (15896)Termination reason: Unknown 21.78/3.53 % (15896)Termination phase: Property scanning 21.78/3.53 21.78/3.53 % (15896)Memory used [KB]: 1918 21.78/3.53 % (15896)Time elapsed: 0.058 s 21.78/3.53 % (15896)Instructions burned: 284 (million) 21.78/3.53 % (15896)------------------------------ 21.78/3.53 % (15896)------------------------------ 21.78/3.54 % (15900)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on E---3.1_15619 for (1768ds/102Mi) 21.92/3.56 % (15900)Instruction limit reached! 21.92/3.56 % (15900)------------------------------ 21.92/3.56 % (15900)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 21.92/3.56 % (15900)Termination reason: Unknown 21.92/3.56 % (15900)Termination phase: Function definition elimination 21.92/3.56 21.92/3.56 % (15900)Memory used [KB]: 1918 21.92/3.56 % (15900)Time elapsed: 0.024 s 21.92/3.56 % (15900)Instructions burned: 103 (million) 21.92/3.56 % (15900)------------------------------ 21.92/3.56 % (15900)------------------------------ 21.92/3.57 % (15901)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on E---3.1_15619 for (1768ds/952Mi) 22.18/3.63 % (15891)Instruction limit reached! 22.18/3.63 % (15891)------------------------------ 22.18/3.63 % (15891)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 22.18/3.63 % (15891)Termination reason: Unknown 22.18/3.63 % (15891)Termination phase: Saturation 22.18/3.63 22.18/3.63 % (15891)Memory used [KB]: 6524 22.18/3.63 % (15891)Time elapsed: 0.376 s 22.18/3.63 % (15891)Instructions burned: 1674 (million) 22.18/3.63 % (15891)------------------------------ 22.18/3.63 % (15891)------------------------------ 22.18/3.64 % (15902)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on E---3.1_15619 for (1767ds/578Mi) 22.18/3.65 % (15878)Instruction limit reached! 22.18/3.65 % (15878)------------------------------ 22.18/3.65 % (15878)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 22.18/3.65 % (15878)Termination reason: Unknown 22.18/3.65 % (15878)Termination phase: Saturation 22.18/3.65 22.18/3.65 % (15878)Memory used [KB]: 6908 22.18/3.65 % (15878)Time elapsed: 0.805 s 22.18/3.65 % (15878)Instructions burned: 3373 (million) 22.18/3.65 % (15878)------------------------------ 22.18/3.65 % (15878)------------------------------ 22.18/3.65 % (15903)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on E---3.1_15619 for (1767ds/643Mi) 22.27/3.68 % (15897)Instruction limit reached! 22.27/3.68 % (15897)------------------------------ 22.27/3.68 % (15897)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 22.27/3.68 % (15897)Termination reason: Unknown 22.27/3.68 % (15897)Termination phase: Property scanning 22.27/3.68 22.27/3.68 % (15897)Memory used [KB]: 1918 22.27/3.68 % (15897)Time elapsed: 0.190 s 22.27/3.68 % (15897)Instructions burned: 866 (million) 22.27/3.68 % (15897)------------------------------ 22.27/3.68 % (15897)------------------------------ 22.27/3.69 % (15904)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on E---3.1_15619 for (1767ds/865Mi) 22.55/3.75 % (15899)Instruction limit reached! 22.55/3.75 % (15899)------------------------------ 22.55/3.75 % (15899)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 22.55/3.75 % (15899)Termination reason: Unknown 22.55/3.75 % (15899)Termination phase: Property scanning 22.55/3.75 22.55/3.75 % (15899)Memory used [KB]: 1918 22.55/3.75 % (15899)Time elapsed: 0.226 s 22.55/3.75 % (15899)Instructions burned: 1001 (million) 22.55/3.75 % (15899)------------------------------ 22.55/3.75 % (15899)------------------------------ 22.55/3.75 % (15905)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on E---3.1_15619 for (1766ds/1174Mi) 22.80/3.79 % (15901)Instruction limit reached! 22.80/3.79 % (15901)------------------------------ 22.80/3.79 % (15901)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 22.80/3.79 % (15901)Termination reason: Unknown 22.80/3.79 % (15901)Termination phase: Property scanning 22.80/3.79 22.80/3.79 % (15901)Memory used [KB]: 1918 22.80/3.79 % (15901)Time elapsed: 0.217 s 22.80/3.79 % (15901)Instructions burned: 954 (million) 22.80/3.79 % (15901)------------------------------ 22.80/3.79 % (15901)------------------------------ 22.80/3.80 % (15903)Instruction limit reached! 22.80/3.80 % (15903)------------------------------ 22.80/3.80 % (15903)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 22.80/3.80 % (15903)Termination reason: Unknown 22.80/3.80 % (15903)Termination phase: Property scanning 22.80/3.80 22.80/3.80 % (15903)Memory used [KB]: 2046 22.80/3.80 % (15903)Time elapsed: 0.142 s 22.80/3.80 % (15903)Instructions burned: 646 (million) 22.80/3.80 % (15903)------------------------------ 22.80/3.80 % (15903)------------------------------ 22.80/3.80 % (15906)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on E---3.1_15619 for (1766ds/644Mi) 22.80/3.80 % (15907)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on E---3.1_15619 for (1766ds/1201Mi) 22.80/3.81 % (15902)Instruction limit reached! 22.80/3.81 % (15902)------------------------------ 22.80/3.81 % (15902)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 22.80/3.81 % (15902)Termination reason: Unknown 22.80/3.81 % (15902)Termination phase: Saturation 22.80/3.81 22.80/3.81 % (15902)Memory used [KB]: 7164 22.80/3.81 % (15902)Time elapsed: 0.177 s 22.80/3.81 % (15902)Instructions burned: 580 (million) 22.80/3.81 % (15902)------------------------------ 22.80/3.81 % (15902)------------------------------ 22.80/3.82 % (15908)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on E---3.1_15619 for (1765ds/1046Mi) 24.30/3.88 % (15904)Instruction limit reached! 24.30/3.88 % (15904)------------------------------ 24.30/3.88 % (15904)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 24.30/3.88 % (15904)Termination reason: Unknown 24.30/3.88 % (15904)Termination phase: Property scanning 24.30/3.88 24.30/3.88 % (15904)Memory used [KB]: 1918 24.30/3.88 % (15904)Time elapsed: 0.193 s 24.30/3.88 % (15904)Instructions burned: 867 (million) 24.30/3.88 % (15904)------------------------------ 24.30/3.88 % (15904)------------------------------ 24.30/3.89 % (15909)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on E---3.1_15619 for (1765ds/222Mi) 24.75/3.94 % (15909)Instruction limit reached! 24.75/3.94 % (15909)------------------------------ 24.75/3.94 % (15909)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 24.75/3.94 % (15909)Termination reason: Unknown 24.75/3.94 % (15909)Termination phase: Function definition elimination 24.75/3.94 24.75/3.94 % (15909)Memory used [KB]: 1918 24.75/3.94 % (15909)Time elapsed: 0.046 s 24.75/3.94 % (15909)Instructions burned: 223 (million) 24.75/3.94 % (15909)------------------------------ 24.75/3.94 % (15909)------------------------------ 24.75/3.94 % (15906)Instruction limit reached! 24.75/3.94 % (15906)------------------------------ 24.75/3.94 % (15906)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 24.75/3.94 % (15906)Termination reason: Unknown 24.75/3.94 % (15906)Termination phase: Property scanning 24.75/3.94 24.75/3.94 % (15906)Memory used [KB]: 1918 24.75/3.94 % (15906)Time elapsed: 0.144 s 24.75/3.94 % (15906)Instructions burned: 645 (million) 24.75/3.94 % (15906)------------------------------ 24.75/3.94 % (15906)------------------------------ 24.75/3.94 % (15910)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on E---3.1_15619 for (1764ds/68Mi) 24.75/3.95 % (15911)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=454:si=on:rtra=on_0 on E---3.1_15619 for (1764ds/454Mi) 24.75/3.96 % (15910)Instruction limit reached! 24.75/3.96 % (15910)------------------------------ 24.75/3.96 % (15910)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 24.75/3.96 % (15910)Termination reason: Unknown 24.75/3.96 % (15910)Termination phase: Function definition elimination 24.75/3.96 24.75/3.96 % (15910)Memory used [KB]: 1791 24.75/3.96 % (15910)Time elapsed: 0.019 s 24.75/3.96 % (15910)Instructions burned: 72 (million) 24.75/3.96 % (15910)------------------------------ 24.75/3.96 % (15910)------------------------------ 25.00/3.97 % (15912)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on E---3.1_15619 for (1764ds/360Mi) 25.31/4.04 % (15911)Instruction limit reached! 25.31/4.04 % (15911)------------------------------ 25.31/4.04 % (15911)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 25.31/4.04 % (15911)Termination reason: Unknown 25.31/4.04 % (15911)Termination phase: Property scanning 25.31/4.04 25.31/4.04 % (15911)Memory used [KB]: 2046 25.31/4.04 % (15911)Time elapsed: 0.096 s 25.31/4.04 % (15911)Instructions burned: 455 (million) 25.31/4.04 % (15911)------------------------------ 25.31/4.04 % (15911)------------------------------ 25.31/4.05 % (15912)Instruction limit reached! 25.31/4.05 % (15912)------------------------------ 25.31/4.05 % (15912)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 25.31/4.05 % (15912)Termination reason: Unknown 25.31/4.05 % (15912)Termination phase: Property scanning 25.31/4.05 25.31/4.05 % (15912)Memory used [KB]: 2046 25.31/4.05 % (15912)Time elapsed: 0.076 s 25.31/4.05 % (15912)Instructions burned: 364 (million) 25.31/4.05 % (15912)------------------------------ 25.31/4.05 % (15912)------------------------------ 25.31/4.05 % (15913)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 E---3.1_15619 for (1763ds/157Mi) 25.31/4.05 % (15905)Instruction limit reached! 25.31/4.05 % (15905)------------------------------ 25.31/4.05 % (15905)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 25.31/4.05 % (15905)Termination reason: Unknown 25.31/4.05 % (15905)Termination phase: Property scanning 25.31/4.05 25.31/4.05 % (15905)Memory used [KB]: 1918 25.31/4.05 % (15905)Time elapsed: 0.299 s 25.31/4.05 % (15905)Instructions burned: 1175 (million) 25.31/4.05 % (15905)------------------------------ 25.31/4.05 % (15905)------------------------------ 25.31/4.05 % (15914)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on E---3.1_15619 for (1763ds/5061Mi) 25.64/4.06 % (15908)Instruction limit reached! 25.64/4.06 % (15908)------------------------------ 25.64/4.06 % (15908)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 25.64/4.06 % (15908)Termination reason: Unknown 25.64/4.06 % (15908)Termination phase: Property scanning 25.64/4.06 25.64/4.06 % (15908)Memory used [KB]: 2046 25.64/4.06 % (15908)Time elapsed: 0.238 s 25.64/4.06 % (15908)Instructions burned: 1046 (million) 25.64/4.06 % (15908)------------------------------ 25.64/4.06 % (15908)------------------------------ 25.64/4.06 % (15915)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on E---3.1_15619 for (1763ds/2401Mi) 25.64/4.07 % (15916)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on E---3.1_15619 for (1763ds/5798Mi) 25.64/4.08 % (15907)Instruction limit reached! 25.64/4.08 % (15907)------------------------------ 25.64/4.08 % (15907)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 25.64/4.08 % (15907)Termination reason: Unknown 25.64/4.08 % (15907)Termination phase: Property scanning 25.64/4.08 25.64/4.08 % (15907)Memory used [KB]: 2046 25.64/4.08 % (15907)Time elapsed: 0.273 s 25.64/4.08 % (15907)Instructions burned: 1204 (million) 25.64/4.08 % (15907)------------------------------ 25.64/4.08 % (15907)------------------------------ 25.64/4.08 % (15917)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on E---3.1_15619 for (1763ds/346Mi) 25.64/4.09 % (15913)Instruction limit reached! 25.64/4.09 % (15913)------------------------------ 25.64/4.09 % (15913)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 25.64/4.09 % (15913)Termination reason: Unknown 25.64/4.09 % (15913)Termination phase: Function definition elimination 25.64/4.09 25.64/4.09 % (15913)Memory used [KB]: 1918 25.64/4.09 % (15913)Time elapsed: 0.035 s 25.64/4.09 % (15913)Instructions burned: 161 (million) 25.64/4.09 % (15913)------------------------------ 25.64/4.09 % (15913)------------------------------ 25.64/4.09 % (15918)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on E---3.1_15619 for (1763ds/1321Mi) 25.64/4.11 % (15918)Refutation not found, incomplete strategy 25.64/4.11 % (15918)------------------------------ 25.64/4.11 % (15918)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 25.64/4.11 % (15918)Termination reason: Refutation not found, incomplete strategy 25.64/4.11 25.64/4.11 25.64/4.11 % (15918)Memory used [KB]: 1918 25.64/4.11 % (15918)Time elapsed: 0.021 s 25.64/4.11 % (15918)Instructions burned: 69 (million) 25.64/4.11 % (15918)------------------------------ 25.64/4.11 % (15918)------------------------------ 25.89/4.12 % (15919)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on E---3.1_15619 for (1762ds/1312Mi) 25.89/4.15 % (15917)Instruction limit reached! 25.89/4.15 % (15917)------------------------------ 25.89/4.15 % (15917)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 25.89/4.15 % (15917)Termination reason: Unknown 25.89/4.15 % (15917)Termination phase: Property scanning 25.89/4.15 25.89/4.15 % (15917)Memory used [KB]: 2046 25.89/4.15 % (15917)Time elapsed: 0.071 s 25.89/4.15 % (15917)Instructions burned: 346 (million) 25.89/4.15 % (15917)------------------------------ 25.89/4.15 % (15917)------------------------------ 26.04/4.16 % (15920)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on E---3.1_15619 for (1762ds/672Mi) 26.25/4.32 % (15851)Instruction limit reached! 26.25/4.32 % (15851)------------------------------ 26.25/4.32 % (15851)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 26.25/4.32 % (15851)Termination reason: Unknown 26.25/4.32 % (15851)Termination phase: Saturation 26.25/4.32 26.25/4.32 % (15851)Memory used [KB]: 15095 26.25/4.32 % (15851)Time elapsed: 2.612 s 26.25/4.32 % (15851)Instructions burned: 8251 (million) 26.25/4.32 % (15851)------------------------------ 26.25/4.32 % (15851)------------------------------ 26.25/4.33 % (15921)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on E---3.1_15619 for (1760ds/1897Mi) 26.36/4.34 % (15921)Refutation not found, incomplete strategy 26.36/4.34 % (15921)------------------------------ 26.36/4.34 % (15921)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 26.36/4.34 % (15921)Termination reason: Refutation not found, incomplete strategy 26.36/4.34 26.36/4.34 26.36/4.34 % (15921)Memory used [KB]: 6140 26.36/4.34 % (15921)Time elapsed: 0.012 s 26.36/4.34 % (15921)Instructions burned: 36 (million) 26.36/4.34 % (15921)------------------------------ 26.36/4.34 % (15921)------------------------------ 26.36/4.35 % (15922)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on E---3.1_15619 for (1760ds/1202Mi) 27.80/4.37 % (15920)Instruction limit reached! 27.80/4.37 % (15920)------------------------------ 27.80/4.37 % (15920)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 27.80/4.37 % (15920)Termination reason: Unknown 27.80/4.37 % (15920)Termination phase: Saturation 27.80/4.37 27.80/4.37 % (15920)Memory used [KB]: 8571 27.80/4.37 % (15920)Time elapsed: 0.207 s 27.80/4.37 % (15920)Instructions burned: 673 (million) 27.80/4.37 % (15920)------------------------------ 27.80/4.37 % (15920)------------------------------ 27.80/4.38 % (15923)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on E---3.1_15619 for (1760ds/1493Mi) 27.80/4.39 % (15923)Refutation not found, incomplete strategy 27.80/4.39 % (15923)------------------------------ 27.80/4.39 % (15923)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 27.80/4.39 % (15923)Termination reason: Refutation not found, incomplete strategy 27.80/4.39 27.80/4.39 27.80/4.39 % (15923)Memory used [KB]: 6140 27.80/4.39 % (15923)Time elapsed: 0.013 s 27.80/4.39 % (15923)Instructions burned: 43 (million) 27.80/4.39 % (15923)------------------------------ 27.80/4.39 % (15923)------------------------------ 27.80/4.40 % (15924)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on E---3.1_15619 for (1760ds/7679Mi) 27.80/4.42 % (15919)Instruction limit reached! 27.80/4.42 % (15919)------------------------------ 27.80/4.42 % (15919)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 27.80/4.42 % (15919)Termination reason: Unknown 27.80/4.42 % (15919)Termination phase: Property scanning 27.80/4.42 27.80/4.42 % (15919)Memory used [KB]: 2046 27.80/4.42 % (15919)Time elapsed: 0.300 s 27.80/4.42 % (15919)Instructions burned: 1315 (million) 27.80/4.42 % (15919)------------------------------ 27.80/4.42 % (15919)------------------------------ 27.80/4.43 % (15925)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on E---3.1_15619 for (1759ds/340Mi) 28.43/4.50 % (15925)Instruction limit reached! 28.43/4.50 % (15925)------------------------------ 28.43/4.50 % (15925)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 28.43/4.50 % (15925)Termination reason: Unknown 28.43/4.50 % (15925)Termination phase: Property scanning 28.43/4.50 28.43/4.50 % (15925)Memory used [KB]: 1918 28.43/4.50 % (15925)Time elapsed: 0.072 s 28.43/4.50 % (15925)Instructions burned: 340 (million) 28.43/4.50 % (15925)------------------------------ 28.43/4.50 % (15925)------------------------------ 28.43/4.51 % (15926)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on E---3.1_15619 for (1758ds/3672Mi) 29.22/4.62 % (15915)Instruction limit reached! 29.22/4.62 % (15915)------------------------------ 29.22/4.62 % (15915)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 29.22/4.62 % (15915)Termination reason: Unknown 29.22/4.62 % (15915)Termination phase: Saturation 29.22/4.62 29.22/4.62 % (15915)Memory used [KB]: 2430 29.22/4.62 % (15915)Time elapsed: 0.557 s 29.22/4.62 % (15915)Instructions burned: 2402 (million) 29.22/4.62 % (15915)------------------------------ 29.22/4.62 % (15915)------------------------------ 29.22/4.63 % (15927)dis-1002_3:1_acc=model:bd=off:bsd=on:bsdmm=1:cnfonf=lazy_not_be_gen:fd=off:fe=off:ntd=on:nwc=10.0:piset=equals:plsq=on:plsqc=1:plsqr=32,1:sp=const_max:uhcvi=on:i=1535:si=on:rtra=on_0 on E---3.1_15619 for (1757ds/1535Mi) 29.39/4.71 % (15922)Instruction limit reached! 29.39/4.71 % (15922)------------------------------ 29.39/4.71 % (15922)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 29.39/4.71 % (15922)Termination reason: Unknown 29.39/4.71 % (15922)Termination phase: Saturation 29.39/4.71 29.39/4.71 % (15922)Memory used [KB]: 3070 29.39/4.71 % (15922)Time elapsed: 0.367 s 29.39/4.71 % (15922)Instructions burned: 1203 (million) 29.39/4.71 % (15922)------------------------------ 29.39/4.71 % (15922)------------------------------ 29.39/4.72 % (15928)dis+10_16:1_hud=1:plsq=on:plsqc=1:plsqr=32,1:prag=on:sd=1:sgt=64:ss=axioms:i=4637:si=on:rtra=on_0 on E---3.1_15619 for (1756ds/4637Mi) 32.01/4.99 % (15927)Instruction limit reached! 32.01/4.99 % (15927)------------------------------ 32.01/4.99 % (15927)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 32.01/4.99 % (15927)Termination reason: Unknown 32.01/4.99 % (15927)Termination phase: Property scanning 32.01/4.99 32.01/4.99 % (15927)Memory used [KB]: 2046 32.01/4.99 % (15927)Time elapsed: 0.363 s 32.01/4.99 % (15927)Instructions burned: 1537 (million) 32.01/4.99 % (15927)------------------------------ 32.01/4.99 % (15927)------------------------------ 32.01/5.00 % (15929)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on E---3.1_15619 for (1754ds/3174Mi) 32.01/5.03 % (15895)Refutation not found, non-redundant clauses discarded% (15895)------------------------------ 32.01/5.03 % (15895)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 32.01/5.03 % (15895)Termination reason: Refutation not found, non-redundant clauses discarded 32.01/5.03 32.01/5.03 % (15895)Memory used [KB]: 10234 32.01/5.03 % (15895)Time elapsed: 1.555 s 32.01/5.03 % (15895)Instructions burned: 6328 (million) 32.01/5.03 % (15895)------------------------------ 32.01/5.03 % (15895)------------------------------ 32.01/5.04 % (15930)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on E---3.1_15619 for (1753ds/307Mi) 32.65/5.10 % (15930)Instruction limit reached! 32.65/5.10 % (15930)------------------------------ 32.65/5.10 % (15930)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 32.65/5.10 % (15930)Termination reason: Unknown 32.65/5.10 % (15930)Termination phase: Property scanning 32.65/5.10 32.65/5.10 % (15930)Memory used [KB]: 2046 32.65/5.10 % (15930)Time elapsed: 0.064 s 32.65/5.10 % (15930)Instructions burned: 308 (million) 32.65/5.10 % (15930)------------------------------ 32.65/5.10 % (15930)------------------------------ 32.65/5.11 % (15931)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=3619:si=on:rtra=on_0 on E---3.1_15619 for (1753ds/3619Mi) 32.95/5.13 % (15931)Refutation not found, incomplete strategy 32.95/5.13 % (15931)------------------------------ 32.95/5.13 % (15931)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 32.95/5.13 % (15931)Termination reason: Refutation not found, incomplete strategy 32.95/5.13 32.95/5.13 32.95/5.13 % (15931)Memory used [KB]: 6268 32.95/5.13 % (15931)Time elapsed: 0.021 s 32.95/5.13 % (15931)Instructions burned: 68 (million) 32.95/5.13 % (15931)------------------------------ 32.95/5.13 % (15931)------------------------------ 32.95/5.14 % (15932)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on E---3.1_15619 for (1752ds/2325Mi) 33.46/5.24 % (15914)Instruction limit reached! 33.46/5.24 % (15914)------------------------------ 33.46/5.24 % (15914)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 33.46/5.24 % (15914)Termination reason: Unknown 33.46/5.24 % (15914)Termination phase: Saturation 33.46/5.24 33.46/5.24 % (15914)Memory used [KB]: 6908 33.46/5.24 % (15914)Time elapsed: 1.184 s 33.46/5.24 % (15914)Instructions burned: 5061 (million) 33.46/5.24 % (15914)------------------------------ 33.46/5.24 % (15914)------------------------------ 33.46/5.25 % (15933)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2341:si=on:rtra=on_0 on E---3.1_15619 for (1751ds/2341Mi) 34.31/5.43 % (15916)Instruction limit reached! 34.31/5.43 % (15916)------------------------------ 34.31/5.43 % (15916)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 34.31/5.43 % (15916)Termination reason: Unknown 34.31/5.43 % (15916)Termination phase: Saturation 34.31/5.43 34.31/5.43 % (15916)Memory used [KB]: 2430 34.31/5.43 % (15916)Time elapsed: 1.365 s 34.31/5.43 % (15916)Instructions burned: 5799 (million) 34.31/5.43 % (15916)------------------------------ 34.31/5.43 % (15916)------------------------------ 34.31/5.44 % (15934)lrs+1010_1:16_apa=on:bsd=on:cnfonf=off:hud=10:sac=on:sos=on:ss=axioms:i=7257:si=on:rtra=on_0 on E---3.1_15619 for (1749ds/7257Mi) 34.31/5.45 % (15926)Instruction limit reached! 34.31/5.45 % (15926)------------------------------ 34.31/5.45 % (15926)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 34.31/5.45 % (15926)Termination reason: Unknown 34.31/5.45 % (15926)Termination phase: Saturation 34.31/5.45 34.31/5.45 % (15926)Memory used [KB]: 7931 34.31/5.45 % (15926)Time elapsed: 0.932 s 34.31/5.45 % (15926)Instructions burned: 3672 (million) 34.31/5.45 % (15926)------------------------------ 34.31/5.45 % (15926)------------------------------ 35.41/5.47 % (15935)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=3710:si=on:rtra=on_0 on E---3.1_15619 for (1749ds/3710Mi) 36.28/5.59 % (15934)Refutation not found, incomplete strategy 36.28/5.59 % (15934)------------------------------ 36.28/5.59 % (15934)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 36.28/5.59 % (15934)Termination reason: Refutation not found, incomplete strategy 36.28/5.59 36.28/5.59 36.28/5.59 % (15934)Memory used [KB]: 7675 36.28/5.59 % (15934)Time elapsed: 0.147 s 36.28/5.59 % (15934)Instructions burned: 419 (million) 36.28/5.59 % (15934)------------------------------ 36.28/5.59 % (15934)------------------------------ 36.28/5.60 % (15936)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=326:si=on:rtra=on_0 on E---3.1_15619 for (1748ds/326Mi) 36.77/5.70 % (15936)Instruction limit reached! 36.77/5.70 % (15936)------------------------------ 36.77/5.70 % (15936)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 36.77/5.70 % (15936)Termination reason: Unknown 36.77/5.70 % (15936)Termination phase: Saturation 36.77/5.70 36.77/5.70 % (15936)Memory used [KB]: 7419 36.77/5.70 % (15936)Time elapsed: 0.106 s 36.77/5.70 % (15936)Instructions burned: 328 (million) 36.77/5.70 % (15936)------------------------------ 36.77/5.70 % (15936)------------------------------ 37.16/5.71 % (15937)lrs+1010_1:64_au=on:c=on:e2e=on:flr=on:hfsq=on:hfsql=off:hfsqr=4,1:ins=1:ntd=on:sp=occurrence:i=1100:si=on:rtra=on_0 on E---3.1_15619 for (1747ds/1100Mi) 37.88/5.85 % (15932)Instruction limit reached! 37.88/5.85 % (15932)------------------------------ 37.88/5.85 % (15932)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 37.88/5.85 % (15932)Termination reason: Unknown 37.88/5.85 % (15932)Termination phase: Saturation 37.88/5.85 37.88/5.85 % (15932)Memory used [KB]: 10618 37.88/5.85 % (15932)Time elapsed: 0.712 s 37.88/5.85 % (15932)Instructions burned: 2327 (million) 37.88/5.85 % (15932)------------------------------ 37.88/5.85 % (15932)------------------------------ 37.88/5.86 % (15938)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on E---3.1_15619 for (1745ds/406Mi) 38.49/5.96 % (15928)Instruction limit reached! 38.49/5.96 % (15928)------------------------------ 38.49/5.96 % (15928)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 38.49/5.96 % (15928)Termination reason: Unknown 38.49/5.96 % (15928)Termination phase: Saturation 38.49/5.96 38.49/5.96 % (15928)Memory used [KB]: 8827 38.49/5.96 % (15928)Time elapsed: 1.236 s 38.49/5.96 % (15928)Instructions burned: 4640 (million) 38.49/5.96 % (15928)------------------------------ 38.49/5.96 % (15928)------------------------------ 38.49/5.96 % (15937)Instruction limit reached! 38.49/5.96 % (15937)------------------------------ 38.49/5.96 % (15937)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 38.49/5.96 % (15937)Termination reason: Unknown 38.49/5.96 % (15937)Termination phase: Property scanning 38.49/5.96 38.49/5.96 % (15937)Memory used [KB]: 2046 38.49/5.96 % (15937)Time elapsed: 0.251 s 38.49/5.96 % (15937)Instructions burned: 1102 (million) 38.49/5.96 % (15937)------------------------------ 38.49/5.96 % (15937)------------------------------ 38.83/5.96 % (15939)dis+1010_1:1_aac=none:bd=preordered:e2e=on:fde=none:fe=axiom:nm=16:nwc=10.0:prag=on:i=1871:si=on:rtra=on_0 on E---3.1_15619 for (1744ds/1871Mi) 38.83/5.97 % (15940)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1194:si=on:rtra=on_0 on E---3.1_15619 for (1744ds/1194Mi) 38.83/5.99 % (15929)Instruction limit reached! 38.83/5.99 % (15929)------------------------------ 38.83/5.99 % (15929)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 38.83/5.99 % (15929)Termination reason: Unknown 38.83/5.99 % (15929)Termination phase: Saturation 38.83/5.99 38.83/5.99 % (15929)Memory used [KB]: 11897 38.83/5.99 % (15929)Time elapsed: 0.992 s 38.83/5.99 % (15929)Instructions burned: 3174 (million) 38.83/5.99 % (15929)------------------------------ 38.83/5.99 % (15929)------------------------------ 38.83/6.00 % (15933)Instruction limit reached! 38.83/6.00 % (15933)------------------------------ 38.83/6.00 % (15933)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 38.83/6.00 % (15933)Termination reason: Unknown 38.83/6.00 % (15933)Termination phase: Saturation 38.83/6.00 38.83/6.00 % (15933)Memory used [KB]: 9850 38.83/6.00 % (15933)Time elapsed: 0.751 s 38.83/6.00 % (15933)Instructions burned: 2343 (million) 38.83/6.00 % (15933)------------------------------ 38.83/6.00 % (15933)------------------------------ 38.83/6.00 % (15941)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on E---3.1_15619 for (1744ds/474Mi) 38.83/6.01 % (15942)dis+1010_1:1_au=on:cnfonf=lazy_gen:ins=3:plsq=on:plsqc=1:plsqr=15142123,262144:sp=reverse_arity:i=3115:si=on:rtra=on_0 on E---3.1_15619 for (1744ds/3115Mi) 39.33/6.04 % (15938)Instruction limit reached! 39.33/6.04 % (15938)------------------------------ 39.33/6.04 % (15938)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 39.33/6.04 % (15938)Termination reason: Unknown 39.33/6.04 % (15938)Termination phase: Saturation 39.33/6.04 39.33/6.04 % (15938)Memory used [KB]: 7419 39.33/6.04 % (15938)Time elapsed: 0.178 s 39.33/6.04 % (15938)Instructions burned: 407 (million) 39.33/6.04 % (15938)------------------------------ 39.33/6.04 % (15938)------------------------------ 39.33/6.04 % (15943)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on E---3.1_15619 for (1743ds/831Mi) 39.59/6.10 % (15941)Instruction limit reached! 39.59/6.10 % (15941)------------------------------ 39.59/6.10 % (15941)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 39.59/6.10 % (15941)Termination reason: Unknown 39.59/6.10 % (15941)Termination phase: Property scanning 39.59/6.10 39.59/6.10 % (15941)Memory used [KB]: 2046 39.59/6.10 % (15941)Time elapsed: 0.101 s 39.59/6.10 % (15941)Instructions burned: 475 (million) 39.59/6.10 % (15941)------------------------------ 39.59/6.10 % (15941)------------------------------ 39.59/6.11 % (15944)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on E---3.1_15619 for (1743ds/1188Mi) 40.27/6.23 % (15943)Instruction limit reached! 40.27/6.23 % (15943)------------------------------ 40.27/6.23 % (15943)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 40.27/6.23 % (15943)Termination reason: Unknown 40.27/6.23 % (15943)Termination phase: Property scanning 40.27/6.23 40.27/6.23 % (15943)Memory used [KB]: 1918 40.27/6.23 % (15943)Time elapsed: 0.183 s 40.27/6.23 % (15943)Instructions burned: 831 (million) 40.27/6.23 % (15943)------------------------------ 40.27/6.23 % (15943)------------------------------ 40.27/6.23 % (15945)ott+1010_1:20_cnfonf=lazy_pi_sigma_gen:fe=axiom:plsq=on:plsqc=2:plsqr=32,1:sac=on:sos=all:i=2868:si=on:rtra=on_0 on E---3.1_15619 for (1741ds/2868Mi) 40.73/6.24 % (15940)Instruction limit reached! 40.73/6.24 % (15940)------------------------------ 40.73/6.24 % (15940)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 40.73/6.24 % (15940)Termination reason: Unknown 40.73/6.24 % (15940)Termination phase: Property scanning 40.73/6.24 40.73/6.24 % (15940)Memory used [KB]: 1918 40.73/6.24 % (15940)Time elapsed: 0.269 s 40.73/6.24 % (15940)Instructions burned: 1197 (million) 40.73/6.24 % (15940)------------------------------ 40.73/6.24 % (15940)------------------------------ 40.73/6.25 % (15946)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1516:si=on:rtra=on_0 on E---3.1_15619 for (1741ds/1516Mi) 41.22/6.37 % (15944)Instruction limit reached! 41.22/6.37 % (15944)------------------------------ 41.22/6.37 % (15944)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 41.22/6.37 % (15944)Termination reason: Unknown 41.22/6.37 % (15944)Termination phase: Property scanning 41.22/6.37 41.22/6.37 % (15944)Memory used [KB]: 2046 41.22/6.37 % (15944)Time elapsed: 0.264 s 41.22/6.37 % (15944)Instructions burned: 1190 (million) 41.22/6.37 % (15944)------------------------------ 41.22/6.37 % (15944)------------------------------ 41.22/6.38 % (15947)lrs+1002_1:20_afp=1000:au=on:bsd=on:cnfonf=lazy_not_gen_be_off:sos=all:sp=const_max:i=2321:si=on:rtra=on_0 on E---3.1_15619 for (1740ds/2321Mi) 41.22/6.40 % (15935)Instruction limit reached! 41.22/6.40 % (15935)------------------------------ 41.22/6.40 % (15935)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 41.22/6.40 % (15935)Termination reason: Unknown 41.22/6.40 % (15935)Termination phase: Saturation 41.22/6.40 41.22/6.40 % (15935)Memory used [KB]: 6908 41.22/6.40 % (15935)Time elapsed: 0.920 s 41.22/6.40 % (15935)Instructions burned: 3710 (million) 41.22/6.40 % (15935)------------------------------ 41.22/6.40 % (15935)------------------------------ 41.22/6.40 % (15948)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on E---3.1_15619 for (1740ds/2812Mi) 42.07/6.55 % (15939)Instruction limit reached! 42.07/6.55 % (15939)------------------------------ 42.07/6.55 % (15939)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 42.07/6.55 % (15939)Termination reason: Unknown 42.07/6.55 % (15939)Termination phase: Saturation 42.07/6.55 42.07/6.55 % (15939)Memory used [KB]: 10362 42.07/6.55 % (15939)Time elapsed: 0.586 s 42.07/6.55 % (15939)Instructions burned: 1872 (million) 42.07/6.55 % (15939)------------------------------ 42.07/6.55 % (15939)------------------------------ 42.07/6.56 % (15949)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on E---3.1_15619 for (1738ds/4604Mi) 43.86/6.72 % (15946)Instruction limit reached! 43.86/6.72 % (15946)------------------------------ 43.86/6.72 % (15946)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 43.86/6.72 % (15946)Termination reason: Unknown 43.86/6.72 % (15946)Termination phase: Saturation 43.86/6.72 43.86/6.72 % (15946)Memory used [KB]: 9338 43.86/6.72 % (15946)Time elapsed: 0.492 s 43.86/6.72 % (15946)Instructions burned: 1518 (million) 43.86/6.72 % (15946)------------------------------ 43.86/6.72 % (15946)------------------------------ 43.86/6.72 % (15950)ott+1002_1:4_c=on:chr=on:cnfonf=lazy_not_be_gen:hud=10:nm=10:piset=all_but_not_eq:rp=on:spb=goal:uhcvi=on:i=2678:si=on:rtra=on_0 on E---3.1_15619 for (1736ds/2678Mi) 43.86/6.73 % (15924)Instruction limit reached! 43.86/6.73 % (15924)------------------------------ 43.86/6.73 % (15924)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 43.86/6.73 % (15924)Termination reason: Unknown 43.86/6.73 % (15924)Termination phase: Saturation 43.86/6.73 43.86/6.73 % (15924)Memory used [KB]: 11769 43.86/6.73 % (15924)Time elapsed: 2.323 s 43.86/6.73 % (15924)Instructions burned: 7681 (million) 43.86/6.73 % (15924)------------------------------ 43.86/6.73 % (15924)------------------------------ 43.86/6.73 % (15951)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on E---3.1_15619 for (1736ds/643Mi) 43.86/6.74 % (15942)Instruction limit reached! 43.86/6.74 % (15942)------------------------------ 43.86/6.74 % (15942)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 43.86/6.74 % (15942)Termination reason: Unknown 43.86/6.74 % (15942)Termination phase: Saturation 43.86/6.74 43.86/6.74 % (15942)Memory used [KB]: 6908 43.86/6.74 % (15942)Time elapsed: 0.733 s 43.86/6.74 % (15942)Instructions burned: 3119 (million) 43.86/6.74 % (15942)------------------------------ 43.86/6.74 % (15942)------------------------------ 44.36/6.75 % (15952)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=458:si=on:rtra=on_0 on E---3.1_15619 for (1736ds/458Mi) 44.67/6.85 % (15952)Instruction limit reached! 44.67/6.85 % (15952)------------------------------ 44.67/6.85 % (15952)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 44.67/6.85 % (15952)Termination reason: Unknown 44.67/6.85 % (15952)Termination phase: Property scanning 44.67/6.85 44.67/6.85 % (15952)Memory used [KB]: 2046 44.67/6.85 % (15952)Time elapsed: 0.098 s 44.67/6.85 % (15952)Instructions burned: 459 (million) 44.67/6.85 % (15952)------------------------------ 44.67/6.85 % (15952)------------------------------ 44.89/6.85 % (15953)lrs+1010_1:1_anc=all_dependent:apa=on:au=on:bd=off:c=on:cnfonf=off:ntd=on:i=2546:si=on:rtra=on_0 on E---3.1_15619 for (1735ds/2546Mi) 44.89/6.87 % (15951)Instruction limit reached! 44.89/6.87 % (15951)------------------------------ 44.89/6.87 % (15951)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 44.89/6.87 % (15951)Termination reason: Unknown 44.89/6.87 % (15951)Termination phase: Property scanning 44.89/6.87 44.89/6.87 % (15951)Memory used [KB]: 2046 44.89/6.87 % (15951)Time elapsed: 0.139 s 44.89/6.87 % (15951)Instructions burned: 644 (million) 44.89/6.87 % (15951)------------------------------ 44.89/6.87 % (15951)------------------------------ 44.89/6.88 % (15954)dis+21_1:1_acc=model:au=on:cnfonf=lazy_gen:ins=2:plsq=on:plsqc=1:plsqr=32,1:i=1432:si=on:rtra=on_0 on E---3.1_15619 for (1735ds/1432Mi) 44.89/6.90 % (15945)Instruction limit reached! 44.89/6.90 % (15945)------------------------------ 44.89/6.90 % (15945)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 44.89/6.90 % (15945)Termination reason: Unknown 44.89/6.90 % (15945)Termination phase: Saturation 44.89/6.90 44.89/6.90 % (15945)Memory used [KB]: 2430 44.89/6.90 % (15945)Time elapsed: 0.669 s 44.89/6.90 % (15945)Instructions burned: 2871 (million) 44.89/6.90 % (15945)------------------------------ 44.89/6.90 % (15945)------------------------------ 44.89/6.91 % (15955)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=386:si=on:rtra=on_0 on E---3.1_15619 for (1734ds/386Mi) 45.31/6.93 % (15947)Instruction limit reached! 45.31/6.93 % (15947)------------------------------ 45.31/6.93 % (15947)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 45.31/6.93 % (15947)Termination reason: Unknown 45.31/6.93 % (15947)Termination phase: Saturation 45.31/6.93 45.31/6.93 % (15947)Memory used [KB]: 2430 45.31/6.93 % (15947)Time elapsed: 0.545 s 45.31/6.93 % (15947)Instructions burned: 2324 (million) 45.31/6.93 % (15947)------------------------------ 45.31/6.93 % (15947)------------------------------ 45.31/6.94 % (15956)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on E---3.1_15619 for (1734ds/360Mi) 45.42/6.99 % (15955)Instruction limit reached! 45.42/6.99 % (15955)------------------------------ 45.42/6.99 % (15955)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 45.42/6.99 % (15955)Termination reason: Unknown 45.42/6.99 % (15955)Termination phase: Property scanning 45.42/6.99 45.42/6.99 % (15955)Memory used [KB]: 1918 45.42/6.99 % (15955)Time elapsed: 0.081 s 45.42/6.99 % (15955)Instructions burned: 388 (million) 45.42/6.99 % (15955)------------------------------ 45.42/6.99 % (15955)------------------------------ 45.42/7.00 % (15957)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=5446:si=on:rtra=on_0 on E---3.1_15619 for (1734ds/5446Mi) 45.42/7.01 % (15956)Instruction limit reached! 45.42/7.01 % (15956)------------------------------ 45.42/7.01 % (15956)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 45.42/7.01 % (15956)Termination reason: Unknown 45.42/7.01 % (15956)Termination phase: Property scanning 45.42/7.01 45.42/7.01 % (15956)Memory used [KB]: 2046 45.42/7.01 % (15956)Time elapsed: 0.076 s 45.42/7.01 % (15956)Instructions burned: 364 (million) 45.42/7.01 % (15956)------------------------------ 45.42/7.01 % (15956)------------------------------ 45.42/7.02 % (15958)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=2573:si=on:rtra=on_0 on E---3.1_15619 for (1733ds/2573Mi) 45.80/7.08 % (15948)Instruction limit reached! 45.80/7.08 % (15948)------------------------------ 45.80/7.08 % (15948)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 45.80/7.08 % (15948)Termination reason: Unknown 45.80/7.08 % (15948)Termination phase: Saturation 45.80/7.08 45.80/7.08 % (15948)Memory used [KB]: 6908 45.80/7.08 % (15948)Time elapsed: 0.666 s 45.80/7.08 % (15948)Instructions burned: 2812 (million) 45.80/7.08 % (15948)------------------------------ 45.80/7.08 % (15948)------------------------------ 45.80/7.09 % (15959)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=2655:si=on:rtra=on_0 on E---3.1_15619 for (1733ds/2655Mi) 47.30/7.20 % (15954)Instruction limit reached! 47.30/7.20 % (15954)------------------------------ 47.30/7.20 % (15954)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 47.30/7.20 % (15954)Termination reason: Unknown 47.30/7.20 % (15954)Termination phase: Property scanning 47.30/7.20 47.30/7.20 % (15954)Memory used [KB]: 2046 47.30/7.20 % (15954)Time elapsed: 0.324 s 47.30/7.20 % (15954)Instructions burned: 1432 (million) 47.30/7.20 % (15954)------------------------------ 47.30/7.20 % (15954)------------------------------ 47.30/7.21 % (15960)dis+1002_16:1_apa=on:au=on:av=off:cnfonf=off:e2e=on:nm=0:nwc=10.0:i=2781:si=on:rtra=on_0 on E---3.1_15619 for (1731ds/2781Mi) 48.37/7.35 % (15950)Instruction limit reached! 48.37/7.35 % (15950)------------------------------ 48.37/7.35 % (15950)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 48.37/7.35 % (15950)Termination reason: Unknown 48.37/7.35 % (15950)Termination phase: Saturation 48.37/7.35 48.37/7.35 % (15950)Memory used [KB]: 6908 48.37/7.35 % (15950)Time elapsed: 0.627 s 48.37/7.35 % (15950)Instructions burned: 2679 (million) 48.37/7.35 % (15950)------------------------------ 48.37/7.35 % (15950)------------------------------ 48.54/7.36 % (15961)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on E---3.1_15619 for (1730ds/307Mi) 48.54/7.42 % (15961)Instruction limit reached! 48.54/7.42 % (15961)------------------------------ 48.54/7.42 % (15961)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 48.54/7.42 % (15961)Termination reason: Unknown 48.54/7.42 % (15961)Termination phase: Property scanning 48.54/7.42 48.54/7.42 % (15961)Memory used [KB]: 2046 48.54/7.42 % (15961)Time elapsed: 0.064 s 48.54/7.42 % (15961)Instructions burned: 309 (million) 48.54/7.42 % (15961)------------------------------ 48.54/7.42 % (15961)------------------------------ 48.93/7.43 % (15962)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=1548:si=on:rtra=on_0 on E---3.1_15619 for (1729ds/1548Mi) 48.93/7.45 % (15953)Instruction limit reached! 48.93/7.45 % (15953)------------------------------ 48.93/7.45 % (15953)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 48.93/7.45 % (15953)Termination reason: Unknown 48.93/7.45 % (15953)Termination phase: Saturation 48.93/7.45 48.93/7.45 % (15953)Memory used [KB]: 6908 48.93/7.45 % (15953)Time elapsed: 0.592 s 48.93/7.45 % (15953)Instructions burned: 2547 (million) 48.93/7.45 % (15953)------------------------------ 48.93/7.45 % (15953)------------------------------ 48.93/7.45 % (15963)lrs+10_1:3_alpa=true:hud=3:ins=1:ntd=on:plsq=on:plsqc=1:plsqr=32,1:prag=on:s2a=on:s2agt=10:i=5214:si=on:rtra=on_0 on E---3.1_15619 for (1729ds/5214Mi) 49.54/7.62 % (15958)Instruction limit reached! 49.54/7.62 % (15958)------------------------------ 49.54/7.62 % (15958)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 49.54/7.62 % (15958)Termination reason: Unknown 49.54/7.62 % (15958)Termination phase: Saturation 49.54/7.62 49.54/7.62 % (15958)Memory used [KB]: 6908 49.54/7.62 % (15958)Time elapsed: 0.605 s 49.54/7.62 % (15958)Instructions burned: 2576 (million) 49.54/7.62 % (15958)------------------------------ 49.54/7.62 % (15958)------------------------------ 49.79/7.63 % (15964)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on E---3.1_15619 for (1727ds/3201Mi) 50.84/7.70 % (15959)Instruction limit reached! 50.84/7.70 % (15959)------------------------------ 50.84/7.70 % (15959)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 50.84/7.70 % (15959)Termination reason: Unknown 50.84/7.70 % (15959)Termination phase: Saturation 50.84/7.70 50.84/7.70 % (15959)Memory used [KB]: 2430 50.84/7.70 % (15959)Time elapsed: 0.611 s 50.84/7.70 % (15959)Instructions burned: 2657 (million) 50.84/7.70 % (15959)------------------------------ 50.84/7.70 % (15959)------------------------------ 50.84/7.71 % (15965)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=454:si=on:rtra=on_0 on E---3.1_15619 for (1726ds/454Mi) 51.49/7.81 % (15965)Instruction limit reached! 51.49/7.81 % (15965)------------------------------ 51.49/7.81 % (15965)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 51.49/7.81 % (15965)Termination reason: Unknown 51.49/7.81 % (15965)Termination phase: Property scanning 51.49/7.81 51.49/7.81 % (15965)Memory used [KB]: 2046 51.49/7.81 % (15965)Time elapsed: 0.099 s 51.49/7.81 % (15965)Instructions burned: 455 (million) 51.49/7.81 % (15965)------------------------------ 51.49/7.81 % (15965)------------------------------ 51.49/7.82 % (15966)lrs+1002_1:32_au=on:ins=2:nm=16:ntd=on:piset=all_but_not_eq:sp=occurrence:i=3049:si=on:rtra=on_0 on E---3.1_15619 for (1725ds/3049Mi) 52.12/7.86 % (15960)Instruction limit reached! 52.12/7.86 % (15960)------------------------------ 52.12/7.86 % (15960)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 52.12/7.86 % (15960)Termination reason: Unknown 52.12/7.86 % (15960)Termination phase: Saturation 52.12/7.86 52.12/7.86 % (15960)Memory used [KB]: 2430 52.12/7.86 % (15960)Time elapsed: 0.650 s 52.12/7.86 % (15960)Instructions burned: 2782 (million) 52.12/7.86 % (15960)------------------------------ 52.12/7.86 % (15960)------------------------------ 52.12/7.87 % (15967)lrs+1010_1:1_bd=preordered:cnfonf=off:e2e=on:kws=inv_precedence:lwlo=on:sd=2:ss=axioms:i=7311:si=on:rtra=on_0 on E---3.1_15619 for (1725ds/7311Mi) 52.43/7.93 % (15962)Instruction limit reached! 52.43/7.93 % (15962)------------------------------ 52.43/7.93 % (15962)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 52.43/7.93 % (15962)Termination reason: Unknown 52.43/7.93 % (15962)Termination phase: Saturation 52.43/7.93 52.43/7.93 % (15962)Memory used [KB]: 10618 52.43/7.93 % (15962)Time elapsed: 0.490 s 52.43/7.93 % (15962)Instructions burned: 1548 (million) 52.43/7.93 % (15962)------------------------------ 52.43/7.93 % (15962)------------------------------ 52.43/7.94 % (15968)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=6804:si=on:rtra=on_0 on E---3.1_15619 for (1724ds/6804Mi) 52.43/7.96 % (15968)Refutation not found, incomplete strategy 52.43/7.96 % (15968)------------------------------ 52.43/7.96 % (15968)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 52.43/7.96 % (15968)Termination reason: Refutation not found, incomplete strategy 52.43/7.96 52.43/7.96 52.43/7.96 % (15968)Memory used [KB]: 6396 52.43/7.96 % (15968)Time elapsed: 0.020 s 52.43/7.96 % (15968)Instructions burned: 65 (million) 52.43/7.96 % (15968)------------------------------ 52.43/7.96 % (15968)------------------------------ 52.63/7.97 % (15949)Instruction limit reached! 52.63/7.97 % (15949)------------------------------ 52.63/7.97 % (15949)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 52.63/7.97 % (15949)Termination reason: Unknown 52.63/7.97 % (15949)Termination phase: Saturation 52.63/7.97 52.63/7.97 % (15949)Memory used [KB]: 13176 52.63/7.97 % (15949)Time elapsed: 1.419 s 52.63/7.97 % (15949)Instructions burned: 4604 (million) 52.63/7.97 % (15949)------------------------------ 52.63/7.97 % (15949)------------------------------ 52.63/7.97 % (15969)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1683:si=on:rtra=on_0 on E---3.1_15619 for (1724ds/1683Mi) 52.63/7.97 % (15970)lrs+10_8:1_au=on:av=off:bd=off:cs=on:e2e=on:hfsq=on:hfsqc=50:hfsql=off:nm=0:i=4688:si=on:rtra=on_0 on E---3.1_15619 for (1724ds/4688Mi) 55.02/8.30 % (15957)Instruction limit reached! 55.02/8.30 % (15957)------------------------------ 55.02/8.30 % (15957)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 55.02/8.30 % (15957)Termination reason: Unknown 55.02/8.30 % (15957)Termination phase: Saturation 55.02/8.30 55.02/8.30 % (15957)Memory used [KB]: 6908 55.02/8.30 % (15957)Time elapsed: 1.305 s 55.02/8.30 % (15957)Instructions burned: 5448 (million) 55.02/8.30 % (15957)------------------------------ 55.02/8.30 % (15957)------------------------------ 55.02/8.31 % (15971)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on E---3.1_15619 for (1720ds/2207Mi) 55.68/8.39 % (15964)Instruction limit reached! 55.68/8.39 % (15964)------------------------------ 55.68/8.39 % (15964)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 55.68/8.39 % (15964)Termination reason: Unknown 55.68/8.39 % (15964)Termination phase: Saturation 55.68/8.39 55.68/8.39 % (15964)Memory used [KB]: 6908 55.68/8.39 % (15964)Time elapsed: 0.761 s 55.68/8.39 % (15964)Instructions burned: 3204 (million) 55.68/8.39 % (15964)------------------------------ 55.68/8.39 % (15964)------------------------------ 55.68/8.40 % (15972)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=8216:si=on:rtra=on_0 on E---3.1_15619 for (1720ds/8216Mi) 56.06/8.50 % (15969)Instruction limit reached! 56.06/8.50 % (15969)------------------------------ 56.06/8.50 % (15969)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 56.06/8.50 % (15969)Termination reason: Unknown 56.06/8.50 % (15969)Termination phase: Saturation 56.06/8.50 56.06/8.50 % (15969)Memory used [KB]: 9850 56.06/8.50 % (15969)Time elapsed: 0.536 s 56.06/8.50 % (15969)Instructions burned: 1685 (million) 56.06/8.50 % (15969)------------------------------ 56.06/8.50 % (15969)------------------------------ 56.06/8.51 % (15973)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=430:si=on:rtra=on_0 on E---3.1_15619 for (1719ds/430Mi) 56.44/8.53 % (15966)Instruction limit reached! 56.44/8.53 % (15966)------------------------------ 56.44/8.53 % (15966)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 56.44/8.53 % (15966)Termination reason: Unknown 56.44/8.53 % (15966)Termination phase: Saturation 56.44/8.53 56.44/8.53 % (15966)Memory used [KB]: 6908 56.44/8.53 % (15966)Time elapsed: 0.716 s 56.44/8.53 % (15966)Instructions burned: 3052 (million) 56.44/8.53 % (15966)------------------------------ 56.44/8.53 % (15966)------------------------------ 56.44/8.54 % (15974)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=2012:si=on:rtra=on_0 on E---3.1_15619 for (1718ds/2012Mi) 56.62/8.60 % (15973)Instruction limit reached! 56.62/8.60 % (15973)------------------------------ 56.62/8.60 % (15973)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 56.62/8.60 % (15973)Termination reason: Unknown 56.62/8.60 % (15973)Termination phase: Property scanning 56.62/8.60 56.62/8.60 % (15973)Memory used [KB]: 2046 56.62/8.60 % (15973)Time elapsed: 0.092 s 56.62/8.60 % (15973)Instructions burned: 434 (million) 56.62/8.60 % (15973)------------------------------ 56.62/8.60 % (15973)------------------------------ 56.62/8.61 % (15975)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=631:si=on:rtra=on_0 on E---3.1_15619 for (1718ds/631Mi) 57.02/8.71 % (15963)Instruction limit reached! 57.02/8.71 % (15963)------------------------------ 57.02/8.71 % (15963)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 57.02/8.71 % (15963)Termination reason: Unknown 57.02/8.71 % (15963)Termination phase: Saturation 57.02/8.71 57.02/8.71 % (15963)Memory used [KB]: 6908 57.02/8.71 % (15963)Time elapsed: 1.255 s 57.02/8.71 % (15963)Instructions burned: 5216 (million) 57.02/8.71 % (15963)------------------------------ 57.02/8.71 % (15963)------------------------------ 57.02/8.72 % (15976)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=8785:si=on:rtra=on_0 on E---3.1_15619 for (1716ds/8785Mi) 57.16/8.75 % (15975)Instruction limit reached! 57.16/8.75 % (15975)------------------------------ 57.16/8.75 % (15975)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 57.16/8.75 % (15975)Termination reason: Unknown 57.16/8.75 % (15975)Termination phase: Property scanning 57.16/8.75 57.16/8.75 % (15975)Memory used [KB]: 1918 57.16/8.75 % (15975)Time elapsed: 0.139 s 57.16/8.75 % (15975)Instructions burned: 634 (million) 57.16/8.75 % (15975)------------------------------ 57.16/8.75 % (15975)------------------------------ 58.43/8.76 % (15977)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=739:si=on:rtra=on_0 on E---3.1_15619 for (1716ds/739Mi) 58.43/8.82 % (15971)Instruction limit reached! 58.43/8.82 % (15971)------------------------------ 58.43/8.82 % (15971)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 58.43/8.82 % (15971)Termination reason: Unknown 58.43/8.82 % (15971)Termination phase: Saturation 58.43/8.82 58.43/8.82 % (15971)Memory used [KB]: 6908 58.43/8.82 % (15971)Time elapsed: 0.513 s 58.43/8.82 % (15971)Instructions burned: 2209 (million) 58.43/8.82 % (15971)------------------------------ 58.43/8.82 % (15971)------------------------------ 58.86/8.83 % (15978)dis+1002_1:1024_fe=off:hud=5:prag=on:i=5473:si=on:rtra=on_0 on E---3.1_15619 for (1715ds/5473Mi) 59.51/9.00 % (15977)Instruction limit reached! 59.51/9.00 % (15977)------------------------------ 59.51/9.00 % (15977)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 59.51/9.00 % (15977)Termination reason: Unknown 59.51/9.00 % (15977)Termination phase: Saturation 59.51/9.00 59.51/9.00 % (15977)Memory used [KB]: 7803 59.51/9.00 % (15977)Time elapsed: 0.240 s 59.51/9.00 % (15977)Instructions burned: 741 (million) 59.51/9.00 % (15977)------------------------------ 59.51/9.00 % (15977)------------------------------ 59.51/9.00 % (15974)Instruction limit reached! 59.51/9.00 % (15974)------------------------------ 59.51/9.00 % (15974)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 59.51/9.00 % (15974)Termination reason: Unknown 59.51/9.00 % (15974)Termination phase: Saturation 59.51/9.00 59.51/9.00 % (15974)Memory used [KB]: 11385 59.51/9.00 % (15974)Time elapsed: 0.460 s 59.51/9.00 % (15974)Instructions burned: 2012 (million) 59.51/9.00 % (15974)------------------------------ 59.51/9.00 % (15974)------------------------------ 59.51/9.01 % (15979)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=43570:si=on:rtra=on_0 on E---3.1_15619 for (1714ds/43570Mi) 59.51/9.01 % (15980)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=8382:si=on:rtra=on_0 on E---3.1_15619 for (1714ds/8382Mi) 60.00/9.02 % (15979)Refutation not found, incomplete strategy 60.00/9.02 % (15979)------------------------------ 60.00/9.02 % (15979)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 60.00/9.02 % (15979)Termination reason: Refutation not found, incomplete strategy 60.00/9.02 60.00/9.02 60.00/9.02 % (15979)Memory used [KB]: 6140 60.00/9.02 % (15979)Time elapsed: 0.012 s 60.00/9.02 % (15979)Instructions burned: 34 (million) 60.00/9.02 % (15979)------------------------------ 60.00/9.02 % (15979)------------------------------ 60.00/9.02 % (15981)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=407:si=on:rtra=on_0 on E---3.1_15619 for (1713ds/407Mi) 60.16/9.10 % (15970)Instruction limit reached! 60.16/9.10 % (15970)------------------------------ 60.16/9.10 % (15970)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 60.16/9.10 % (15970)Termination reason: Unknown 60.16/9.10 % (15970)Termination phase: Saturation 60.16/9.10 60.16/9.10 % (15970)Memory used [KB]: 2814 60.16/9.10 % (15970)Time elapsed: 1.126 s 60.16/9.10 % (15970)Instructions burned: 4691 (million) 60.16/9.10 % (15970)------------------------------ 60.16/9.10 % (15970)------------------------------ 60.16/9.11 % (15982)lrs+10_1:50_cbe=off:cnfonf=lazy_pi_sigma_gen:fe=off:hud=5:plsq=on:plsqr=1,32:sos=all:i=2971:si=on:rtra=on_0 on E---3.1_15619 for (1713ds/2971Mi) 60.16/9.11 % (15981)Instruction limit reached! 60.16/9.11 % (15981)------------------------------ 60.16/9.11 % (15981)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 60.16/9.11 % (15981)Termination reason: Unknown 60.16/9.11 % (15981)Termination phase: Property scanning 60.16/9.11 60.16/9.11 % (15981)Memory used [KB]: 1918 60.16/9.11 % (15981)Time elapsed: 0.088 s 60.16/9.11 % (15981)Instructions burned: 410 (million) 60.16/9.11 % (15981)------------------------------ 60.16/9.11 % (15981)------------------------------ 60.16/9.12 % (15983)lrs+1002_1:1_aac=none:bd=off:e2e=on:fde=none:fe=off:piset=or:prag=on:rawr=on:sos=on:updr=off:i=9822:si=on:rtra=on_0 on E---3.1_15619 for (1712ds/9822Mi) 60.57/9.14 % (15983)Refutation not found, incomplete strategy 60.57/9.14 % (15983)------------------------------ 60.57/9.14 % (15983)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 60.57/9.14 % (15983)Termination reason: Refutation not found, incomplete strategy 60.57/9.14 60.57/9.14 60.57/9.14 % (15983)Memory used [KB]: 6396 60.57/9.14 % (15983)Time elapsed: 0.022 s 60.57/9.14 % (15983)Instructions burned: 70 (million) 60.57/9.14 % (15983)------------------------------ 60.57/9.14 % (15983)------------------------------ 60.57/9.15 % (15984)dis+10_5:1_av=off:ntd=on:s2a=on:s2at=3.0:sgt=16:sp=unary_frequency:ss=axioms:i=8425:si=on:rtra=on_0 on E---3.1_15619 for (1712ds/8425Mi) 65.56/9.80 % (15982)Instruction limit reached! 65.56/9.80 % (15982)------------------------------ 65.56/9.80 % (15982)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 65.56/9.80 % (15982)Termination reason: Unknown 65.56/9.80 % (15982)Termination phase: Saturation 65.56/9.80 65.56/9.80 % (15982)Memory used [KB]: 2430 65.56/9.80 % (15982)Time elapsed: 0.692 s 65.56/9.80 % (15982)Instructions burned: 2973 (million) 65.56/9.80 % (15982)------------------------------ 65.56/9.80 % (15982)------------------------------ 65.56/9.81 % (15985)lrs+30_1:1_aac=none:au=on:cbe=off:cs=on:nm=2:rawr=on:sos=on:i=3107:si=on:rtra=on_0 on E---3.1_15619 for (1705ds/3107Mi) 66.88/9.99 % (15967)Instruction limit reached! 66.88/9.99 % (15967)------------------------------ 66.88/9.99 % (15967)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 66.88/9.99 % (15967)Termination reason: Unknown 66.88/9.99 % (15967)Termination phase: Saturation 66.88/9.99 66.88/9.99 % (15967)Memory used [KB]: 21492 66.88/9.99 % (15967)Time elapsed: 2.123 s 66.88/9.99 % (15967)Instructions burned: 7312 (million) 66.88/9.99 % (15967)------------------------------ 66.88/9.99 % (15967)------------------------------ 66.88/10.00 % (15986)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=7967:si=on:rtra=on_0 on E---3.1_15619 for (1704ds/7967Mi) 67.55/10.12 % (15978)Instruction limit reached! 67.55/10.12 % (15978)------------------------------ 67.55/10.12 % (15978)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 67.55/10.12 % (15978)Termination reason: Unknown 67.55/10.12 % (15978)Termination phase: Saturation 67.55/10.12 67.55/10.12 % (15978)Memory used [KB]: 6908 67.55/10.12 % (15978)Time elapsed: 1.289 s 67.55/10.12 % (15978)Instructions burned: 5475 (million) 67.55/10.12 % (15978)------------------------------ 67.55/10.12 % (15978)------------------------------ 67.86/10.13 % (15987)lrs+1010_10:959_abs=on:acc=on:bd=off:ccuc=small_ones:cha=on:cnfonf=lazy_simp:fd=preordered:fe=off:hud=3:ile=on:kws=inv_frequency:nm=2:piset=and:sd=5:sp=frequency:spb=goal_then_units:ss=axioms:st=4.5:i=3629:si=on:rtra=on_0 on E---3.1_15619 for (1702ds/3629Mi) 70.83/10.53 % (15985)Instruction limit reached! 70.83/10.53 % (15985)------------------------------ 70.83/10.53 % (15985)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 70.83/10.53 % (15985)Termination reason: Unknown 70.83/10.53 % (15985)Termination phase: Saturation 70.83/10.53 70.83/10.53 % (15985)Memory used [KB]: 2430 70.83/10.53 % (15985)Time elapsed: 0.727 s 70.83/10.53 % (15985)Instructions burned: 3110 (million) 70.83/10.53 % (15985)------------------------------ 70.83/10.53 % (15985)------------------------------ 70.83/10.54 % (15988)lrs+1010_1:1024_au=on:fe=axiom:lwlo=on:nm=0:ntd=on:nwc=10.0:spb=non_intro:uhcvi=on:i=939:si=on:rtra=on_0 on E---3.1_15619 for (1698ds/939Mi) 71.97/10.75 % (15988)Instruction limit reached! 71.97/10.75 % (15988)------------------------------ 71.97/10.75 % (15988)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 71.97/10.75 % (15988)Termination reason: Unknown 71.97/10.75 % (15988)Termination phase: Property scanning 71.97/10.75 71.97/10.75 % (15988)Memory used [KB]: 1918 71.97/10.75 % (15988)Time elapsed: 0.209 s 71.97/10.75 % (15988)Instructions burned: 939 (million) 71.97/10.75 % (15988)------------------------------ 71.97/10.75 % (15988)------------------------------ 71.97/10.76 % (15989)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on E---3.1_15619 for (1696ds/1188Mi) 72.40/10.81 % (15976)Instruction limit reached! 72.40/10.81 % (15976)------------------------------ 72.40/10.81 % (15976)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 72.40/10.81 % (15976)Termination reason: Unknown 72.40/10.81 % (15976)Termination phase: Saturation 72.40/10.81 72.40/10.81 % (15976)Memory used [KB]: 6908 72.40/10.81 % (15976)Time elapsed: 2.066 s 72.40/10.81 % (15976)Instructions burned: 8785 (million) 72.40/10.81 % (15976)------------------------------ 72.40/10.81 % (15976)------------------------------ 72.40/10.82 % (15990)dis+21_3:2_avsq=on:cbe=off:e2e=on:flr=on:ile=on:nwc=5.0:piset=or:rawr=on:sp=occurrence:i=3205:si=on:rtra=on_0 on E---3.1_15619 for (1695ds/3205Mi) 72.99/10.89 % (15972)Instruction limit reached! 72.99/10.89 % (15972)------------------------------ 72.99/10.89 % (15972)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 72.99/10.89 % (15972)Termination reason: Unknown 72.99/10.89 % (15972)Termination phase: Saturation 72.99/10.89 72.99/10.89 % (15972)Memory used [KB]: 11513 72.99/10.89 % (15972)Time elapsed: 2.493 s 72.99/10.89 % (15972)Instructions burned: 8216 (million) 72.99/10.89 % (15972)------------------------------ 72.99/10.89 % (15972)------------------------------ 72.99/10.90 % (15991)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on E---3.1_15619 for (1695ds/865Mi) 73.29/10.95 % (15980)Instruction limit reached! 73.29/10.95 % (15980)------------------------------ 73.29/10.95 % (15980)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 73.29/10.95 % (15980)Termination reason: Unknown 73.29/10.95 % (15980)Termination phase: Saturation 73.29/10.95 73.29/10.95 % (15980)Memory used [KB]: 7036 73.29/10.95 % (15980)Time elapsed: 1.942 s 73.29/10.95 % (15980)Instructions burned: 8386 (million) 73.29/10.95 % (15980)------------------------------ 73.29/10.95 % (15980)------------------------------ 73.29/10.96 % (15992)ott+1002_1:1_au=on:bd=off:cbe=off:cha=on:cnfonf=lazy_pi_sigma_gen:fd=off:fe=off:ntd=on:sp=const_frequency:i=7469:si=on:rtra=on_0 on E---3.1_15619 for (1694ds/7469Mi) 73.85/10.98 % (15987)Instruction limit reached! 73.85/10.98 % (15987)------------------------------ 73.85/10.98 % (15987)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 73.85/10.98 % (15987)Termination reason: Unknown 73.85/10.98 % (15987)Termination phase: Saturation 73.85/10.98 73.85/10.98 % (15987)Memory used [KB]: 6908 73.85/10.98 % (15987)Time elapsed: 0.853 s 73.85/10.98 % (15987)Instructions burned: 3629 (million) 73.85/10.98 % (15987)------------------------------ 73.85/10.98 % (15987)------------------------------ 73.85/10.99 % (15993)dis+10_1:10_bd=preordered:e2e=on:fde=none:fe=axiom:hud=3:kws=precedence:nwc=3.0:prag=on:sp=const_max:tgt=full:i=4165:si=on:rtra=on_0 on E---3.1_15619 for (1694ds/4165Mi) 73.85/11.02 % (15989)Instruction limit reached! 73.85/11.02 % (15989)------------------------------ 73.85/11.02 % (15989)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 73.85/11.02 % (15989)Termination reason: Unknown 73.85/11.02 % (15989)Termination phase: Property scanning 73.85/11.02 73.85/11.02 % (15989)Memory used [KB]: 2046 73.85/11.02 % (15989)Time elapsed: 0.264 s 73.85/11.02 % (15989)Instructions burned: 1192 (million) 73.85/11.02 % (15989)------------------------------ 73.85/11.02 % (15989)------------------------------ 73.85/11.03 % (15994)dis+1010_1:1_au=on:avsq=on:cnfonf=lazy_simp:fsr=off:ntd=on:nwc=10.0:sp=reverse_frequency:ss=axioms:st=1.5:i=13468:si=on:rtra=on_0 on E---3.1_15619 for (1693ds/13468Mi) 74.46/11.09 % (15991)Instruction limit reached! 74.46/11.09 % (15991)------------------------------ 74.46/11.09 % (15991)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 74.46/11.09 % (15991)Termination reason: Unknown 74.46/11.09 % (15991)Termination phase: Property scanning 74.46/11.09 74.46/11.09 % (15991)Memory used [KB]: 2046 74.46/11.09 % (15991)Time elapsed: 0.195 s 74.46/11.09 % (15991)Instructions burned: 866 (million) 74.46/11.10 % (15991)------------------------------ 74.46/11.10 % (15991)------------------------------ 74.46/11.10 % (15995)dis+1002_1:1_au=on:bsr=unit_only:cbe=off:fe=off:fsr=off:nm=10:nwc=6.0:plsq=on:plsqc=1:plsqr=32,1:sos=all:i=2635:si=on:rtra=on_0 on E---3.1_15619 for (1693ds/2635Mi) 74.46/11.11 % (15984)Instruction limit reached! 74.46/11.11 % (15984)------------------------------ 74.46/11.11 % (15984)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 74.46/11.11 % (15984)Termination reason: Unknown 74.46/11.11 % (15984)Termination phase: Saturation 74.46/11.11 74.46/11.11 % (15984)Memory used [KB]: 2430 74.46/11.11 % (15984)Time elapsed: 1.966 s 74.46/11.11 % (15984)Instructions burned: 8428 (million) 74.46/11.11 % (15984)------------------------------ 74.46/11.11 % (15984)------------------------------ 74.46/11.12 % (15996)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=631:si=on:rtra=on_0 on E---3.1_15619 for (1692ds/631Mi) 75.09/11.26 % (15996)Instruction limit reached! 75.09/11.26 % (15996)------------------------------ 75.09/11.26 % (15996)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 75.09/11.26 % (15996)Termination reason: Unknown 75.09/11.26 % (15996)Termination phase: Property scanning 75.09/11.26 75.09/11.26 % (15996)Memory used [KB]: 2046 75.09/11.26 % (15996)Time elapsed: 0.139 s 75.09/11.26 % (15996)Instructions burned: 633 (million) 75.09/11.26 % (15996)------------------------------ 75.09/11.26 % (15996)------------------------------ 75.09/11.27 % (15997)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=15557:si=on:rtra=on_0 on E---3.1_15619 for (1691ds/15557Mi) 78.06/11.60 % (15990)Instruction limit reached! 78.06/11.60 % (15990)------------------------------ 78.06/11.60 % (15990)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 78.06/11.60 % (15990)Termination reason: Unknown 78.06/11.60 % (15990)Termination phase: Saturation 78.06/11.60 78.06/11.60 % (15990)Memory used [KB]: 6908 78.06/11.60 % (15990)Time elapsed: 0.770 s 78.06/11.60 % (15990)Instructions burned: 3207 (million) 78.06/11.60 % (15990)------------------------------ 78.06/11.60 % (15990)------------------------------ 78.06/11.61 % (15998)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2142:si=on:rtra=on_0 on E---3.1_15619 for (1688ds/2142Mi) 79.00/11.73 % (15995)Instruction limit reached! 79.00/11.73 % (15995)------------------------------ 79.00/11.73 % (15995)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 79.00/11.73 % (15995)Termination reason: Unknown 79.00/11.73 % (15995)Termination phase: Saturation 79.00/11.73 79.00/11.73 % (15995)Memory used [KB]: 2430 79.00/11.73 % (15995)Time elapsed: 0.630 s 79.00/11.73 % (15995)Instructions burned: 2638 (million) 79.00/11.73 % (15995)------------------------------ 79.00/11.73 % (15995)------------------------------ 79.00/11.74 % (15999)dis+1002_1:1_aac=none:au=on:bd=off:cnfonf=conj_eager:nwc=5.0:sgt=5:sp=reverse_arity:ss=axioms:i=5624:si=on:rtra=on_0 on E---3.1_15619 for (1686ds/5624Mi) 79.13/11.76 % (15999)Refutation not found, incomplete strategy 79.13/11.76 % (15999)------------------------------ 79.13/11.76 % (15999)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 79.13/11.76 % (15999)Termination reason: Refutation not found, incomplete strategy 79.13/11.76 79.13/11.76 79.13/11.76 % (15999)Memory used [KB]: 6396 79.13/11.76 % (15999)Time elapsed: 0.017 s 79.13/11.76 % (15999)Instructions burned: 54 (million) 79.13/11.76 % (15999)------------------------------ 79.13/11.76 % (15999)------------------------------ 79.13/11.77 % (16000)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=1665:si=on:rtra=on_0 on E---3.1_15619 for (1686ds/1665Mi) 79.78/11.92 % (15986)Instruction limit reached! 79.78/11.92 % (15986)------------------------------ 79.78/11.92 % (15986)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 79.78/11.92 % (15986)Termination reason: Unknown 79.78/11.92 % (15986)Termination phase: Saturation 79.78/11.92 79.78/11.92 % (15986)Memory used [KB]: 2558 79.78/11.92 % (15986)Time elapsed: 1.918 s 79.78/11.92 % (15986)Instructions burned: 7970 (million) 79.78/11.92 % (15986)------------------------------ 79.78/11.92 % (15986)------------------------------ 79.78/11.93 % (16001)dis+1002_1:1_av=off:prag=on:sd=1:sos=on:sp=occurrence:ss=axioms:i=64912:si=on:rtra=on_0 on E---3.1_15619 for (1684ds/64912Mi) 81.97/12.14 % (16000)Instruction limit reached! 81.97/12.14 % (16000)------------------------------ 81.97/12.14 % (16000)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 81.97/12.14 % (16000)Termination reason: Unknown 81.97/12.14 % (16000)Termination phase: Saturation 81.97/12.14 81.97/12.14 % (16000)Memory used [KB]: 6652 81.97/12.14 % (16000)Time elapsed: 0.375 s 81.97/12.14 % (16000)Instructions burned: 1667 (million) 81.97/12.14 % (16000)------------------------------ 81.97/12.14 % (16000)------------------------------ 81.97/12.15 % (16002)lrs+10_1:32_atotf=0.1:avsq=on:bsr=on:cnfonf=lazy_gen:fde=unused:i=7801:si=on:rtra=on_0 on E---3.1_15619 for (1682ds/7801Mi) 82.75/12.30 % (15998)Instruction limit reached! 82.75/12.30 % (15998)------------------------------ 82.75/12.30 % (15998)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 82.75/12.30 % (15998)Termination reason: Unknown 82.75/12.30 % (15998)Termination phase: Saturation 82.75/12.30 82.75/12.30 % (15998)Memory used [KB]: 9594 82.75/12.30 % (15998)Time elapsed: 0.687 s 82.75/12.30 % (15998)Instructions burned: 2143 (million) 82.75/12.30 % (15998)------------------------------ 82.75/12.30 % (15998)------------------------------ 82.75/12.30 % (16003)ott+2_1:1_au=on:hfsq=on:hfsqc=5:hfsql=off:nwc=5.0:sd=3:ss=axioms:st=5.0:i=15194:si=on:rtra=on_0 on E---3.1_15619 for (1681ds/15194Mi) 83.05/12.34 % (15993)Instruction limit reached! 83.05/12.34 % (15993)------------------------------ 83.05/12.34 % (15993)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 83.05/12.34 % (15993)Termination reason: Unknown 83.05/12.34 % (15993)Termination phase: Saturation 83.05/12.34 83.05/12.34 % (15993)Memory used [KB]: 15095 83.05/12.34 % (15993)Time elapsed: 1.353 s 83.05/12.34 % (15993)Instructions burned: 4167 (million) 83.05/12.34 % (15993)------------------------------ 83.05/12.34 % (15993)------------------------------ 83.23/12.35 % (16004)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=6753:si=on:rtra=on_0 on E---3.1_15619 for (1680ds/6753Mi) 83.23/12.37 % (16004)Refutation not found, incomplete strategy 83.23/12.37 % (16004)------------------------------ 83.23/12.37 % (16004)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 83.23/12.37 % (16004)Termination reason: Refutation not found, incomplete strategy 83.23/12.37 83.23/12.37 83.23/12.37 % (16004)Memory used [KB]: 6396 83.23/12.37 % (16004)Time elapsed: 0.022 s 83.23/12.37 % (16004)Instructions burned: 69 (million) 83.23/12.37 % (16004)------------------------------ 83.23/12.37 % (16004)------------------------------ 83.23/12.38 % (16005)lrs+1002_1:28_bd=off:cnfonf=lazy_simp:plsq=on:plsqr=1,1:prag=on:i=1003:si=on:rtra=on_0 on E---3.1_15619 for (1680ds/1003Mi) 84.12/12.61 % (16005)Instruction limit reached! 84.12/12.61 % (16005)------------------------------ 84.12/12.61 % (16005)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 84.12/12.61 % (16005)Termination reason: Unknown 84.12/12.61 % (16005)Termination phase: Property scanning 84.12/12.61 84.12/12.61 % (16005)Memory used [KB]: 2046 84.12/12.61 % (16005)Time elapsed: 0.228 s 84.12/12.61 % (16005)Instructions burned: 1004 (million) 84.12/12.61 % (16005)------------------------------ 84.12/12.61 % (16005)------------------------------ 84.12/12.62 % (16006)ott-21_5:4_atotf=0.3:e2e=on:hud=15:ins=1:plsq=on:plsqc=1:plsqr=32,1:sp=unary_frequency:tnu=2:i=13018:si=on:rtra=on_0 on E---3.1_15619 for (1677ds/13018Mi) 86.24/12.76 % (15992)Instruction limit reached! 86.24/12.76 % (15992)------------------------------ 86.24/12.76 % (15992)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 86.24/12.76 % (15992)Termination reason: Unknown 86.24/12.76 % (15992)Termination phase: Saturation 86.24/12.76 86.24/12.76 % (15992)Memory used [KB]: 6908 86.24/12.76 % (15992)Time elapsed: 1.803 s 86.24/12.76 % (15992)Instructions burned: 7470 (million) 86.24/12.76 % (15992)------------------------------ 86.24/12.76 % (15992)------------------------------ 86.24/12.77 % (16007)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1267:si=on:rtra=on_0 on E---3.1_15619 for (1676ds/1267Mi) 89.11/13.17 % (16007)Instruction limit reached! 89.11/13.17 % (16007)------------------------------ 89.11/13.17 % (16007)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 89.11/13.17 % (16007)Termination reason: Unknown 89.11/13.17 % (16007)Termination phase: Saturation 89.11/13.17 89.11/13.17 % (16007)Memory used [KB]: 8443 89.11/13.17 % (16007)Time elapsed: 0.400 s 89.11/13.17 % (16007)Instructions burned: 1269 (million) 89.11/13.17 % (16007)------------------------------ 89.11/13.17 % (16007)------------------------------ 89.11/13.18 % (16008)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=2570:si=on:rtra=on_0 on E---3.1_15619 for (1672ds/2570Mi) 93.32/13.78 % (16008)Instruction limit reached! 93.32/13.78 % (16008)------------------------------ 93.32/13.78 % (16008)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 93.32/13.78 % (16008)Termination reason: Unknown 93.32/13.78 % (16008)Termination phase: Saturation 93.32/13.78 93.32/13.78 % (16008)Memory used [KB]: 6908 93.32/13.78 % (16008)Time elapsed: 0.603 s 93.32/13.78 % (16008)Instructions burned: 2572 (million) 93.32/13.78 % (16008)------------------------------ 93.32/13.78 % (16008)------------------------------ 93.32/13.79 % (16009)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=13163:si=on:rtra=on_0 on E---3.1_15619 for (1666ds/13163Mi) 98.90/14.61 % (16002)Instruction limit reached! 98.90/14.61 % (16002)------------------------------ 98.90/14.61 % (16002)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 98.90/14.61 % (16002)Termination reason: Unknown 98.90/14.61 % (16002)Termination phase: Saturation 98.90/14.61 98.90/14.61 % (16002)Memory used [KB]: 19829 98.90/14.61 % (16002)Time elapsed: 2.474 s 98.90/14.61 % (16002)Instructions burned: 7803 (million) 98.90/14.61 % (16002)------------------------------ 98.90/14.61 % (16002)------------------------------ 98.90/14.62 % (16010)lrs+1666_1:1_au=on:s2a=on:sd=2:ss=axioms:st=5.0:i=5087:si=on:rtra=on_0 on E---3.1_15619 for (1657ds/5087Mi) 101.76/14.98 % (15997)Instruction limit reached! 101.76/14.98 % (15997)------------------------------ 101.76/14.98 % (15997)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 101.76/14.98 % (15997)Termination reason: Unknown 101.76/14.98 % (15997)Termination phase: Saturation 101.76/14.98 101.76/14.98 % (15997)Memory used [KB]: 7164 101.76/14.98 % (15997)Time elapsed: 3.696 s 101.76/14.98 % (15997)Instructions burned: 15559 (million) 101.76/14.98 % (15997)------------------------------ 101.76/14.98 % (15997)------------------------------ 101.76/14.99 % (16011)lrs+1002_1:1_aac=none:au=on:bd=off:cnfonf=lazy_pi_sigma_gen:s2a=on:sac=on:sd=1:sgt=20:ss=axioms:i=10380:si=on:rtra=on_0 on E---3.1_15619 for (1654ds/10380Mi) 101.76/15.02 % (16011)Refutation not found, incomplete strategy 101.76/15.02 % (16011)------------------------------ 101.76/15.02 % (16011)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 101.76/15.02 % (16011)Termination reason: Refutation not found, incomplete strategy 101.76/15.02 101.76/15.02 101.76/15.02 % (16011)Memory used [KB]: 6396 101.76/15.02 % (16011)Time elapsed: 0.032 s 101.76/15.02 % (16011)Instructions burned: 96 (million) 101.76/15.02 % (16011)------------------------------ 101.76/15.02 % (16011)------------------------------ 102.11/15.03 % (16012)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4218:si=on:rtra=on_0 on E---3.1_15619 for (1653ds/4218Mi) 104.98/15.48 % (15994)Instruction limit reached! 104.98/15.48 % (15994)------------------------------ 104.98/15.48 % (15994)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 104.98/15.48 % (15994)Termination reason: Unknown 104.98/15.48 % (15994)Termination phase: Saturation 104.98/15.48 104.98/15.48 % (15994)Memory used [KB]: 24690 104.98/15.48 % (15994)Time elapsed: 4.447 s 104.98/15.48 % (15994)Instructions burned: 13470 (million) 104.98/15.48 % (15994)------------------------------ 104.98/15.48 % (15994)------------------------------ 105.34/15.49 % (16013)ott+1666_1:1_hfaw=0:hfsq=on:hfsql=off:hfsqr=1,16:hud=15:slsq=on:slsqr=1,2:tnu=2:i=3971:si=on:rtra=on_0 on E---3.1_15619 for (1649ds/3971Mi) 105.81/15.57 % (16006)Instruction limit reached! 105.81/15.57 % (16006)------------------------------ 105.81/15.57 % (16006)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 105.81/15.57 % (16006)Termination reason: Unknown 105.81/15.57 % (16006)Termination phase: Saturation 105.81/15.57 105.81/15.57 % (16006)Memory used [KB]: 6908 105.81/15.57 % (16006)Time elapsed: 2.954 s 105.81/15.57 % (16006)Instructions burned: 13019 (million) 105.81/15.57 % (16006)------------------------------ 105.81/15.57 % (16006)------------------------------ 105.81/15.58 % (16014)dis+1010_1:1_anc=all_dependent:au=on:bs=on:sd=5:sp=occurrence:ss=axioms:st=2.0:i=14014:si=on:rtra=on_0 on E---3.1_15619 for (1648ds/14014Mi) 106.70/15.77 % (16003)Instruction limit reached! 106.70/15.77 % (16003)------------------------------ 106.70/15.77 % (16003)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 106.70/15.77 % (16003)Termination reason: Unknown 106.70/15.77 % (16003)Termination phase: Saturation 106.70/15.77 106.70/15.77 % (16003)Memory used [KB]: 6652 106.70/15.77 % (16003)Time elapsed: 3.451 s 106.70/15.77 % (16003)Instructions burned: 15194 (million) 106.70/15.77 % (16003)------------------------------ 106.70/15.77 % (16003)------------------------------ 106.93/15.78 % (16015)lrs+10_1:1_ins=1:sgt=8:ss=axioms:i=8517:si=on:rtra=on_0 on E---3.1_15619 for (1646ds/8517Mi) 110.37/16.25 % (16010)Instruction limit reached! 110.37/16.25 % (16010)------------------------------ 110.37/16.25 % (16010)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 110.37/16.25 % (16010)Termination reason: Unknown 110.37/16.25 % (16010)Termination phase: Saturation 110.37/16.25 110.37/16.25 % (16010)Memory used [KB]: 13560 110.37/16.25 % (16010)Time elapsed: 1.633 s 110.37/16.25 % (16010)Instructions burned: 5089 (million) 110.37/16.25 % (16010)------------------------------ 110.37/16.25 % (16010)------------------------------ 110.73/16.26 % (16016)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=10148:si=on:rtra=on_0 on E---3.1_15619 for (1641ds/10148Mi) 110.73/16.30 % (16012)Instruction limit reached! 110.73/16.30 % (16012)------------------------------ 110.73/16.30 % (16012)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 110.73/16.30 % (16012)Termination reason: Unknown 110.73/16.30 % (16012)Termination phase: Saturation 110.73/16.30 110.73/16.30 % (16012)Memory used [KB]: 14456 110.73/16.30 % (16012)Time elapsed: 1.287 s 110.73/16.30 % (16012)Instructions burned: 4219 (million) 110.73/16.30 % (16012)------------------------------ 110.73/16.30 % (16012)------------------------------ 110.73/16.31 % (16017)lrs+10_1:2_ntd=on:nwc=10.0:plsq=on:plsqc=1:plsqr=2,1:ss=axioms:i=9078:si=on:rtra=on_0 on E---3.1_15619 for (1640ds/9078Mi) 111.42/16.43 % (16013)Instruction limit reached! 111.42/16.43 % (16013)------------------------------ 111.42/16.43 % (16013)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 111.42/16.43 % (16013)Termination reason: Unknown 111.42/16.43 % (16013)Termination phase: Saturation 111.42/16.43 111.42/16.43 % (16013)Memory used [KB]: 6908 111.42/16.43 % (16013)Time elapsed: 0.935 s 111.42/16.43 % (16013)Instructions burned: 3973 (million) 111.42/16.43 % (16013)------------------------------ 111.42/16.43 % (16013)------------------------------ 111.69/16.44 % (16018)lrs+2_1:1_bet=on:bsr=on:cnfonf=lazy_pi_sigma_gen:er=filter:kws=inv_frequency:ntd=on:sd=3:ss=axioms:i=16164:si=on:rtra=on_0 on E---3.1_15619 for (1639ds/16164Mi) 114.16/16.79 % (16009)Instruction limit reached! 114.16/16.79 % (16009)------------------------------ 114.16/16.79 % (16009)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 114.16/16.79 % (16009)Termination reason: Unknown 114.16/16.79 % (16009)Termination phase: Saturation 114.16/16.79 114.16/16.79 % (16009)Memory used [KB]: 6908 114.16/16.79 % (16009)Time elapsed: 3.007 s 114.16/16.79 % (16009)Instructions burned: 13165 (million) 114.16/16.79 % (16009)------------------------------ 114.16/16.79 % (16009)------------------------------ 114.16/16.80 % (16019)lrs+32_1:1_au=on:bet=on:cbe=off:cs=on:ins=3:i=6102:si=on:rtra=on_0 on E---3.1_15619 for (1636ds/6102Mi) 121.90/17.88 % (16015)Instruction limit reached! 121.90/17.88 % (16015)------------------------------ 121.90/17.88 % (16015)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 121.90/17.88 % (16015)Termination reason: Unknown 121.90/17.88 % (16015)Termination phase: Saturation 121.90/17.88 121.90/17.88 % (16015)Memory used [KB]: 6908 121.90/17.88 % (16015)Time elapsed: 2.098 s 121.90/17.88 % (16015)Instructions burned: 8518 (million) 121.90/17.88 % (16015)------------------------------ 121.90/17.88 % (16015)------------------------------ 121.90/17.89 % (16020)lrs+1010_1:1_au=on:bd=off:e2e=on:fde=unused:nm=4:s2a=on:sos=all:sp=const_frequency:i=10308:si=on:rtra=on_0 on E---3.1_15619 for (1625ds/10308Mi) 121.90/17.91 % (16020)Refutation not found, incomplete strategy 121.90/17.91 % (16020)------------------------------ 121.90/17.91 % (16020)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 121.90/17.91 % (16020)Termination reason: Refutation not found, incomplete strategy 121.90/17.91 121.90/17.91 121.90/17.91 % (16020)Memory used [KB]: 6396 121.90/17.91 % (16020)Time elapsed: 0.022 s 121.90/17.91 % (16020)Instructions burned: 71 (million) 121.90/17.91 % (16020)------------------------------ 121.90/17.91 % (16020)------------------------------ 121.90/17.92 % (16021)dis+1010_1:1_au=on:avsq=on:bd=off:cbe=off:cnfonf=off:cs=on:hud=5:nm=0:plsq=on:plsqc=1:plsqr=7,1:ss=axioms:tgt=full:i=4041:si=on:rtra=on_0 on E---3.1_15619 for (1624ds/4041Mi) 122.61/18.00 % (16021)Refutation not found, incomplete strategy 122.61/18.00 % (16021)------------------------------ 122.61/18.00 % (16021)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 122.61/18.00 % (16021)Termination reason: Refutation not found, incomplete strategy 122.61/18.00 122.61/18.00 122.61/18.00 % (16021)Memory used [KB]: 6524 122.61/18.00 % (16021)Time elapsed: 0.080 s 122.61/18.00 % (16021)Instructions burned: 245 (million) 122.61/18.00 % (16021)------------------------------ 122.61/18.00 % (16021)------------------------------ 122.61/18.01 % (16022)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=6901:si=on:rtra=on_0 on E---3.1_15619 for (1623ds/6901Mi) 124.09/18.23 % (16019)Instruction limit reached! 124.09/18.23 % (16019)------------------------------ 124.09/18.23 % (16019)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 124.09/18.23 % (16019)Termination reason: Unknown 124.09/18.23 % (16019)Termination phase: Saturation 124.09/18.23 124.09/18.23 % (16019)Memory used [KB]: 6524 124.09/18.23 % (16019)Time elapsed: 1.430 s 124.09/18.23 % (16019)Instructions burned: 6102 (million) 124.09/18.23 % (16019)------------------------------ 124.09/18.23 % (16019)------------------------------ 124.09/18.24 % (16023)lrs-1_1:1_au=on:cbe=off:ntd=on:i=5576:si=on:rtra=on_0 on E---3.1_15619 for (1621ds/5576Mi) 126.54/18.60 % (16016)Instruction limit reached! 126.54/18.60 % (16016)------------------------------ 126.54/18.60 % (16016)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 126.54/18.60 % (16016)Termination reason: Unknown 126.54/18.60 % (16016)Termination phase: Saturation 126.54/18.60 126.54/18.60 % (16016)Memory used [KB]: 2430 126.54/18.60 % (16016)Time elapsed: 2.337 s 126.54/18.60 % (16016)Instructions burned: 10149 (million) 126.54/18.60 % (16016)------------------------------ 126.54/18.60 % (16016)------------------------------ 126.54/18.61 % (16024)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=2014:si=on:rtra=on_0 on E---3.1_15619 for (1618ds/2014Mi) 129.47/18.97 % (16017)Instruction limit reached! 129.47/18.97 % (16017)------------------------------ 129.47/18.97 % (16017)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 129.47/18.97 % (16017)Termination reason: Unknown 129.47/18.97 % (16017)Termination phase: Saturation 129.47/18.97 129.47/18.97 % (16017)Memory used [KB]: 17654 129.47/18.97 % (16017)Time elapsed: 2.656 s 129.47/18.97 % (16017)Instructions burned: 9081 (million) 129.47/18.97 % (16017)------------------------------ 129.47/18.97 % (16017)------------------------------ 129.47/18.98 % (16025)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=5115:si=on:rtra=on_0 on E---3.1_15619 for (1614ds/5115Mi) 130.06/19.07 % (16024)Instruction limit reached! 130.06/19.07 % (16024)------------------------------ 130.06/19.07 % (16024)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 130.06/19.07 % (16024)Termination reason: Unknown 130.06/19.07 % (16024)Termination phase: Saturation 130.06/19.07 130.06/19.07 % (16024)Memory used [KB]: 6908 130.06/19.07 % (16024)Time elapsed: 0.459 s 130.06/19.07 % (16024)Instructions burned: 2015 (million) 130.06/19.07 % (16024)------------------------------ 130.06/19.07 % (16024)------------------------------ 130.06/19.08 % (16026)lrs+2_1:1_au=on:cnfonf=lazy_pi_sigma_gen:sos=on:ss=axioms:i=13001:si=on:rtra=on_0 on E---3.1_15619 for (1613ds/13001Mi) 130.35/19.09 % (16026)Refutation not found, incomplete strategy 130.35/19.09 % (16026)------------------------------ 130.35/19.09 % (16026)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 130.35/19.09 % (16026)Termination reason: Refutation not found, incomplete strategy 130.35/19.09 130.35/19.09 130.35/19.09 % (16026)Memory used [KB]: 6140 130.35/19.09 % (16026)Time elapsed: 0.013 s 130.35/19.09 % (16026)Instructions burned: 43 (million) 130.35/19.09 % (16026)------------------------------ 130.35/19.09 % (16026)------------------------------ 130.35/19.10 % (16027)dis+10_1:2_aac=none:acc=on:atotf=0.1:au=on:fde=none:ins=1:ixr=off:nwc=5.0:i=11105:si=on:rtra=on_0 on E---3.1_15619 for (1613ds/11105Mi) 133.74/19.57 % (16023)Instruction limit reached! 133.74/19.57 % (16023)------------------------------ 133.74/19.57 % (16023)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 133.74/19.57 % (16023)Termination reason: Unknown 133.74/19.57 % (16023)Termination phase: Saturation 133.74/19.57 133.74/19.57 % (16023)Memory used [KB]: 6908 133.74/19.57 % (16023)Time elapsed: 1.329 s 133.74/19.57 % (16023)Instructions burned: 5580 (million) 133.74/19.57 % (16023)------------------------------ 133.74/19.57 % (16023)------------------------------ 133.74/19.58 % (16028)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=13832:si=on:rtra=on_0 on E---3.1_15619 for (1608ds/13832Mi) 135.17/19.80 % (16022)Instruction limit reached! 135.17/19.80 % (16022)------------------------------ 135.17/19.80 % (16022)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 135.17/19.80 % (16022)Termination reason: Unknown 135.17/19.80 % (16022)Termination phase: Saturation 135.17/19.80 135.17/19.80 % (16022)Memory used [KB]: 9466 135.17/19.80 % (16022)Time elapsed: 1.792 s 135.17/19.80 % (16022)Instructions burned: 6902 (million) 135.17/19.80 % (16022)------------------------------ 135.17/19.80 % (16022)------------------------------ 135.17/19.81 % (16029)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=32887:si=on:rtra=on_0 on E---3.1_15619 for (1605ds/32887Mi) 137.37/20.13 % (16014)Instruction limit reached! 137.37/20.13 % (16014)------------------------------ 137.37/20.13 % (16014)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 137.37/20.13 % (16014)Termination reason: Unknown 137.37/20.13 % (16014)Termination phase: Saturation 137.37/20.13 137.37/20.13 % (16014)Memory used [KB]: 27376 137.37/20.13 % (16014)Time elapsed: 4.571 s 137.37/20.13 % (16014)Instructions burned: 14014 (million) 137.37/20.13 % (16014)------------------------------ 137.37/20.13 % (16014)------------------------------ 137.37/20.14 % (16030)dis+1010_2:1_avsq=on:fde=unused:prag=on:i=3362:si=on:rtra=on_0 on E---3.1_15619 for (1602ds/3362Mi) 137.37/20.16 % (16025)Instruction limit reached! 137.37/20.16 % (16025)------------------------------ 137.37/20.16 % (16025)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 137.37/20.16 % (16025)Termination reason: Unknown 137.37/20.16 % (16025)Termination phase: Saturation 137.37/20.16 137.37/20.16 % (16025)Memory used [KB]: 6908 137.37/20.16 % (16025)Time elapsed: 1.178 s 137.37/20.16 % (16025)Instructions burned: 5118 (million) 137.37/20.16 % (16025)------------------------------ 137.37/20.16 % (16025)------------------------------ 137.64/20.17 % (16031)ott+1002_1:1_au=on:cnfonf=lazy_simp:nwc=5.0:sgt=5:ss=axioms:st=1.5:i=24965:si=on:rtra=on_0 on E---3.1_15619 for (1602ds/24965Mi) 144.66/21.16 % (16030)Instruction limit reached! 144.66/21.16 % (16030)------------------------------ 144.66/21.16 % (16030)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 144.66/21.16 % (16030)Termination reason: Unknown 144.66/21.16 % (16030)Termination phase: Saturation 144.66/21.16 144.66/21.16 % (16030)Memory used [KB]: 14711 144.66/21.16 % (16030)Time elapsed: 1.023 s 144.66/21.16 % (16030)Instructions burned: 3364 (million) 144.66/21.16 % (16030)------------------------------ 144.66/21.16 % (16030)------------------------------ 144.95/21.17 % (16032)lrs+1010_2:1_amm=off:avsq=on:c=on:cbe=off:e2e=on:fsr=off:ins=3:s2a=on:s2at=-1.0:i=15705:si=on:rtra=on_0 on E---3.1_15619 for (1592ds/15705Mi) 146.83/21.47 % (16018)Instruction limit reached! 146.83/21.47 % (16018)------------------------------ 146.83/21.47 % (16018)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 146.83/21.47 % (16018)Termination reason: Unknown 146.83/21.47 % (16018)Termination phase: Saturation 146.83/21.47 146.83/21.47 % (16018)Memory used [KB]: 18677 146.83/21.47 % (16018)Time elapsed: 5.038 s 146.83/21.47 % (16018)Instructions burned: 16165 (million) 146.83/21.47 % (16018)------------------------------ 146.83/21.47 % (16018)------------------------------ 147.13/21.48 % (16033)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1536:si=on:rtra=on_0 on E---3.1_15619 for (1589ds/1536Mi) 150.48/22.02 % (16033)Instruction limit reached! 150.48/22.02 % (16033)------------------------------ 150.48/22.02 % (16033)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 150.48/22.02 % (16033)Termination reason: Unknown 150.48/22.02 % (16033)Termination phase: Saturation 150.48/22.02 150.48/22.02 % (16033)Memory used [KB]: 8699 150.48/22.02 % (16033)Time elapsed: 0.557 s 150.48/22.02 % (16033)Instructions burned: 1537 (million) 150.48/22.02 % (16033)------------------------------ 150.48/22.02 % (16033)------------------------------ 150.48/22.03 % (16034)dis+10_1:1_fde=none:kws=precedence:piset=not:prag=on:slsq=on:slsqc=1:sp=unary_frequency:i=23684:si=on:rtra=on_0 on E---3.1_15619 for (1583ds/23684Mi) 153.16/22.43 % (16027)Instruction limit reached! 153.16/22.43 % (16027)------------------------------ 153.16/22.43 % (16027)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 153.16/22.43 % (16027)Termination reason: Unknown 153.16/22.43 % (16027)Termination phase: Saturation 153.16/22.43 153.16/22.43 % (16027)Memory used [KB]: 19445 153.16/22.43 % (16027)Time elapsed: 3.341 s 153.16/22.43 % (16027)Instructions burned: 11107 (million) 153.16/22.43 % (16027)------------------------------ 153.16/22.43 % (16027)------------------------------ 153.16/22.44 % (16035)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=4925:si=on:rtra=on_0 on E---3.1_15619 for (1579ds/4925Mi) 155.60/22.73 % (16028)Instruction limit reached! 155.60/22.73 % (16028)------------------------------ 155.60/22.73 % (16028)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 155.60/22.73 % (16028)Termination reason: Unknown 155.60/22.73 % (16028)Termination phase: Saturation 155.60/22.73 155.60/22.73 % (16028)Memory used [KB]: 7036 155.60/22.73 % (16028)Time elapsed: 3.161 s 155.60/22.73 % (16028)Instructions burned: 13833 (million) 155.60/22.73 % (16028)------------------------------ 155.60/22.73 % (16028)------------------------------ 155.98/22.74 % (16036)lrs-1010_1:50_au=on:awrs=converge:awrsf=430:bet=on:cbe=off:cha=on:nm=20:sac=on:i=14666:si=on:rtra=on_0 on E---3.1_15619 for (1576ds/14666Mi) 161.78/23.63 % (16035)Instruction limit reached! 161.78/23.63 % (16035)------------------------------ 161.78/23.63 % (16035)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 161.78/23.63 % (16035)Termination reason: Unknown 161.78/23.63 % (16035)Termination phase: Saturation 161.78/23.63 161.78/23.63 % (16035)Memory used [KB]: 6908 161.78/23.63 % (16035)Time elapsed: 1.186 s 161.78/23.63 % (16035)Instructions burned: 4925 (million) 161.78/23.63 % (16035)------------------------------ 161.78/23.63 % (16035)------------------------------ 161.78/23.64 % (16037)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=3322:si=on:rtra=on_0 on E---3.1_15619 for (1567ds/3322Mi) 167.65/24.43 % (16037)Instruction limit reached! 167.65/24.43 % (16037)------------------------------ 167.65/24.43 % (16037)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 167.65/24.43 % (16037)Termination reason: Unknown 167.65/24.43 % (16037)Termination phase: Saturation 167.65/24.43 167.65/24.43 % (16037)Memory used [KB]: 6908 167.65/24.43 % (16037)Time elapsed: 0.794 s 167.65/24.43 % (16037)Instructions burned: 3324 (million) 167.65/24.43 % (16037)------------------------------ 167.65/24.43 % (16037)------------------------------ 167.65/24.44 % (16038)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1810:si=on:rtra=on_0 on E---3.1_15619 for (1559ds/1810Mi) 170.67/24.85 % (16038)Instruction limit reached! 170.67/24.85 % (16038)------------------------------ 170.67/24.85 % (16038)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 170.67/24.85 % (16038)Termination reason: Unknown 170.67/24.85 % (16038)Termination phase: Saturation 170.67/24.85 170.67/24.85 % (16038)Memory used [KB]: 6908 170.67/24.85 % (16038)Time elapsed: 0.414 s 170.67/24.85 % (16038)Instructions burned: 1812 (million) 170.67/24.85 % (16038)------------------------------ 170.67/24.85 % (16038)------------------------------ 170.67/24.85 % (16032)Instruction limit reached! 170.67/24.85 % (16032)------------------------------ 170.67/24.85 % (16032)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 170.67/24.85 % (16032)Termination reason: Unknown 170.67/24.85 % (16032)Termination phase: Saturation 170.67/24.85 170.67/24.85 % (16032)Memory used [KB]: 6908 170.67/24.85 % (16032)Time elapsed: 3.664 s 170.67/24.85 % (16032)Instructions burned: 15706 (million) 170.67/24.85 % (16032)------------------------------ 170.67/24.85 % (16032)------------------------------ 170.67/24.86 % (16039)dis+1666_1:1_anc=none:bs=on:cbe=off:cha=on:cnfonf=lazy_gen:fe=off:fsr=off:hud=5:kws=precedence:piset=pi_sigma:prag=on:sos=on:sp=frequency:i=2465:si=on:rtra=on_0 on E---3.1_15619 for (1555ds/2465Mi) 170.67/24.86 % (16040)dis+1002_1:1_cbe=off:cnfonf=lazy_pi_sigma_gen:fsr=off:ins=1:kws=inv_precedence:nwc=10.0:ss=axioms:st=2.0:i=41234:si=on:rtra=on_0 on E---3.1_15619 for (1555ds/41234Mi) 174.41/25.42 % (16039)Instruction limit reached! 174.41/25.42 % (16039)------------------------------ 174.41/25.42 % (16039)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 174.41/25.42 % (16039)Termination reason: Unknown 174.41/25.42 % (16039)Termination phase: Saturation 174.41/25.42 174.41/25.42 % (16039)Memory used [KB]: 2430 174.41/25.42 % (16039)Time elapsed: 0.559 s 174.41/25.42 % (16039)Instructions burned: 2465 (million) 174.41/25.42 % (16039)------------------------------ 174.41/25.42 % (16039)------------------------------ 174.41/25.43 % (16041)dis+1002_1:1_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:nm=0:i=14027:si=on:rtra=on_0 on E---3.1_15619 for (1549ds/14027Mi) 181.06/26.34 % (16036)Instruction limit reached! 181.06/26.34 % (16036)------------------------------ 181.06/26.34 % (16036)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 181.06/26.34 % (16036)Termination reason: Unknown 181.06/26.34 % (16036)Termination phase: Saturation 181.06/26.34 181.06/26.34 % (16036)Memory used [KB]: 7036 181.06/26.34 % (16036)Time elapsed: 3.592 s 181.06/26.34 % (16036)Instructions burned: 14666 (million) 181.06/26.34 % (16036)------------------------------ 181.06/26.34 % (16036)------------------------------ 181.06/26.35 % (16042)dis+1010_1:1_au=on:cnfonf=conj_eager:nwc=10.0:sac=on:i=27021:si=on:rtra=on_0 on E---3.1_15619 for (1540ds/27021Mi) 183.25/26.66 % (16001)Instruction limit reached! 183.25/26.66 % (16001)------------------------------ 183.25/26.66 % (16001)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 183.25/26.66 % (16001)Termination reason: Unknown 183.25/26.66 % (16001)Termination phase: Saturation 183.25/26.66 183.25/26.66 % (16001)Memory used [KB]: 14967 183.25/26.66 % (16001)Time elapsed: 14.730 s 183.25/26.66 % (16001)Instructions burned: 64913 (million) 183.25/26.66 % (16001)------------------------------ 183.25/26.66 % (16001)------------------------------ 183.25/26.67 % (16043)dis-1666_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:i=5643:si=on:rtra=on_0 on E---3.1_15619 for (1537ds/5643Mi) 187.50/27.27 % (16029)Instruction limit reached! 187.50/27.27 % (16029)------------------------------ 187.50/27.27 % (16029)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 187.50/27.27 % (16029)Termination reason: Unknown 187.50/27.27 % (16029)Termination phase: Saturation 187.50/27.27 187.50/27.27 % (16029)Memory used [KB]: 13944 187.50/27.27 % (16029)Time elapsed: 7.468 s 187.50/27.27 % (16029)Instructions burned: 32889 (million) 187.50/27.27 % (16029)------------------------------ 187.50/27.27 % (16029)------------------------------ 187.50/27.28 % (16044)dis+1002_1:1_apa=on:au=on:cnfonf=off:e2e=on:flr=on:nm=4:s2a=on:i=8612:si=on:rtra=on_0 on E---3.1_15619 for (1531ds/8612Mi) 188.96/27.53 % (16031)Instruction limit reached! 188.96/27.53 % (16031)------------------------------ 188.96/27.53 % (16031)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 188.96/27.53 % (16031)Termination reason: Unknown 188.96/27.53 % (16031)Termination phase: Saturation 188.96/27.53 188.96/27.53 % (16031)Memory used [KB]: 23411 188.96/27.53 % (16031)Time elapsed: 7.359 s 188.96/27.53 % (16031)Instructions burned: 24965 (million) 188.96/27.53 % (16031)------------------------------ 188.96/27.53 % (16031)------------------------------ 189.46/27.54 % (16045)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=3743:si=on:rtra=on_0 on E---3.1_15619 for (1528ds/3743Mi) 191.93/27.98 % (16043)Instruction limit reached! 191.93/27.98 % (16043)------------------------------ 191.93/27.98 % (16043)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 191.93/27.98 % (16043)Termination reason: Unknown 191.93/27.98 % (16043)Termination phase: Saturation 191.93/27.98 191.93/27.98 % (16043)Memory used [KB]: 6908 191.93/27.98 % (16043)Time elapsed: 1.315 s 191.93/27.98 % (16043)Instructions burned: 5643 (million) 191.93/27.98 % (16043)------------------------------ 191.93/27.98 % (16043)------------------------------ 191.93/27.99 % (16046)dis+10_1:2_amm=off:bd=preordered:cnfonf=off:e2e=on:fe=off:fsr=off:hud=5:nm=3:s2a=on:sos=on:i=2571:si=on:rtra=on_0 on E---3.1_15619 for (1524ds/2571Mi) 196.50/28.63 % (16046)Instruction limit reached! 196.50/28.63 % (16046)------------------------------ 196.50/28.63 % (16046)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 196.50/28.63 % (16046)Termination reason: Unknown 196.50/28.63 % (16046)Termination phase: Saturation 196.50/28.63 196.50/28.63 % (16046)Memory used [KB]: 2430 196.50/28.63 % (16046)Time elapsed: 0.616 s 196.50/28.63 % (16046)Instructions burned: 2571 (million) 196.50/28.63 % (16046)------------------------------ 196.50/28.63 % (16046)------------------------------ 197.06/28.64 % (16047)dis+1010_1:16_cbe=off:cnfonf=conj_eager:fe=off:hud=15:nwc=3.0:piset=pi_sigma:prag=on:sd=5:sp=weighted_frequency:ss=axioms:st=2.0:i=35728:si=on:rtra=on_0 on E---3.1_15619 for (1517ds/35728Mi) 197.06/28.64 % (16041)Instruction limit reached! 197.06/28.64 % (16041)------------------------------ 197.06/28.64 % (16041)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 197.06/28.64 % (16041)Termination reason: Unknown 197.06/28.64 % (16041)Termination phase: Saturation 197.06/28.64 197.06/28.64 % (16041)Memory used [KB]: 6908 197.06/28.64 % (16041)Time elapsed: 3.209 s 197.06/28.64 % (16041)Instructions burned: 14029 (million) 197.06/28.64 % (16041)------------------------------ 197.06/28.64 % (16041)------------------------------ 197.06/28.65 % (16048)lrs+1004_1:24_i=5433:si=on:rtra=on_0 on E---3.1_15619 for (1517ds/5433Mi) 197.32/28.72 % (16045)Instruction limit reached! 197.32/28.72 % (16045)------------------------------ 197.32/28.72 % (16045)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 197.32/28.72 % (16045)Termination reason: Unknown 197.32/28.72 % (16045)Termination phase: Saturation 197.32/28.72 197.32/28.72 % (16045)Memory used [KB]: 10618 197.32/28.72 % (16045)Time elapsed: 1.185 s 197.32/28.72 % (16045)Instructions burned: 3743 (million) 197.32/28.72 % (16045)------------------------------ 197.32/28.72 % (16045)------------------------------ 197.32/28.73 % (16049)ott+1002_1:1_anc=all_dependent:au=on:avsq=on:cnfonf=lazy_pi_sigma_gen:piset=not:i=27944:si=on:rtra=on_0 on E---3.1_15619 for (1516ds/27944Mi) 202.00/29.35 % (16044)Instruction limit reached! 202.00/29.35 % (16044)------------------------------ 202.00/29.35 % (16044)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 202.00/29.35 % (16044)Termination reason: Unknown 202.00/29.35 % (16044)Termination phase: Saturation 202.00/29.35 202.00/29.35 % (16044)Memory used [KB]: 6908 202.00/29.35 % (16044)Time elapsed: 2.066 s 202.00/29.35 % (16044)Instructions burned: 8612 (million) 202.00/29.35 % (16044)------------------------------ 202.00/29.35 % (16044)------------------------------ 202.08/29.36 % (16050)ott+10_1:10_cnfonf=lazy_gen:fde=none:sp=const_frequency:i=15814:si=on:rtra=on_0 on E---3.1_15619 for (1510ds/15814Mi) 204.24/29.71 % (16034)Instruction limit reached! 204.24/29.71 % (16034)------------------------------ 204.24/29.71 % (16034)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 204.24/29.71 % (16034)Termination reason: Unknown 204.24/29.71 % (16034)Termination phase: Saturation 204.24/29.71 204.24/29.71 % (16034)Memory used [KB]: 52323 204.24/29.71 % (16034)Time elapsed: 7.681 s 204.24/29.71 % (16034)Instructions burned: 23686 (million) 204.24/29.71 % (16034)------------------------------ 204.24/29.71 % (16034)------------------------------ 204.64/29.72 % (16051)lrs+1002_1:128_atotf=0.1:au=on:cbe=off:ntd=on:sp=const_frequency:i=9867:si=on:rtra=on_0 on E---3.1_15619 for (1506ds/9867Mi) 205.90/29.95 % (16048)Instruction limit reached! 205.90/29.95 % (16048)------------------------------ 205.90/29.95 % (16048)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 205.90/29.95 % (16048)Termination reason: Unknown 205.90/29.95 % (16048)Termination phase: Saturation 205.90/29.95 205.90/29.95 % (16048)Memory used [KB]: 6908 205.90/29.95 % (16048)Time elapsed: 1.303 s 205.90/29.95 % (16048)Instructions burned: 5434 (million) 205.90/29.95 % (16048)------------------------------ 205.90/29.95 % (16048)------------------------------ 206.03/29.96 % (16052)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=5419:si=on:rtra=on_0 on E---3.1_15619 for (1504ds/5419Mi) 216.90/31.51 % (16052)Instruction limit reached! 216.90/31.51 % (16052)------------------------------ 216.90/31.51 % (16052)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 216.90/31.51 % (16052)Termination reason: Unknown 216.90/31.51 % (16052)Termination phase: Saturation 216.90/31.51 216.90/31.51 % (16052)Memory used [KB]: 6908 216.90/31.51 % (16052)Time elapsed: 1.552 s 216.90/31.51 % (16052)Instructions burned: 5421 (million) 216.90/31.51 % (16052)------------------------------ 216.90/31.51 % (16052)------------------------------ 217.19/31.53 % (16053)dis+1010_1:28_au=on:cnfonf=off:e2e=on:fde=none:nicw=on:s2a=on:s2at=5.0:tgt=full:i=15386:si=on:rtra=on_0 on E---3.1_15619 for (1488ds/15386Mi) 220.09/31.99 % (16051)Instruction limit reached! 220.09/31.99 % (16051)------------------------------ 220.09/31.99 % (16051)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 220.09/31.99 % (16051)Termination reason: Unknown 220.09/31.99 % (16051)Termination phase: Saturation 220.09/31.99 220.09/31.99 % (16051)Memory used [KB]: 6908 220.09/31.99 % (16051)Time elapsed: 2.266 s 220.09/31.99 % (16051)Instructions burned: 9871 (million) 220.09/31.99 % (16051)------------------------------ 220.09/31.99 % (16051)------------------------------ 220.50/32.00 % (16070)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on E---3.1_15619 for (1484ds/4714Mi) 224.35/32.58 % (16042)Instruction limit reached! 224.35/32.58 % (16042)------------------------------ 224.35/32.58 % (16042)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 224.35/32.58 % (16042)Termination reason: Unknown 224.35/32.58 % (16042)Termination phase: Saturation 224.35/32.58 224.35/32.58 % (16042)Memory used [KB]: 6908 224.35/32.58 % (16042)Time elapsed: 6.226 s 224.35/32.58 % (16042)Instructions burned: 27023 (million) 224.35/32.58 % (16042)------------------------------ 224.35/32.58 % (16042)------------------------------ 224.35/32.59 % (16071)lrs+10_1:1_bd=off:c=on:fsr=off:ntd=on:prag=on:sd=1:sos=all:ss=axioms:st=5.0:i=42749:si=on:rtra=on_0 on E---3.1_15619 for (1478ds/42749Mi) 224.66/32.61 % (16071)Refutation not found, incomplete strategy 224.66/32.61 % (16071)------------------------------ 224.66/32.61 % (16071)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 224.66/32.61 % (16071)Termination reason: Refutation not found, incomplete strategy 224.66/32.61 224.66/32.61 224.66/32.61 % (16071)Memory used [KB]: 6396 224.66/32.61 % (16071)Time elapsed: 0.020 s 224.66/32.61 % (16071)Instructions burned: 64 (million) 224.66/32.61 % (16071)------------------------------ 224.66/32.61 % (16071)------------------------------ 224.66/32.61 % (16072)lrs+10_1:156_afp=4000:avsq=on:avsqr=4,1:fe=axiom:ss=axioms:tgt=ground:i=19001:si=on:rtra=on_0 on E---3.1_15619 for (1477ds/19001Mi) 227.95/33.09 % (16070)Instruction limit reached! 227.95/33.09 % (16070)------------------------------ 227.95/33.09 % (16070)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 227.95/33.09 % (16070)Termination reason: Unknown 227.95/33.09 % (16070)Termination phase: Saturation 227.95/33.09 227.95/33.09 % (16070)Memory used [KB]: 2430 227.95/33.09 % (16070)Time elapsed: 1.093 s 227.95/33.09 % (16070)Instructions burned: 4717 (million) 227.95/33.09 % (16070)------------------------------ 227.95/33.09 % (16070)------------------------------ 227.95/33.10 % (16073)lrs+1_1:1_au=on:cbe=off:cs=on:nm=4:i=14341:si=on:rtra=on_0 on E---3.1_15619 for (1473ds/14341Mi) 235.54/34.15 % (16050)Instruction limit reached! 235.54/34.15 % (16050)------------------------------ 235.54/34.15 % (16050)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 235.54/34.15 % (16050)Termination reason: Unknown 235.54/34.15 % (16050)Termination phase: Saturation 235.54/34.15 235.54/34.15 % (16050)Memory used [KB]: 14967 235.54/34.15 % (16050)Time elapsed: 4.805 s 235.54/34.15 % (16050)Instructions burned: 15817 (million) 235.54/34.15 % (16050)------------------------------ 235.54/34.15 % (16050)------------------------------ 235.54/34.16 % (16104)lrs+10_1:1_cnfonf=off:sd=1:ss=axioms:st=3.0:i=13159:si=on:rtra=on_0 on E---3.1_15619 for (1462ds/13159Mi) 237.82/34.53 % (16040)Instruction limit reached! 237.82/34.53 % (16040)------------------------------ 237.82/34.53 % (16040)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 237.82/34.53 % (16040)Termination reason: Unknown 237.82/34.53 % (16040)Termination phase: Saturation 237.82/34.53 237.82/34.53 % (16040)Memory used [KB]: 7036 237.82/34.53 % (16040)Time elapsed: 9.638 s 237.82/34.53 % (16040)Instructions burned: 41234 (million) 237.82/34.53 % (16040)------------------------------ 237.82/34.53 % (16040)------------------------------ 237.82/34.54 % (16105)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=6604:si=on:rtra=on_0 on E---3.1_15619 for (1458ds/6604Mi) 237.96/34.56 % (16105)Refutation not found, incomplete strategy 237.96/34.56 % (16105)------------------------------ 237.96/34.56 % (16105)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 237.96/34.56 % (16105)Termination reason: Refutation not found, incomplete strategy 237.96/34.56 237.96/34.56 237.96/34.56 % (16105)Memory used [KB]: 6140 237.96/34.56 % (16105)Time elapsed: 0.014 s 237.96/34.56 % (16105)Instructions burned: 41 (million) 237.96/34.56 % (16105)------------------------------ 237.96/34.56 % (16105)------------------------------ 237.96/34.56 % (16106)dis+1002_1:1_au=on:bsr=unit_only:cbe=off:fe=off:fsr=off:nm=10:nwc=6.0:plsq=on:plsqc=1:plsqr=32,1:sos=all:i=2635:si=on:rtra=on_0 on E---3.1_15619 for (1458ds/2635Mi) 242.02/35.11 % (16049)Instruction limit reached! 242.02/35.11 % (16049)------------------------------ 242.02/35.11 % (16049)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 242.02/35.11 % (16049)Termination reason: Unknown 242.02/35.11 % (16049)Termination phase: Saturation 242.02/35.11 242.02/35.11 % (16049)Memory used [KB]: 7803 242.02/35.11 % (16049)Time elapsed: 6.373 s 242.02/35.11 % (16049)Instructions burned: 27947 (million) 242.02/35.11 % (16049)------------------------------ 242.02/35.11 % (16049)------------------------------ 242.31/35.11 % (16107)lrs+1666_1:1_au=on:s2a=on:sd=2:ss=axioms:st=5.0:i=41131:si=on:rtra=on_0 on E---3.1_15619 for (1452ds/41131Mi) 242.51/35.18 % (16106)Instruction limit reached! 242.51/35.18 % (16106)------------------------------ 242.51/35.18 % (16106)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 242.51/35.18 % (16106)Termination reason: Unknown 242.51/35.18 % (16106)Termination phase: Saturation 242.51/35.18 242.51/35.18 % (16106)Memory used [KB]: 2430 242.51/35.18 % (16106)Time elapsed: 0.615 s 242.51/35.18 % (16106)Instructions burned: 2635 (million) 242.51/35.18 % (16106)------------------------------ 242.51/35.18 % (16106)------------------------------ 242.51/35.19 % (16108)ott+1666_1:1_hfaw=0:hfsq=on:hfsql=off:hfsqr=1,16:hud=15:slsq=on:slsqr=1,2:tnu=2:i=3971:si=on:rtra=on_0 on E---3.1_15619 for (1452ds/3971Mi) 248.81/36.14 % (16108)Instruction limit reached! 248.81/36.14 % (16108)------------------------------ 248.81/36.14 % (16108)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 248.81/36.14 % (16108)Termination reason: Unknown 248.81/36.14 % (16108)Termination phase: Saturation 248.81/36.14 248.81/36.14 % (16108)Memory used [KB]: 6908 248.81/36.14 % (16108)Time elapsed: 0.955 s 248.81/36.14 % (16108)Instructions burned: 3971 (million) 248.81/36.14 % (16108)------------------------------ 248.81/36.14 % (16108)------------------------------ 249.50/36.15 % (16109)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2142:si=on:rtra=on_0 on E---3.1_15619 for (1442ds/2142Mi) 251.58/36.45 % (16073)Instruction limit reached! 251.58/36.45 % (16073)------------------------------ 251.58/36.45 % (16073)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 251.58/36.45 % (16073)Termination reason: Unknown 251.58/36.45 % (16073)Termination phase: Saturation 251.58/36.45 251.58/36.45 % (16073)Memory used [KB]: 7036 251.58/36.45 % (16073)Time elapsed: 3.354 s 251.58/36.45 % (16073)Instructions burned: 14343 (million) 251.58/36.45 % (16073)------------------------------ 251.58/36.45 % (16073)------------------------------ 251.58/36.46 % (16110)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=1314:si=on:rtra=on_0 on E---3.1_15619 for (1439ds/1314Mi) 252.61/36.65 % (16053)Instruction limit reached! 252.61/36.65 % (16053)------------------------------ 252.61/36.65 % (16053)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 252.61/36.65 % (16053)Termination reason: Unknown 252.61/36.65 % (16053)Termination phase: Saturation 252.61/36.65 252.61/36.65 % (16053)Memory used [KB]: 29551 252.61/36.65 % (16053)Time elapsed: 5.109 s 252.61/36.65 % (16053)Instructions burned: 15388 (million) 252.61/36.65 % (16053)------------------------------ 252.61/36.65 % (16053)------------------------------ 252.61/36.66 % (16111)dis+1010_2:1_avsq=on:fde=unused:prag=on:i=3362:si=on:rtra=on_0 on E---3.1_15619 for (1437ds/3362Mi) 253.31/36.78 % (16110)Instruction limit reached! 253.31/36.78 % (16110)------------------------------ 253.31/36.78 % (16110)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 253.31/36.78 % (16110)Termination reason: Unknown 253.31/36.78 % (16110)Termination phase: Property scanning 253.31/36.78 253.31/36.78 % (16110)Memory used [KB]: 1918 253.31/36.78 % (16110)Time elapsed: 0.318 s 253.31/36.78 % (16110)Instructions burned: 1316 (million) 253.31/36.78 % (16110)------------------------------ 253.31/36.78 % (16110)------------------------------ 253.81/36.78 % (16112)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=5756:si=on:rtra=on_0 on E---3.1_15619 for (1436ds/5756Mi) 253.81/36.80 % (16112)Refutation not found, incomplete strategy 253.81/36.80 % (16112)------------------------------ 253.81/36.80 % (16112)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 253.81/36.80 % (16112)Termination reason: Refutation not found, incomplete strategy 253.81/36.80 253.81/36.80 253.81/36.80 % (16112)Memory used [KB]: 6396 253.81/36.80 % (16112)Time elapsed: 0.021 s 253.81/36.80 % (16112)Instructions burned: 67 (million) 253.81/36.80 % (16112)------------------------------ 253.81/36.80 % (16112)------------------------------ 253.81/36.81 % (16113)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=2607:si=on:rtra=on_0 on E---3.1_15619 for (1435ds/2607Mi) 253.81/36.84 % (16109)Instruction limit reached! 253.81/36.84 % (16109)------------------------------ 253.81/36.84 % (16109)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 253.81/36.84 % (16109)Termination reason: Unknown 253.81/36.84 % (16109)Termination phase: Saturation 253.81/36.84 253.81/36.84 % (16109)Memory used [KB]: 9466 253.81/36.84 % (16109)Time elapsed: 0.693 s 253.81/36.84 % (16109)Instructions burned: 2142 (million) 253.81/36.84 % (16109)------------------------------ 253.81/36.84 % (16109)------------------------------ 254.38/36.85 % (16114)ott+2_1:1_au=on:hfsq=on:hfsqc=5:hfsql=off:nwc=5.0:sd=3:ss=axioms:st=5.0:i=15187:si=on:rtra=on_0 on E---3.1_15619 for (1435ds/15187Mi) 258.08/37.42 % (16113)Instruction limit reached! 258.08/37.42 % (16113)------------------------------ 258.08/37.42 % (16113)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 258.08/37.42 % (16113)Termination reason: Unknown 258.08/37.42 % (16113)Termination phase: Saturation 258.08/37.42 258.08/37.42 % (16113)Memory used [KB]: 6908 258.08/37.42 % (16113)Time elapsed: 0.606 s 258.08/37.42 % (16113)Instructions burned: 2608 (million) 258.08/37.42 % (16113)------------------------------ 258.08/37.42 % (16113)------------------------------ 258.08/37.43 % (16115)dis-1666_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:i=21027:si=on:rtra=on_0 on E---3.1_15619 for (1429ds/21027Mi) 259.87/37.68 % (16111)Instruction limit reached! 259.87/37.68 % (16111)------------------------------ 259.87/37.68 % (16111)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 259.87/37.68 % (16111)Termination reason: Unknown 259.87/37.68 % (16111)Termination phase: Saturation 259.87/37.68 259.87/37.68 % (16111)Memory used [KB]: 14839 259.87/37.68 % (16111)Time elapsed: 1.024 s 259.87/37.68 % (16111)Instructions burned: 3364 (million) 259.87/37.68 % (16111)------------------------------ 259.87/37.68 % (16111)------------------------------ 259.87/37.69 % (16116)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=35698:si=on:rtra=on_0 on E---3.1_15619 for (1427ds/35698Mi) 260.68/37.83 % (16072)Instruction limit reached! 260.68/37.83 % (16072)------------------------------ 260.68/37.83 % (16072)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 260.68/37.84 % (16072)Termination reason: Unknown 260.68/37.84 % (16072)Termination phase: Saturation 260.68/37.84 260.68/37.84 % (16072)Memory used [KB]: 13304 260.68/37.84 % (16072)Time elapsed: 5.222 s 260.68/37.84 % (16072)Instructions burned: 19003 (million) 260.68/37.84 % (16072)------------------------------ 260.68/37.84 % (16072)------------------------------ 260.68/37.84 % (16117)lrs-1010_1:50_au=on:awrs=converge:awrsf=430:bet=on:cbe=off:cha=on:nm=20:sac=on:i=14573:si=on:rtra=on_0 on E---3.1_15619 for (1425ds/14573Mi) 260.78/37.91 % (16104)Instruction limit reached! 260.78/37.91 % (16104)------------------------------ 260.78/37.91 % (16104)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 260.78/37.91 % (16104)Termination reason: Unknown 260.78/37.91 % (16104)Termination phase: Saturation 260.78/37.91 260.78/37.91 % (16104)Memory used [KB]: 33773 260.78/37.91 % (16104)Time elapsed: 3.762 s 260.78/37.91 % (16104)Instructions burned: 13159 (million) 260.78/37.91 % (16104)------------------------------ 260.78/37.91 % (16104)------------------------------ 260.78/37.92 % (16118)dis+1010_1:1_anc=all_dependent:au=on:bs=on:sd=5:sp=occurrence:ss=axioms:st=2.0:i=14014:si=on:rtra=on_0 on E---3.1_15619 for (1424ds/14014Mi) 276.72/40.07 % (16047)Instruction limit reached! 276.72/40.07 % (16047)------------------------------ 276.72/40.07 % (16047)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 276.72/40.07 % (16047)Termination reason: Unknown 276.72/40.07 % (16047)Termination phase: Saturation 276.72/40.07 276.72/40.07 % (16047)Memory used [KB]: 58847 276.72/40.07 % (16047)Time elapsed: 11.458 s 276.72/40.07 % (16047)Instructions burned: 35728 (million) 276.72/40.07 % (16047)------------------------------ 276.72/40.07 % (16047)------------------------------ 276.96/40.08 % (16119)dis+10_1:10_bd=preordered:e2e=on:fde=none:fe=axiom:hud=3:kws=precedence:nwc=3.0:prag=on:sp=const_max:tgt=full:i=4165:si=on:rtra=on_0 on E---3.1_15619 for (1403ds/4165Mi) 278.21/40.31 % (16114)Instruction limit reached! 278.21/40.31 % (16114)------------------------------ 278.21/40.31 % (16114)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 278.21/40.31 % (16114)Termination reason: Unknown 278.21/40.31 % (16114)Termination phase: Saturation 278.21/40.31 278.21/40.31 % (16114)Memory used [KB]: 6908 278.21/40.31 % (16114)Time elapsed: 3.465 s 278.21/40.31 % (16114)Instructions burned: 15188 (million) 278.21/40.31 % (16114)------------------------------ 278.21/40.31 % (16114)------------------------------ 278.21/40.32 % (16120)dis+1002_1:1_apa=on:au=on:cnfonf=off:e2e=on:flr=on:nm=4:s2a=on:i=8612:si=on:rtra=on_0 on E---3.1_15619 for (1400ds/8612Mi) 285.35/41.31 % (16117)Instruction limit reached! 285.35/41.31 % (16117)------------------------------ 285.35/41.31 % (16117)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 285.35/41.31 % (16117)Termination reason: Unknown 285.35/41.31 % (16117)Termination phase: Saturation 285.35/41.31 285.35/41.31 % (16117)Memory used [KB]: 7036 285.35/41.31 % (16117)Time elapsed: 3.451 s 285.35/41.31 % (16117)Instructions burned: 14577 (million) 285.35/41.31 % (16117)------------------------------ 285.35/41.31 % (16117)------------------------------ 285.35/41.32 % (16121)lrs-1_1:1_au=on:cbe=off:ntd=on:i=5576:si=on:rtra=on_0 on E---3.1_15619 for (1390ds/5576Mi) 286.26/41.44 % (16119)Instruction limit reached! 286.26/41.44 % (16119)------------------------------ 286.26/41.44 % (16119)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 286.26/41.44 % (16119)Termination reason: Unknown 286.26/41.44 % (16119)Termination phase: Saturation 286.26/41.44 286.26/41.44 % (16119)Memory used [KB]: 14967 286.26/41.44 % (16119)Time elapsed: 1.379 s 286.26/41.44 % (16119)Instructions burned: 4165 (million) 286.26/41.44 % (16119)------------------------------ 286.26/41.44 % (16119)------------------------------ 286.26/41.45 % (16122)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=4408:si=on:rtra=on_0 on E---3.1_15619 for (1389ds/4408Mi) 292.48/42.32 % (16115)Instruction limit reached! 292.48/42.32 % (16115)------------------------------ 292.48/42.32 % (16115)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 292.48/42.32 % (16115)Termination reason: Unknown 292.48/42.32 % (16115)Termination phase: Saturation 292.48/42.32 292.48/42.32 % (16115)Memory used [KB]: 7164 292.48/42.32 % (16115)Time elapsed: 4.884 s 292.48/42.32 % (16115)Instructions burned: 21027 (million) 292.48/42.32 % (16115)------------------------------ 292.48/42.32 % (16115)------------------------------ 292.48/42.32 % (16123)dis+1002_1:1_av=off:prag=on:sd=1:sos=on:sp=occurrence:ss=axioms:i=13925:si=on:rtra=on_0 on E---3.1_15619 for (1380ds/13925Mi) 292.74/42.36 % (16120)Instruction limit reached! 292.74/42.36 % (16120)------------------------------ 292.74/42.36 % (16120)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 292.74/42.36 % (16120)Termination reason: Unknown 292.74/42.36 % (16120)Termination phase: Saturation 292.74/42.36 292.74/42.36 % (16120)Memory used [KB]: 7036 292.74/42.36 % (16120)Time elapsed: 2.031 s 292.74/42.36 % (16120)Instructions burned: 8613 (million) 292.74/42.36 % (16120)------------------------------ 292.74/42.36 % (16120)------------------------------ 292.74/42.37 % (16124)lrs+1010_1:1_au=on:bd=off:e2e=on:fde=unused:nm=4:s2a=on:sos=all:sp=const_frequency:i=117046:si=on:rtra=on_0 on E---3.1_15619 for (1380ds/117046Mi) 292.74/42.39 % (16124)Refutation not found, incomplete strategy 292.74/42.39 % (16124)------------------------------ 292.74/42.39 % (16124)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 292.74/42.39 % (16124)Termination reason: Refutation not found, incomplete strategy 292.74/42.39 292.74/42.39 292.74/42.39 % (16124)Memory used [KB]: 6396 292.74/42.39 % (16124)Time elapsed: 0.022 s 292.74/42.39 % (16124)Instructions burned: 72 (million) 292.74/42.39 % (16124)------------------------------ 292.74/42.39 % (16124)------------------------------ 292.74/42.40 % (16125)lrs+1004_1:24_i=5433:si=on:rtra=on_0 on E---3.1_15619 for (1380ds/5433Mi) 293.30/42.48 % (16118)Instruction limit reached! 293.30/42.48 % (16118)------------------------------ 293.30/42.48 % (16118)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 293.30/42.48 % (16118)Termination reason: Unknown 293.30/42.48 % (16118)Termination phase: Saturation 293.30/42.48 293.30/42.48 % (16118)Memory used [KB]: 28272 293.30/42.48 % (16118)Time elapsed: 4.564 s 293.30/42.48 % (16118)Instructions burned: 14016 (million) 293.30/42.48 % (16118)------------------------------ 293.30/42.48 % (16118)------------------------------ 293.30/42.49 % (16126)dis+1002_1:1_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:nm=0:i=8192:si=on:rtra=on_0 on E---3.1_15619 for (1379ds/8192Mi) 293.95/42.62 % (16121)Instruction limit reached! 293.95/42.62 % (16121)------------------------------ 293.95/42.62 % (16121)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 293.95/42.62 % (16121)Termination reason: Unknown 293.95/42.62 % (16121)Termination phase: Saturation 293.95/42.62 293.95/42.62 % (16121)Memory used [KB]: 6908 293.95/42.62 % (16121)Time elapsed: 1.304 s 293.95/42.62 % (16121)Instructions burned: 5577 (million) 293.95/42.62 % (16121)------------------------------ 293.95/42.62 % (16121)------------------------------ 293.95/42.63 % (16127)lrs+32_1:1_au=on:bet=on:cbe=off:cs=on:ins=3:i=6102:si=on:rtra=on_0 on E---3.1_15619 for (1377ds/6102Mi) 296.36/42.87 % (16122)Instruction limit reached! 296.36/42.87 % (16122)------------------------------ 296.36/42.87 % (16122)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 296.36/42.87 % (16122)Termination reason: Unknown 296.36/42.87 % (16122)Termination phase: Saturation 296.36/42.87 296.36/42.87 % (16122)Memory used [KB]: 10874 296.36/42.87 % (16122)Time elapsed: 1.417 s 296.36/42.87 % (16122)Instructions burned: 4410 (million) 296.36/42.87 % (16122)------------------------------ 296.36/42.87 % (16122)------------------------------ 296.36/42.88 % (16128)lrs+1002_8:1_au=on:cs=on:e2e=on:nm=10:s2a=on:i=35602:si=on:rtra=on_0 on E---3.1_15619 for (1375ds/35602Mi) 301.74/43.65 % (16125)Instruction limit reached! 301.74/43.65 % (16125)------------------------------ 301.74/43.65 % (16125)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 301.74/43.65 % (16125)Termination reason: Unknown 301.74/43.65 % (16125)Termination phase: Saturation 301.74/43.65 301.74/43.65 % (16125)Memory used [KB]: 6908 301.74/43.65 % (16125)Time elapsed: 1.252 s 301.74/43.65 % (16125)Instructions burned: 5435 (million) 301.74/43.65 % (16125)------------------------------ 301.74/43.65 % (16125)------------------------------ 301.74/43.66 % (16129)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=6101:si=on:rtra=on_0 on E---3.1_15619 for (1367ds/6101Mi) 304.80/44.09 % (16127)Instruction limit reached! 304.80/44.09 % (16127)------------------------------ 304.80/44.09 % (16127)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 304.80/44.09 % (16127)Termination reason: Unknown 304.80/44.09 % (16127)Termination phase: Saturation 304.80/44.09 304.80/44.09 % (16127)Memory used [KB]: 6524 304.80/44.09 % (16127)Time elapsed: 1.450 s 304.80/44.09 % (16127)Instructions burned: 6106 (million) 304.80/44.09 % (16127)------------------------------ 304.80/44.09 % (16127)------------------------------ 304.80/44.10 % (16130)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=28153:si=on:rtra=on_0 on E---3.1_15619 for (1363ds/28153Mi) 306.63/44.38 % (16126)Instruction limit reached! 306.63/44.38 % (16126)------------------------------ 306.63/44.38 % (16126)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 306.63/44.38 % (16126)Termination reason: Unknown 306.63/44.38 % (16126)Termination phase: Saturation 306.63/44.38 306.63/44.38 % (16126)Memory used [KB]: 6908 306.63/44.38 % (16126)Time elapsed: 1.892 s 306.63/44.38 % (16126)Instructions burned: 8192 (million) 306.63/44.38 % (16126)------------------------------ 306.63/44.38 % (16126)------------------------------ 306.63/44.39 % (16131)lrs+10_1:1_cnfonf=off:sd=1:ss=axioms:st=3.0:i=13159:si=on:rtra=on_0 on E---3.1_15619 for (1360ds/13159Mi) 311.68/45.12 % (16129)Instruction limit reached! 311.68/45.12 % (16129)------------------------------ 311.68/45.12 % (16129)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 311.68/45.12 % (16129)Termination reason: Unknown 311.68/45.12 % (16129)Termination phase: Saturation 311.68/45.12 311.68/45.12 % (16129)Memory used [KB]: 6908 311.68/45.12 % (16129)Time elapsed: 1.461 s 311.68/45.12 % (16129)Instructions burned: 6103 (million) 311.68/45.12 % (16129)------------------------------ 311.68/45.12 % (16129)------------------------------ 311.68/45.13 % (16132)lrs+2_1:1_bet=on:bsr=on:cnfonf=lazy_pi_sigma_gen:er=filter:kws=inv_frequency:ntd=on:sd=3:ss=axioms:i=12389:si=on:rtra=on_0 on E---3.1_15619 for (1352ds/12389Mi) 319.32/46.23 % (16116)Instruction limit reached! 319.32/46.23 % (16116)------------------------------ 319.32/46.23 % (16116)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 319.32/46.23 % (16116)Termination reason: Unknown 319.32/46.23 % (16116)Termination phase: Saturation 319.32/46.23 319.32/46.23 % (16116)Memory used [KB]: 7036 319.32/46.23 % (16116)Time elapsed: 8.540 s 319.32/46.23 % (16116)Instructions burned: 35699 (million) 319.32/46.23 % (16116)------------------------------ 319.32/46.23 % (16116)------------------------------ 319.32/46.24 % (16134)dis+1002_16:1_au=on:nwc=5.0:i=37202:si=on:rtra=on_0 on E---3.1_15619 for (1341ds/37202Mi) 321.34/46.48 % (16123)Instruction limit reached! 321.34/46.48 % (16123)------------------------------ 321.34/46.48 % (16123)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 321.34/46.48 % (16123)Termination reason: Unknown 321.34/46.48 % (16123)Termination phase: Saturation 321.34/46.48 321.34/46.48 % (16123)Memory used [KB]: 6396 321.34/46.48 % (16123)Time elapsed: 4.168 s 321.34/46.48 % (16123)Instructions burned: 13925 (million) 321.34/46.48 % (16123)------------------------------ 321.34/46.48 % (16123)------------------------------ 321.34/46.49 % (16135)ott+10_1:10_cnfonf=lazy_gen:fde=none:sp=const_frequency:i=15814:si=on:rtra=on_0 on E---3.1_15619 for (1339ds/15814Mi) 332.29/48.02 % (16107)Instruction limit reached! 332.29/48.02 % (16107)------------------------------ 332.29/48.02 % (16107)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 332.29/48.02 % (16107)Termination reason: Unknown 332.29/48.02 % (16107)Termination phase: Saturation 332.29/48.02 332.29/48.02 % (16107)Memory used [KB]: 27888 332.29/48.02 % (16107)Time elapsed: 12.896 s 332.29/48.02 % (16107)Instructions burned: 41131 (million) 332.29/48.02 % (16107)------------------------------ 332.29/48.02 % (16107)------------------------------ 332.29/48.03 % (16136)dis+1010_1:28_add=off:cnfonf=lazy_not_gen:kws=frequency:piset=all:i=8801:si=on:rtra=on_0 on E---3.1_15619 for (1323ds/8801Mi) 332.80/48.11 % (16131)Instruction limit reached! 332.80/48.11 % (16131)------------------------------ 332.80/48.11 % (16131)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 332.80/48.11 % (16131)Termination reason: Unknown 332.80/48.11 % (16131)Termination phase: Saturation 332.80/48.11 332.80/48.11 % (16131)Memory used [KB]: 35436 332.80/48.11 % (16131)Time elapsed: 3.715 s 332.80/48.11 % (16131)Instructions burned: 13162 (million) 332.80/48.11 % (16131)------------------------------ 332.80/48.11 % (16131)------------------------------ 332.80/48.12 % (16156)ott-21_5:4_atotf=0.3:e2e=on:hud=15:ins=1:plsq=on:plsqc=1:plsqr=32,1:sp=unary_frequency:tnu=2:i=12360:si=on:rtra=on_0 on E---3.1_15619 for (1323ds/12360Mi) 339.15/48.98 % (16132)Instruction limit reached! 339.15/48.98 % (16132)------------------------------ 339.15/48.98 % (16132)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 339.15/48.98 % (16132)Termination reason: Unknown 339.15/48.98 % (16132)Termination phase: Saturation 339.15/48.98 339.15/48.98 % (16132)Memory used [KB]: 17398 339.15/48.98 % (16132)Time elapsed: 3.848 s 339.15/48.98 % (16132)Instructions burned: 12389 (million) 339.15/48.98 % (16132)------------------------------ 339.15/48.98 % (16132)------------------------------ 339.15/48.99 % (16371)lrs+10_1:156_afp=4000:avsq=on:avsqr=4,1:fe=axiom:ss=axioms:tgt=ground:i=19001:si=on:rtra=on_0 on E---3.1_15619 for (1314ds/19001Mi) 346.79/50.09 % (16136)Instruction limit reached! 346.79/50.09 % (16136)------------------------------ 346.79/50.09 % (16136)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 346.79/50.09 % (16136)Termination reason: Unknown 346.79/50.09 % (16136)Termination phase: Saturation 346.79/50.09 346.79/50.09 % (16136)Memory used [KB]: 6908 346.79/50.09 % (16136)Time elapsed: 2.057 s 346.79/50.09 % (16136)Instructions burned: 8801 (million) 346.79/50.09 % (16136)------------------------------ 346.79/50.09 % (16136)------------------------------ 346.79/50.10 % (16379)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=28134:si=on:rtra=on_0 on E---3.1_15619 for (1303ds/28134Mi) 347.07/50.11 % (16379)Refutation not found, incomplete strategy 347.07/50.11 % (16379)------------------------------ 347.07/50.11 % (16379)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 347.07/50.11 % (16379)Termination reason: Refutation not found, incomplete strategy 347.07/50.11 347.07/50.11 347.07/50.11 % (16379)Memory used [KB]: 6268 347.07/50.11 % (16379)Time elapsed: 0.015 s 347.07/50.11 % (16379)Instructions burned: 43 (million) 347.07/50.11 % (16379)------------------------------ 347.07/50.11 % (16379)------------------------------ 347.07/50.12 % (16380)dis+10_1:1_fde=none:kws=precedence:piset=not:prag=on:slsq=on:slsqc=1:sp=unary_frequency:i=23684:si=on:rtra=on_0 on E---3.1_15619 for (1302ds/23684Mi) 349.75/50.49 % (16130)Instruction limit reached! 349.75/50.49 % (16130)------------------------------ 349.75/50.49 % (16130)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 349.75/50.49 % (16130)Termination reason: Unknown 349.75/50.49 % (16130)Termination phase: Saturation 349.75/50.49 349.75/50.49 % (16130)Memory used [KB]: 7036 349.75/50.49 % (16130)Time elapsed: 6.397 s 349.75/50.49 % (16130)Instructions burned: 28157 (million) 349.75/50.49 % (16130)------------------------------ 349.75/50.49 % (16130)------------------------------ 349.75/50.50 % (16381)ott+10_1:10_avsq=on:bd=off:cnfonf=lazy_gen:sd=2:sgt=16:sos=on:ss=axioms:i=56001:si=on:rtra=on_0 on E---3.1_15619 for (1299ds/56001Mi) 352.96/50.97 % (16156)Instruction limit reached! 352.96/50.97 % (16156)------------------------------ 352.96/50.97 % (16156)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 352.96/50.97 % (16156)Termination reason: Unknown 352.96/50.97 % (16156)Termination phase: Saturation 352.96/50.97 352.96/50.97 % (16156)Memory used [KB]: 7036 352.96/50.97 % (16156)Time elapsed: 2.854 s 352.96/50.97 % (16156)Instructions burned: 12363 (million) 352.96/50.97 % (16156)------------------------------ 352.96/50.97 % (16156)------------------------------ 352.96/50.98 % (16382)dis+2_1:1_cbe=off:fe=off:i=13068:si=on:rtra=on_0 on E---3.1_15619 for (1294ds/13068Mi) 352.96/51.01 % (16128)Instruction limit reached! 352.96/51.01 % (16128)------------------------------ 352.96/51.01 % (16128)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 352.96/51.01 % (16128)Termination reason: Unknown 352.96/51.01 % (16128)Termination phase: Saturation 352.96/51.01 352.96/51.01 % (16128)Memory used [KB]: 7036 352.96/51.01 % (16128)Time elapsed: 8.133 s 352.96/51.01 % (16128)Instructions burned: 35604 (million) 352.96/51.01 % (16128)------------------------------ 352.96/51.01 % (16128)------------------------------ 352.96/51.02 % (16383)dis+10_3:1_anc=all:avsq=on:c=on:cnfonf=off:e2e=on:fd=off:fde=none:ins=3:nwc=5.0:plsq=on:plsqc=1:plsqr=4964065,131072:prag=on:s2a=on:s2agt=64:i=8801:si=on:rtra=on_0 on E---3.1_15619 for (1294ds/8801Mi) 353.80/51.13 % (16135)Instruction limit reached! 353.80/51.13 % (16135)------------------------------ 353.80/51.13 % (16135)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 353.80/51.13 % (16135)Termination reason: Unknown 353.80/51.13 % (16135)Termination phase: Saturation 353.80/51.13 353.80/51.13 % (16135)Memory used [KB]: 30063 353.80/51.13 % (16135)Time elapsed: 4.641 s 353.80/51.13 % (16135)Instructions burned: 15814 (million) 353.80/51.13 % (16135)------------------------------ 353.80/51.13 % (16135)------------------------------ 353.80/51.14 % (16385)dis+1010_1:64_bet=on:cond=fast:e2e=on:fe=off:hud=5:nm=0:ntd=on:nwc=7.0:piset=and:prag=on:rawr=on:sgt=40:ss=included:uhcvi=on:i=42318:si=on:rtra=on_0 on E---3.1_15619 for (1292ds/42318Mi) 369.81/53.39 % (16371)Instruction limit reached! 369.81/53.39 % (16371)------------------------------ 369.81/53.39 % (16371)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 369.81/53.39 % (16371)Termination reason: Unknown 369.81/53.39 % (16371)Termination phase: Saturation 369.81/53.39 369.81/53.39 % (16371)Memory used [KB]: 12025 369.81/53.39 % (16371)Time elapsed: 4.430 s 369.81/53.39 % (16371)Instructions burned: 19003 (million) 369.81/53.39 % (16371)------------------------------ 369.81/53.39 % (16371)------------------------------ 370.24/53.40 % (16386)dis+1010_1:1_au=on:avsq=on:bd=off:cbe=off:cnfonf=off:cs=on:hud=5:nm=0:plsq=on:plsqc=1:plsqr=7,1:ss=axioms:tgt=full:i=10924:si=on:rtra=on_0 on E---3.1_15619 for (1270ds/10924Mi) 370.24/53.45 % (16386)Refutation not found, incomplete strategy 370.24/53.45 % (16386)------------------------------ 370.24/53.45 % (16386)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 370.24/53.45 % (16386)Termination reason: Refutation not found, incomplete strategy 370.24/53.45 370.24/53.45 370.24/53.45 % (16386)Memory used [KB]: 6396 370.24/53.45 % (16386)Time elapsed: 0.050 s 370.24/53.45 % (16386)Instructions burned: 144 (million) 370.24/53.45 % (16386)------------------------------ 370.24/53.45 % (16386)------------------------------ 370.66/53.46 % (16387)lrs+1010_1:1_anc=all_dependent:cnfonf=conj_eager:cond=fast:fe=axiom:nm=16:s2a=on:s2at=4.0:sd=2:ss=axioms:st=3.0:i=96745:si=on:rtra=on_0 on E---3.1_15619 for (1269ds/96745Mi) 372.02/53.67 % (16383)Instruction limit reached! 372.02/53.67 % (16383)------------------------------ 372.02/53.67 % (16383)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 372.02/53.67 % (16383)Termination reason: Unknown 372.02/53.67 % (16383)Termination phase: Saturation 372.02/53.67 372.02/53.67 % (16383)Memory used [KB]: 37995 372.02/53.67 % (16383)Time elapsed: 2.686 s 372.02/53.67 % (16383)Instructions burned: 8801 (million) 372.02/53.67 % (16383)------------------------------ 372.02/53.67 % (16383)------------------------------ 372.02/53.69 % (16388)lrs-1010_8:1_au=on:c=on:ins=1:i=70437:si=on:rtra=on_0 on E---3.1_15619 for (1267ds/70437Mi) 374.99/54.18 % (16382)Instruction limit reached! 374.99/54.18 % (16382)------------------------------ 374.99/54.18 % (16382)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 374.99/54.18 % (16382)Termination reason: Unknown 374.99/54.18 % (16382)Termination phase: Saturation 374.99/54.18 374.99/54.18 % (16382)Memory used [KB]: 7036 374.99/54.18 % (16382)Time elapsed: 3.201 s 374.99/54.18 % (16382)Instructions burned: 13071 (million) 374.99/54.18 % (16382)------------------------------ 374.99/54.18 % (16382)------------------------------ 374.99/54.19 % (16389)lrs+1002_1:1_aac=none:bd=off:e2e=on:fde=none:fe=off:piset=or:prag=on:rawr=on:sos=on:updr=off:i=11540:si=on:rtra=on_0 on E---3.1_15619 for (1262ds/11540Mi) 375.83/54.21 % (16389)Refutation not found, incomplete strategy 375.83/54.21 % (16389)------------------------------ 375.83/54.21 % (16389)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 375.83/54.21 % (16389)Termination reason: Refutation not found, incomplete strategy 375.83/54.21 375.83/54.21 375.83/54.21 % (16389)Memory used [KB]: 6396 375.83/54.21 % (16389)Time elapsed: 0.022 s 375.83/54.21 % (16389)Instructions burned: 71 (million) 375.83/54.21 % (16389)------------------------------ 375.83/54.21 % (16389)------------------------------ 375.83/54.22 % (16390)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=32059:si=on:rtra=on_0 on E---3.1_15619 for (1261ds/32059Mi) 380.07/54.80 % (16134)Instruction limit reached! 380.07/54.80 % (16134)------------------------------ 380.07/54.80 % (16134)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 380.07/54.80 % (16134)Termination reason: Unknown 380.07/54.80 % (16134)Termination phase: Saturation 380.07/54.80 380.07/54.80 % (16134)Memory used [KB]: 7036 380.07/54.80 % (16134)Time elapsed: 8.566 s 380.07/54.80 % (16134)Instructions burned: 37204 (million) 380.07/54.80 % (16134)------------------------------ 380.07/54.80 % (16134)------------------------------ 380.07/54.81 % (16391)lrs+1002_1:128_atotf=0.1:au=on:cbe=off:ntd=on:sp=const_frequency:i=14041:si=on:rtra=on_0 on E---3.1_15619 for (1256ds/14041Mi) 399.71/57.63 % (16380)Instruction limit reached! 399.71/57.63 % (16380)------------------------------ 399.71/57.63 % (16380)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 399.71/57.63 % (16380)Termination reason: Unknown 399.71/57.63 % (16380)Termination phase: Saturation 399.71/57.63 399.71/57.63 % (16380)Memory used [KB]: 50404 399.71/57.63 % (16380)Time elapsed: 7.506 s 399.71/57.63 % (16380)Instructions burned: 23684 (million) 399.71/57.63 % (16380)------------------------------ 399.71/57.63 % (16380)------------------------------ 399.71/57.64 % (16392)dis+10_1:1_fe=axiom:fsr=off:hud=5:nwc=6.0:plsq=on:plsqc=2:plsqr=32,1:s2a=on:s2agt=40:sp=weighted_frequency:i=15424:si=on:rtra=on_0 on E---3.1_15619 for (1227ds/15424Mi) 402.39/58.05 % (16391)Instruction limit reached! 402.39/58.05 % (16391)------------------------------ 402.39/58.05 % (16391)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 402.39/58.05 % (16391)Termination reason: Unknown 402.39/58.05 % (16391)Termination phase: Saturation 402.39/58.05 402.39/58.05 % (16391)Memory used [KB]: 6908 402.39/58.05 % (16391)Time elapsed: 3.237 s 402.39/58.05 % (16391)Instructions burned: 14043 (million) 402.39/58.05 % (16391)------------------------------ 402.39/58.05 % (16391)------------------------------ 402.39/58.05 % (16393)ott+1666_1:1_hfaw=0:hfsq=on:hfsql=off:hfsqr=1,16:hud=15:slsq=on:slsqr=1,2:tnu=2:i=3971:si=on:rtra=on_0 on E---3.1_15619 for (1223ds/3971Mi) 409.38/59.00 % (16393)Instruction limit reached! 409.38/59.00 % (16393)------------------------------ 409.38/59.00 % (16393)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 409.38/59.00 % (16393)Termination reason: Unknown 409.38/59.00 % (16393)Termination phase: Saturation 409.38/59.00 409.38/59.00 % (16393)Memory used [KB]: 6908 409.38/59.00 % (16393)Time elapsed: 0.945 s 409.38/59.00 % (16393)Instructions burned: 3974 (million) 409.38/59.00 % (16393)------------------------------ 409.38/59.00 % (16393)------------------------------ 409.38/59.01 % (16394)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on E---3.1_15619 for (1214ds/2207Mi) 412.76/59.53 % (16394)Instruction limit reached! 412.76/59.53 % (16394)------------------------------ 412.76/59.53 % (16394)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 412.76/59.53 % (16394)Termination reason: Unknown 412.76/59.53 % (16394)Termination phase: Saturation 412.76/59.53 412.76/59.53 % (16394)Memory used [KB]: 6908 412.76/59.53 % (16394)Time elapsed: 0.528 s 412.76/59.53 % (16394)Instructions burned: 2210 (million) 412.76/59.53 % (16394)------------------------------ 412.76/59.53 % (16394)------------------------------ 413.32/59.54 % (16444)dis+1002_1:1_au=on:bsr=unit_only:cbe=off:fe=off:fsr=off:nm=10:nwc=6.0:plsq=on:plsqc=1:plsqr=32,1:sos=all:i=2635:si=on:rtra=on_0 on E---3.1_15619 for (1208ds/2635Mi) 417.52/60.16 % (16444)Instruction limit reached! 417.52/60.16 % (16444)------------------------------ 417.52/60.16 % (16444)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 417.52/60.16 % (16444)Termination reason: Unknown 417.52/60.16 % (16444)Termination phase: Saturation 417.52/60.16 417.52/60.16 % (16444)Memory used [KB]: 2430 417.52/60.16 % (16444)Time elapsed: 0.617 s 417.52/60.16 % (16444)Instructions burned: 2638 (million) 417.52/60.16 % (16444)------------------------------ 417.52/60.16 % (16444)------------------------------ 417.52/60.17 % (16659)dis+1010_2:1_avsq=on:fde=unused:prag=on:i=3362:si=on:rtra=on_0 on E---3.1_15619 for (1202ds/3362Mi) 420.17/60.52 % (16381)First to succeed. 420.49/60.60 % (16381)Refutation found. Thanks to Tanya! 420.49/60.60 % SZS status Theorem for E---3.1_15619 420.49/60.60 % SZS output start Proof for E---3.1_15619 420.49/60.60 thf(func_def_0, type, is_of: $i > ($i > $o) > $o). 420.49/60.60 thf(func_def_2, type, all_of: ($i > $o) > ($i > $o) > $o). 420.49/60.60 thf(func_def_3, type, eps: ($i > $o) > $i). 420.49/60.60 thf(func_def_4, type, in: $i > $i > $o). 420.49/60.60 thf(func_def_5, type, d_Subq: $i > $i > $o). 420.49/60.60 thf(func_def_7, type, union: $i > $i). 420.49/60.60 thf(func_def_8, type, power: $i > $i). 420.49/60.60 thf(func_def_9, type, repl: $i > ($i > $i) > $i). 420.49/60.60 thf(func_def_10, type, d_Union_closed: $i > $o). 420.49/60.60 thf(func_def_11, type, d_Power_closed: $i > $o). 420.49/60.60 thf(func_def_12, type, d_Repl_closed: $i > $o). 420.49/60.60 thf(func_def_13, type, d_ZF_closed: $i > $o). 420.49/60.60 thf(func_def_14, type, univof: $i > $i). 420.49/60.60 thf(func_def_15, type, if: $o > $i > $i > $i). 420.49/60.60 thf(func_def_16, type, nIn: $i > $i > $o). 420.49/60.60 thf(func_def_17, type, d_UPair: $i > $i > $i). 420.49/60.60 thf(func_def_18, type, d_Sing: $i > $i). 420.49/60.60 thf(func_def_19, type, binunion: $i > $i > $i). 420.49/60.60 thf(func_def_20, type, famunion: $i > ($i > $i) > $i). 420.49/60.60 thf(func_def_21, type, d_Sep: $i > ($i > $o) > $i). 420.49/60.60 thf(func_def_22, type, d_ReplSep: $i > ($i > $o) > ($i > $i) > $i). 420.49/60.60 thf(func_def_23, type, setminus: $i > $i > $i). 420.49/60.60 thf(func_def_24, type, d_In_rec_G: ($i > ($i > $i) > $i) > $i > $i > $o). 420.49/60.60 thf(func_def_25, type, d_In_rec: ($i > ($i > $i) > $i) > $i > $i). 420.49/60.60 thf(func_def_26, type, ordsucc: $i > $i). 420.49/60.60 thf(func_def_27, type, nat_p: $i > $o). 420.49/60.60 thf(func_def_29, type, d_Inj1: $i > $i). 420.49/60.60 thf(func_def_30, type, d_Inj0: $i > $i). 420.49/60.60 thf(func_def_31, type, d_Unj: $i > $i). 420.49/60.60 thf(func_def_32, type, pair: $i > $i > $i). 420.49/60.60 thf(func_def_33, type, proj0: $i > $i). 420.49/60.60 thf(func_def_34, type, proj1: $i > $i). 420.49/60.60 thf(func_def_35, type, d_Sigma: $i > ($i > $i) > $i). 420.49/60.60 thf(func_def_36, type, setprod: $i > $i > $i). 420.49/60.60 thf(func_def_37, type, ap: $i > $i > $i). 420.49/60.60 thf(func_def_38, type, pair_p: $i > $o). 420.49/60.60 thf(func_def_39, type, d_Pi: $i > ($i > $i) > $i). 420.49/60.60 thf(func_def_40, type, imp: $o > $o > $o). 420.49/60.60 thf(func_def_41, type, d_not: $o > $o). 420.49/60.60 thf(func_def_42, type, wel: $o > $o). 420.49/60.60 thf(func_def_44, type, l_ec: $o > $o > $o). 420.49/60.60 thf(func_def_45, type, d_and: $o > $o > $o). 420.49/60.60 thf(func_def_46, type, l_or: $o > $o > $o). 420.49/60.60 thf(func_def_47, type, orec: $o > $o > $o). 420.49/60.60 thf(func_def_48, type, l_iff: $o > $o > $o). 420.49/60.60 thf(func_def_49, type, all: $i > ($i > $o) > $o). 420.49/60.60 thf(func_def_50, type, non: $i > ($i > $o) > $i > $o). 420.49/60.60 thf(func_def_51, type, l_some: $i > ($i > $o) > $o). 420.49/60.60 thf(func_def_52, type, or3: $o > $o > $o > $o). 420.49/60.60 thf(func_def_53, type, and3: $o > $o > $o > $o). 420.49/60.60 thf(func_def_54, type, ec3: $o > $o > $o > $o). 420.49/60.60 thf(func_def_55, type, orec3: $o > $o > $o > $o). 420.49/60.60 thf(func_def_56, type, e_is: $i > $i > $i > $o). 420.49/60.60 thf(func_def_57, type, amone: $i > ($i > $o) > $o). 420.49/60.60 thf(func_def_58, type, one: $i > ($i > $o) > $o). 420.49/60.60 thf(func_def_59, type, ind: $i > ($i > $o) > $i). 420.49/60.60 thf(func_def_60, type, injective: $i > $i > $i > $o). 420.49/60.60 thf(func_def_61, type, image: $i > $i > $i > $i > $o). 420.49/60.60 thf(func_def_62, type, tofs: $i > $i > $i > $i > $i). 420.49/60.60 thf(func_def_63, type, soft: $i > $i > $i > $i > $i). 420.49/60.60 thf(func_def_64, type, inverse: $i > $i > $i > $i). 420.49/60.60 thf(func_def_65, type, surjective: $i > $i > $i > $o). 420.49/60.60 thf(func_def_66, type, bijective: $i > $i > $i > $o). 420.49/60.60 thf(func_def_67, type, invf: $i > $i > $i > $i). 420.49/60.60 thf(func_def_68, type, inj_h: $i > $i > $i > $i > $i > $i). 420.49/60.60 thf(func_def_69, type, e_in: $i > ($i > $o) > $i > $i). 420.49/60.60 thf(func_def_70, type, out: $i > ($i > $o) > $i > $i). 420.49/60.60 thf(func_def_71, type, d_pair: $i > $i > $i > $i > $i). 420.49/60.60 thf(func_def_72, type, first: $i > $i > $i > $i). 420.49/60.60 thf(func_def_73, type, second: $i > $i > $i > $i). 420.49/60.60 thf(func_def_74, type, prop1: $o > $i > $i > $i > $i > $o). 420.49/60.60 thf(func_def_75, type, ite: $o > $i > $i > $i > $i). 420.49/60.60 thf(func_def_76, type, wissel_wa: $i > $i > $i > $i > $i). 420.49/60.60 thf(func_def_77, type, wissel_wb: $i > $i > $i > $i > $i). 420.49/60.60 thf(func_def_78, type, wissel: $i > $i > $i > $i). 420.49/60.60 thf(func_def_79, type, changef: $i > $i > $i > $i > $i > $i). 420.49/60.60 thf(func_def_80, type, r_ec: $o > $o > $o). 420.49/60.60 thf(func_def_81, type, esti: $i > $i > $i > $o). 420.49/60.60 thf(func_def_82, type, empty: $i > $i > $o). 420.49/60.60 thf(func_def_83, type, nonempty: $i > $i > $o). 420.49/60.60 thf(func_def_84, type, incl: $i > $i > $i > $o). 420.49/60.60 thf(func_def_85, type, st_disj: $i > $i > $i > $o). 420.49/60.60 thf(func_def_86, type, nissetprop: $i > $i > $i > $i > $o). 420.49/60.60 thf(func_def_87, type, unmore: $i > $i > $i > $i). 420.49/60.60 thf(func_def_88, type, ecelt: $i > ($i > $i > $o) > $i > $i). 420.49/60.60 thf(func_def_89, type, ecp: $i > ($i > $i > $o) > $i > $i > $o). 420.49/60.60 thf(func_def_90, type, anec: $i > ($i > $i > $o) > $i > $o). 420.49/60.60 thf(func_def_91, type, ect: $i > ($i > $i > $o) > $i). 420.49/60.60 thf(func_def_92, type, ectset: $i > ($i > $i > $o) > $i > $i). 420.49/60.60 thf(func_def_93, type, ectelt: $i > ($i > $i > $o) > $i > $i). 420.49/60.60 thf(func_def_94, type, ecect: $i > ($i > $i > $o) > $i > $i). 420.49/60.60 thf(func_def_95, type, fixfu: $i > ($i > $i > $o) > $i > $i > $o). 420.49/60.60 thf(func_def_96, type, d_10_prop1: $i > ($i > $i > $o) > $i > $i > $i > $i > $i > $o). 420.49/60.60 thf(func_def_97, type, prop2: $i > ($i > $i > $o) > $i > $i > $i > $i > $o). 420.49/60.60 thf(func_def_98, type, indeq: $i > ($i > $i > $o) > $i > $i > $i > $i). 420.49/60.60 thf(func_def_99, type, fixfu2: $i > ($i > $i > $o) > $i > $i > $o). 420.49/60.60 thf(func_def_100, type, d_11_i: $i > ($i > $i > $o) > $i > $i > $i > $i). 420.49/60.60 thf(func_def_101, type, indeq2: $i > ($i > $i > $o) > $i > $i > $i > $i > $i). 420.49/60.60 thf(func_def_103, type, n_is: $i > $i > $o). 420.49/60.60 thf(func_def_104, type, nis: $i > $i > $o). 420.49/60.60 thf(func_def_105, type, n_in: $i > $i > $o). 420.49/60.60 thf(func_def_106, type, n_some: ($i > $o) > $o). 420.49/60.60 thf(func_def_107, type, n_all: ($i > $o) > $o). 420.49/60.60 thf(func_def_108, type, n_one: ($i > $o) > $o). 420.49/60.60 thf(func_def_110, type, cond1: $i > $o). 420.49/60.60 thf(func_def_111, type, cond2: $i > $o). 420.49/60.60 thf(func_def_112, type, i1_s: ($i > $o) > $i). 420.49/60.60 thf(func_def_113, type, d_22_prop1: $i > $o). 420.49/60.60 thf(func_def_114, type, d_23_prop1: $i > $o). 420.49/60.60 thf(func_def_115, type, d_24_prop1: $i > $o). 420.49/60.60 thf(func_def_116, type, d_24_prop2: $i > $i > $o). 420.49/60.60 thf(func_def_117, type, prop3: $i > $i > $i > $o). 420.49/60.60 thf(func_def_118, type, prop4: $i > $o). 420.49/60.60 thf(func_def_119, type, d_24_g: $i > $i). 420.49/60.60 thf(func_def_120, type, plus: $i > $i). 420.49/60.60 thf(func_def_121, type, n_pl: $i > $i > $i). 420.49/60.60 thf(func_def_122, type, d_25_prop1: $i > $i > $i > $o). 420.49/60.60 thf(func_def_123, type, d_26_prop1: $i > $i > $o). 420.49/60.60 thf(func_def_124, type, d_27_prop1: $i > $i > $o). 420.49/60.60 thf(func_def_125, type, d_28_prop1: $i > $i > $i > $o). 420.49/60.60 thf(func_def_126, type, diffprop: $i > $i > $i > $o). 420.49/60.60 thf(func_def_127, type, d_29_ii: $i > $i > $o). 420.49/60.60 thf(func_def_128, type, iii: $i > $i > $o). 420.49/60.60 thf(func_def_129, type, d_29_prop1: $i > $i > $o). 420.49/60.60 thf(func_def_130, type, moreis: $i > $i > $o). 420.49/60.60 thf(func_def_131, type, lessis: $i > $i > $o). 420.49/60.60 thf(func_def_152, type, ph1: !>[X0: $tType]:(X0)). 420.49/60.60 thf(f16832,plain,( 420.49/60.60 $false), 420.49/60.60 inference(avatar_sat_refutation,[],[f16813,f16831])). 420.49/60.60 thf(f16831,plain,( 420.49/60.60 ~spl0_897), 420.49/60.60 inference(avatar_contradiction_clause,[],[f16830])). 420.49/60.60 thf(f16830,plain,( 420.49/60.60 $false | ~spl0_897), 420.49/60.60 inference(trivial_inequality_removal,[],[f16829])). 420.49/60.60 thf(f16829,plain,( 420.49/60.60 (((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK39 @ Y0)))))) => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK39 = (n_pl @ sK38 @ Y0)))))) != ((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK39 @ Y0)))))) => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK39 = (n_pl @ sK38 @ Y0))))))) | ~spl0_897), 420.49/60.60 inference(boolean_simplification,[],[f16828])). 420.49/60.60 thf(f16828,plain,( 420.49/60.60 (((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK39 @ Y0)))))) => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK39 = (n_pl @ sK38 @ Y0)))))) != (~ (~ ((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK39 @ Y0)))))) => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK39 = (n_pl @ sK38 @ Y0))))))))) | ~spl0_897), 420.49/60.60 inference(boolean_simplification,[],[f16827])). 420.49/60.60 thf(f16827,plain,( 420.49/60.60 ((~ ($true => (~ ((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK39 @ Y0)))))) => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK39 = (n_pl @ sK38 @ Y0))))))))) != ((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK39 @ Y0)))))) => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK39 = (n_pl @ sK38 @ Y0))))))) | ~spl0_897), 420.49/60.60 inference(boolean_simplification,[],[f16826])). 420.49/60.60 thf(f16826,plain,( 420.49/60.60 ((~ (($false => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK39 @ Y0)))))) => (~ ((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK39 @ Y0)))))) => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK39 = (n_pl @ sK38 @ Y0))))))))) != ((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK39 @ Y0)))))) => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK39 = (n_pl @ sK38 @ Y0))))))) | ~spl0_897), 420.49/60.60 inference(boolean_simplification,[],[f16825])). 420.49/60.60 thf(f16825,plain,( 420.49/60.60 ((~ (($false => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK39 @ Y0)))))) => (((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK39 @ Y0)))))) => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK39 = (n_pl @ sK38 @ Y0)))))) => $false))) != ((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK39 @ Y0)))))) => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK39 = (n_pl @ sK38 @ Y0))))))) | ~spl0_897), 420.49/60.60 inference(boolean_simplification,[],[f16824])). 420.49/60.60 thf(f16824,plain,( 420.49/60.60 (((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK39 @ Y0)))))) => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK39 = (n_pl @ sK38 @ Y0)))))) != (~ (($false => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK39 @ Y0)))))) => (((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK39 @ Y0)))))) => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK39 = (n_pl @ sK38 @ Y0)))))) => (~ $true))))) | ~spl0_897), 420.49/60.60 inference(boolean_simplification,[],[f16823])). 420.49/60.60 thf(f16823,plain,( 420.49/60.60 ((~ (($false => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK39 @ Y0)))))) => (((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK39 @ Y0)))))) => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK39 = (n_pl @ sK38 @ Y0)))))) => (~ ((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK39 = (n_pl @ sK38 @ Y0)))))) => $true))))) != ((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK39 @ Y0)))))) => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK39 = (n_pl @ sK38 @ Y0))))))) | ~spl0_897), 420.49/60.60 inference(boolean_simplification,[],[f16822])). 420.49/60.60 thf(f16822,plain,( 420.49/60.60 ((~ (($false => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK39 @ Y0)))))) => (((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK39 @ Y0)))))) => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK39 = (n_pl @ sK38 @ Y0)))))) => (~ ((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK39 = (n_pl @ sK38 @ Y0)))))) => (~ $false)))))) != ((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK39 @ Y0)))))) => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK39 = (n_pl @ sK38 @ Y0))))))) | ~spl0_897), 420.49/60.60 inference(boolean_simplification,[],[f16821])). 420.49/60.60 thf(f16821,plain,( 420.49/60.60 ((~ (($false => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK39 @ Y0)))))) => (((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK39 @ Y0)))))) => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK39 = (n_pl @ sK38 @ Y0)))))) => (~ ((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK39 = (n_pl @ sK38 @ Y0)))))) => (~ $false)))))) != (((all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK39 @ Y0))))) => $false) => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK39 = (n_pl @ sK38 @ Y0))))))) | ~spl0_897), 420.49/60.60 inference(superposition,[],[f8624,f9255])). 420.49/60.60 thf(f9255,plain,( 420.49/60.60 ((sK38 = sK39) = $false) | ~spl0_897), 420.49/60.60 inference(avatar_component_clause,[],[f9254])). 420.49/60.60 thf(f9254,plain,( 420.49/60.60 spl0_897 <=> ((sK38 = sK39) = $false)), 420.49/60.60 introduced(avatar_definition,[new_symbols(naming,[spl0_897])])). 420.49/60.60 thf(f8624,plain,( 420.49/60.60 ((((all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK39 @ Y0))))) => (sK38 = sK39)) => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK39 = (n_pl @ sK38 @ Y0)))))) != (~ (((sK38 = sK39) => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK39 @ Y0)))))) => (((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK39 @ Y0)))))) => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK39 = (n_pl @ sK38 @ Y0)))))) => (~ ((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK39 = (n_pl @ sK38 @ Y0)))))) => (~ (sK38 = sK39))))))))), 420.49/60.60 inference(beta_eta_normalization,[],[f8623])). 420.49/60.60 thf(f8623,plain,( 420.49/60.60 (((^[Y0 : $i]: (~ (((sK38 = Y0) => (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((emptyset = Y3) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (~ (sK38 = (n_pl @ Y0 @ Y1)))))) => (((~ (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((emptyset = Y3) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (~ (sK38 = (n_pl @ Y0 @ Y1)))))) => (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((emptyset = Y3) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (~ (Y0 = (n_pl @ sK38 @ Y1)))))) => (~ ((~ (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((emptyset = Y3) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (~ (Y0 = (n_pl @ sK38 @ Y1)))))) => (~ (sK38 = Y0)))))))) @ sK39) != ((^[Y0 : $i]: (((all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((emptyset = Y3) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (~ (sK38 = (n_pl @ Y0 @ Y1))))) => (sK38 = Y0)) => (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((emptyset = Y3) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (~ (Y0 = (n_pl @ sK38 @ Y1))))))) @ sK39))), 420.49/60.60 inference(negative_extensionality,[],[f8511])). 420.49/60.60 thf(f8511,plain,( 420.49/60.60 ((^[Y0 : $i]: (((all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((emptyset = Y3) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (~ (sK38 = (n_pl @ Y0 @ Y1))))) => (sK38 = Y0)) => (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((emptyset = Y3) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (~ (Y0 = (n_pl @ sK38 @ Y1))))))) != (^[Y0 : $i]: (~ (((sK38 = Y0) => (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((emptyset = Y3) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (~ (sK38 = (n_pl @ Y0 @ Y1)))))) => (((~ (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((emptyset = Y3) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (~ (sK38 = (n_pl @ Y0 @ Y1)))))) => (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((emptyset = Y3) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (~ (Y0 = (n_pl @ sK38 @ Y1)))))) => (~ ((~ (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((emptyset = Y3) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (~ (Y0 = (n_pl @ sK38 @ Y1)))))) => (~ (sK38 = Y0)))))))))), 420.49/60.60 inference(equality_resolution,[],[f8484])). 420.49/60.60 thf(f8484,plain,( 420.49/60.60 ((all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (((all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((emptyset = Y3) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (~ (sK38 = (n_pl @ Y0 @ Y1))))) => (sK38 = Y0)) => (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((emptyset = Y3) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (~ (Y0 = (n_pl @ sK38 @ Y1)))))))) != (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (((sK38 = Y0) => (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((emptyset = Y3) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (~ (sK38 = (n_pl @ Y0 @ Y1)))))) => (((~ (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((emptyset = Y3) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (~ (sK38 = (n_pl @ Y0 @ Y1)))))) => (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((emptyset = Y3) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (~ (Y0 = (n_pl @ sK38 @ Y1)))))) => (~ ((~ (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((emptyset = Y3) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (~ (Y0 = (n_pl @ sK38 @ Y1)))))) => (~ (sK38 = Y0))))))))))), 420.49/60.60 inference(beta_eta_normalization,[],[f8483])). 420.49/60.60 thf(f8483,plain,( 420.49/60.60 (((^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((emptyset = Y3) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y0 = (n_pl @ Y1 @ Y2))))) => (Y0 = Y1)) => (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y1 = (n_pl @ Y0 @ Y2))))))))) @ sK38) != ((^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((emptyset = Y3) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (~ (((Y0 = Y1) => (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y0 = (n_pl @ Y1 @ Y2)))))) => (((~ (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y0 = (n_pl @ Y1 @ Y2)))))) => (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y1 = (n_pl @ Y0 @ Y2)))))) => (~ ((~ (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y1 = (n_pl @ Y0 @ Y2)))))) => (~ (Y0 = Y1)))))))))) @ sK38))), 420.49/60.60 inference(negative_extensionality,[],[f1004])). 420.49/60.60 thf(f1004,plain,( 420.49/60.60 ((^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((emptyset = Y3) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (~ (((Y0 = Y1) => (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y0 = (n_pl @ Y1 @ Y2)))))) => (((~ (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y0 = (n_pl @ Y1 @ Y2)))))) => (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y1 = (n_pl @ Y0 @ Y2)))))) => (~ ((~ (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y1 = (n_pl @ Y0 @ Y2)))))) => (~ (Y0 = Y1)))))))))) != (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((emptyset = Y3) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y0 = (n_pl @ Y1 @ Y2))))) => (Y0 = Y1)) => (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y1 = (n_pl @ Y0 @ Y2))))))))))), 420.49/60.60 inference(trivial_inequality_removal,[],[f1003])). 420.49/60.60 thf(f1003,plain,( 420.49/60.60 ((^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((emptyset = Y3) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (~ (((Y0 = Y1) => (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y0 = (n_pl @ Y1 @ Y2)))))) => (((~ (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y0 = (n_pl @ Y1 @ Y2)))))) => (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y1 = (n_pl @ Y0 @ Y2)))))) => (~ ((~ (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y1 = (n_pl @ Y0 @ Y2)))))) => (~ (Y0 = Y1)))))))))) != (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((emptyset = Y3) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y0 = (n_pl @ Y1 @ Y2))))) => (Y0 = Y1)) => (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y1 = (n_pl @ Y0 @ Y2)))))))))) | ($false = $true)), 420.49/60.60 inference(boolean_simplification,[],[f953])). 420.49/60.60 thf(f953,plain,( 420.49/60.60 ((^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((emptyset = Y3) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (~ (((Y0 = Y1) => (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y0 = (n_pl @ Y1 @ Y2)))))) => (((~ (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y0 = (n_pl @ Y1 @ Y2)))))) => (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y1 = (n_pl @ Y0 @ Y2)))))) => (~ ((~ (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y1 = (n_pl @ Y0 @ Y2)))))) => (~ (Y0 = Y1)))))))))) != (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((emptyset = Y3) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y0 = (n_pl @ Y1 @ Y2))))) => (Y0 = Y1)) => (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y1 = (n_pl @ Y0 @ Y2)))))))))) | ($true = (~ $true))), 420.49/60.60 inference(constrained_superposition,[],[f946,f854])). 420.49/60.60 thf(f854,plain,( 420.49/60.60 ((all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((emptyset = Y3) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (~ (((Y0 = Y1) => (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y0 = (n_pl @ Y1 @ Y2)))))) => (((~ (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y0 = (n_pl @ Y1 @ Y2)))))) => (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y1 = (n_pl @ Y0 @ Y2)))))) => (~ ((~ (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y1 = (n_pl @ Y0 @ Y2)))))) => (~ (Y0 = Y1))))))))))) = $true)), 420.49/60.60 inference(boolean_simplification,[],[f853])). 420.49/60.60 thf(f853,plain,( 420.49/60.60 ($true = (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((emptyset = Y3) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (~ (((Y0 = Y1) => (~ (~ (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y0 = (n_pl @ Y1 @ Y2)))))))) => (((~ (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y0 = (n_pl @ Y1 @ Y2)))))) => (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y1 = (n_pl @ Y0 @ Y2)))))) => (~ ((~ (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y1 = (n_pl @ Y0 @ Y2)))))) => (~ (Y0 = Y1))))))))))))), 420.49/60.60 inference(boolean_simplification,[],[f852])). 420.49/60.60 thf(f852,plain,( 420.49/60.60 ($true = (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((emptyset = Y3) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (~ (((Y0 = Y1) => ((~ (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y0 = (n_pl @ Y1 @ Y2)))))) => $false)) => (((~ (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y0 = (n_pl @ Y1 @ Y2)))))) => (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y1 = (n_pl @ Y0 @ Y2)))))) => (~ ((~ (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y1 = (n_pl @ Y0 @ Y2)))))) => (~ (Y0 = Y1))))))))))))), 420.49/60.60 inference(boolean_simplification,[],[f851])). 420.49/60.60 thf(f851,plain,( 420.49/60.60 ((all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((emptyset = Y3) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (~ (((Y0 = Y1) => ((~ (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y0 = (n_pl @ Y1 @ Y2)) => $false)))) => $false)) => (((~ (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y0 = (n_pl @ Y1 @ Y2)) => $false)))) => (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y1 = (n_pl @ Y0 @ Y2)))))) => (~ ((~ (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y1 = (n_pl @ Y0 @ Y2)))))) => (~ (Y0 = Y1))))))))))) = $true)), 420.49/60.60 inference(boolean_simplification,[],[f850])). 420.49/60.60 thf(f850,plain,( 420.49/60.60 ($true = (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((emptyset = Y3) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (~ (((Y0 = Y1) => (((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y0 = (n_pl @ Y1 @ Y2)) => $false))) => $false) => $false)) => ((((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y0 = (n_pl @ Y1 @ Y2)) => $false))) => $false) => (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y1 = (n_pl @ Y0 @ Y2)))))) => (~ ((~ (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y1 = (n_pl @ Y0 @ Y2)))))) => (~ (Y0 = Y1))))))))))))), 420.49/60.60 inference(boolean_simplification,[],[f849])). 420.49/60.60 thf(f849,plain,( 420.49/60.60 ($true = (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((emptyset = Y3) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (~ (((Y0 = Y1) => (((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y0 = (n_pl @ Y1 @ Y2)) => $false))) => $false) => $false)) => ((((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y0 = (n_pl @ Y1 @ Y2)) => $false))) => $false) => (~ (~ (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y1 = (n_pl @ Y0 @ Y2)))))))) => (~ ((~ (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y1 = (n_pl @ Y0 @ Y2)))))) => (~ (Y0 = Y1))))))))))))), 420.49/60.60 inference(boolean_simplification,[],[f848])). 420.49/60.60 thf(f848,plain,( 420.49/60.60 ((all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((emptyset = Y3) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (~ (((Y0 = Y1) => (((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y0 = (n_pl @ Y1 @ Y2)) => $false))) => $false) => $false)) => ((((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y0 = (n_pl @ Y1 @ Y2)) => $false))) => $false) => ((~ (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y1 = (n_pl @ Y0 @ Y2)))))) => $false)) => (~ ((~ (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y1 = (n_pl @ Y0 @ Y2)))))) => (~ (Y0 = Y1))))))))))) = $true)), 420.49/60.60 inference(boolean_simplification,[],[f847])). 420.49/60.60 thf(f847,plain,( 420.49/60.60 ($true = (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((~ (~ (emptyset = Y2))) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((~ (~ (emptyset = Y3))) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (~ (((Y0 = Y1) => (((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y0 = (n_pl @ Y1 @ Y2)) => $false))) => $false) => $false)) => ((((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y0 = (n_pl @ Y1 @ Y2)) => $false))) => $false) => ((~ (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y1 = (n_pl @ Y0 @ Y2)))))) => $false)) => (~ ((~ (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y1 = (n_pl @ Y0 @ Y2)))))) => (~ (Y0 = Y1))))))))))))), 420.49/60.60 inference(boolean_simplification,[],[f846])). 420.49/60.60 thf(f846,plain,( 420.49/60.60 ($true = (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((~ (~ (emptyset = Y2))) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((~ (~ (emptyset = Y3))) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (~ (((Y0 = Y1) => (((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y0 = (n_pl @ Y1 @ Y2)) => $false))) => $false) => $false)) => ((((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y0 = (n_pl @ Y1 @ Y2)) => $false))) => $false) => ((~ (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y1 = (n_pl @ Y0 @ Y2)) => $false)))) => $false)) => (~ ((~ (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y1 = (n_pl @ Y0 @ Y2)) => $false)))) => (~ (Y0 = Y1))))))))))))), 420.49/60.60 inference(boolean_simplification,[],[f845])). 420.49/60.60 thf(f845,plain,( 420.49/60.60 ((all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((~ (~ (emptyset = Y2))) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((~ (~ (emptyset = Y3))) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (~ (((Y0 = Y1) => (((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y0 = (n_pl @ Y1 @ Y2)) => $false))) => $false) => $false)) => ((((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y0 = (n_pl @ Y1 @ Y2)) => $false))) => $false) => (((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y1 = (n_pl @ Y0 @ Y2)) => $false))) => $false) => $false)) => (~ (((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y1 = (n_pl @ Y0 @ Y2)) => $false))) => $false) => (~ (Y0 = Y1))))))))))) = $true)), 420.49/60.60 inference(boolean_simplification,[],[f844])). 420.49/60.60 thf(f844,plain,( 420.49/60.60 ((all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((~ (~ (emptyset = Y2))) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((~ (~ (emptyset = Y3))) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (~ (((Y0 = Y1) => (((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y0 = (n_pl @ Y1 @ Y2)) => $false))) => $false) => $false)) => ((((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y0 = (n_pl @ Y1 @ Y2)) => $false))) => $false) => (((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y1 = (n_pl @ Y0 @ Y2)) => $false))) => $false) => $false)) => (~ (((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y1 = (n_pl @ Y0 @ Y2)) => $false))) => $false) => ((Y0 = Y1) => $false)))))))))) = $true)), 420.49/60.60 inference(boolean_simplification,[],[f843])). 420.49/60.60 thf(f843,plain,( 420.49/60.60 ($true = (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((~ (~ (emptyset = Y2))) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((~ (~ (emptyset = Y3))) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (~ (((Y0 = Y1) => (((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y0 = (n_pl @ Y1 @ Y2)) => $false))) => $false) => $false)) => ((((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y0 = (n_pl @ Y1 @ Y2)) => $false))) => $false) => (((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y1 = (n_pl @ Y0 @ Y2)) => $false))) => $false) => $false)) => ((((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y1 = (n_pl @ Y0 @ Y2)) => $false))) => $false) => ((Y0 = Y1) => $false)) => $false)))))))))), 420.49/60.60 inference(boolean_simplification,[],[f842])). 420.49/60.60 thf(f842,plain,( 420.49/60.60 ($true = (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((~ (~ (emptyset = Y2))) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((~ (~ (emptyset = Y3))) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (~ (((Y0 = Y1) => (((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y0 = (n_pl @ Y1 @ Y2)) => $false))) => $false) => $false)) => (~ (~ ((((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y0 = (n_pl @ Y1 @ Y2)) => $false))) => $false) => (((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y1 = (n_pl @ Y0 @ Y2)) => $false))) => $false) => $false)) => ((((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y1 = (n_pl @ Y0 @ Y2)) => $false))) => $false) => ((Y0 = Y1) => $false)) => $false)))))))))))), 420.49/60.60 inference(boolean_simplification,[],[f841])). 420.49/60.60 thf(f841,plain,( 420.49/60.60 ((all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((~ (~ (emptyset = Y2))) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((~ (~ (emptyset = Y3))) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (~ (((Y0 = Y1) => (((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y0 = (n_pl @ Y1 @ Y2)) => $false))) => $false) => $false)) => (~ (((((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y0 = (n_pl @ Y1 @ Y2)) => $false))) => $false) => (((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y1 = (n_pl @ Y0 @ Y2)) => $false))) => $false) => $false)) => ((((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y1 = (n_pl @ Y0 @ Y2)) => $false))) => $false) => ((Y0 = Y1) => $false)) => $false)) => $false)))))))) = $true)), 420.49/60.60 inference(boolean_simplification,[],[f840])). 420.49/60.60 thf(f840,plain,( 420.49/60.60 ((all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((~ (~ (emptyset = Y2))) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((~ (~ (emptyset = Y3))) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (~ (((Y0 = Y1) => (((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y0 = (n_pl @ Y1 @ Y2)) => $false))) => $false) => $false)) => ((((((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y0 = (n_pl @ Y1 @ Y2)) => $false))) => $false) => (((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y1 = (n_pl @ Y0 @ Y2)) => $false))) => $false) => $false)) => ((((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y1 = (n_pl @ Y0 @ Y2)) => $false))) => $false) => ((Y0 = Y1) => $false)) => $false)) => $false) => $false))))))) = $true)), 420.49/60.61 inference(boolean_simplification,[],[f839])). 420.49/60.61 thf(f839,plain,( 420.49/60.61 ((all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((~ (~ (emptyset = Y2))) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((~ (~ (emptyset = Y3))) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: ((((Y0 = Y1) => (((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y0 = (n_pl @ Y1 @ Y2)) => $false))) => $false) => $false)) => ((((((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y0 = (n_pl @ Y1 @ Y2)) => $false))) => $false) => (((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y1 = (n_pl @ Y0 @ Y2)) => $false))) => $false) => $false)) => ((((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y1 = (n_pl @ Y0 @ Y2)) => $false))) => $false) => ((Y0 = Y1) => $false)) => $false)) => $false) => $false)) => $false))))) = $true)), 420.49/60.61 inference(beta_eta_normalization,[],[f765])). 420.49/60.61 thf(f765,plain,( 420.49/60.61 ((all_of @ (^[Y0 : $i]: (in @ Y0 @ ((^[Y1 : $i]: ((^[Y2 : $i > $o]: ((^[Y3 : $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: (eps @ (^[Y6 : $i]: ((Y3 & (Y4 = Y6)) | ((~ Y3) & (Y5 = Y6)))))))))) @ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (Y2 @ Y3)))) @ (repl @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (eps @ (^[Y7 : $i]: ((Y4 & (Y5 = Y7)) | ((~ Y4) & (Y6 = Y7)))))))))) @ (Y2 @ Y3) @ Y3 @ (eps @ (^[Y4 : $i]: ((Y2 @ Y4) & (in @ Y4 @ Y1))))))) @ emptyset)))) @ ((^[Y1 : $i]: ((^[Y2 : $i > $o]: ((^[Y3 : $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: (eps @ (^[Y6 : $i]: ((Y3 & (Y4 = Y6)) | ((~ Y3) & (Y5 = Y6)))))))))) @ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (Y2 @ Y3)))) @ (repl @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (eps @ (^[Y7 : $i]: ((Y4 & (Y5 = Y7)) | ((~ Y4) & (Y6 = Y7)))))))))) @ (Y2 @ Y3) @ Y3 @ (eps @ (^[Y4 : $i]: ((Y2 @ Y4) & (in @ Y4 @ Y1))))))) @ emptyset)))) @ (univof @ emptyset) @ nat_p) @ (^[Y1 : $i]: (~ (emptyset = Y1)))))) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: ((^[Y4 : $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (eps @ (^[Y7 : $i]: ((Y4 & (Y5 = Y7)) | ((~ Y4) & (Y6 = Y7)))))))))) @ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) & (Y3 @ Y4)))) @ (repl @ Y2 @ (^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (eps @ (^[Y8 : $i]: ((Y5 & (Y6 = Y8)) | ((~ Y5) & (Y7 = Y8)))))))))) @ (Y3 @ Y4) @ Y4 @ (eps @ (^[Y5 : $i]: ((Y3 @ Y5) & (in @ Y5 @ Y2))))))) @ emptyset)))) @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: ((^[Y4 : $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (eps @ (^[Y7 : $i]: ((Y4 & (Y5 = Y7)) | ((~ Y4) & (Y6 = Y7)))))))))) @ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) & (Y3 @ Y4)))) @ (repl @ Y2 @ (^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (eps @ (^[Y8 : $i]: ((Y5 & (Y6 = Y8)) | ((~ Y5) & (Y7 = Y8)))))))))) @ (Y3 @ Y4) @ Y4 @ (eps @ (^[Y5 : $i]: ((Y3 @ Y5) & (in @ Y5 @ Y2))))))) @ emptyset)))) @ (univof @ emptyset) @ nat_p) @ (^[Y2 : $i]: (~ (emptyset = Y2)))))) @ (^[Y1 : $i]: ((^[Y2 : $o]: ((^[Y3 : $o]: ((^[Y4 : $o]: ((^[Y5 : $o]: ((^[Y6 : $o]: ((^[Y7 : $o]: ((^[Y8 : $o]: ((^[Y9 : $o]: ((^[Y10 : $o]: ((^[Y11 : $o]: ((^[Y12 : $o]: (Y11 => Y12)))) @ Y10 @ $false)) @ ((^[Y10 : $o]: ((^[Y11 : $o]: ((^[Y12 : $o]: ((^[Y13 : $o]: (Y12 => Y13)))) @ Y10 @ ((^[Y12 : $o]: ((^[Y13 : $o]: ((^[Y14 : $o]: (Y13 => Y14)))) @ Y12 @ $false)) @ Y11))))) @ Y8 @ Y9))))) @ Y5 @ ((^[Y8 : $o]: ((^[Y9 : $o]: ((^[Y10 : $o]: ((^[Y11 : $o]: ((^[Y12 : $o]: (Y11 => Y12)))) @ Y10 @ $false)) @ ((^[Y10 : $o]: ((^[Y11 : $o]: ((^[Y12 : $o]: ((^[Y13 : $o]: (Y12 => Y13)))) @ Y10 @ ((^[Y12 : $o]: ((^[Y13 : $o]: ((^[Y14 : $o]: (Y13 => Y14)))) @ Y12 @ $false)) @ Y11))))) @ Y8 @ Y9))))) @ Y6 @ Y7))))))) @ ((^[Y5 : $o]: ((^[Y6 : $o]: ((^[Y7 : $o]: ((^[Y8 : $o]: (Y7 => Y8)))) @ Y5 @ ((^[Y7 : $o]: ((^[Y8 : $o]: ((^[Y9 : $o]: (Y8 => Y9)))) @ Y7 @ $false)) @ Y6))))) @ Y2 @ Y3) @ ((^[Y5 : $o]: ((^[Y6 : $o]: ((^[Y7 : $o]: ((^[Y8 : $o]: (Y7 => Y8)))) @ Y5 @ ((^[Y7 : $o]: ((^[Y8 : $o]: ((^[Y9 : $o]: (Y8 => Y9)))) @ Y7 @ $false)) @ Y6))))) @ Y3 @ Y4) @ ((^[Y5 : $o]: ((^[Y6 : $o]: ((^[Y7 : $o]: ((^[Y8 : $o]: (Y7 => Y8)))) @ Y5 @ ((^[Y7 : $o]: ((^[Y8 : $o]: ((^[Y9 : $o]: (Y8 => Y9)))) @ Y7 @ $false)) @ Y6))))) @ Y4 @ Y2))))))) @ ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (Y3 = Y4)))))) @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: ((^[Y4 : $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (eps @ (^[Y7 : $i]: ((Y4 & (Y5 = Y7)) | ((~ Y4) & (Y6 = Y7)))))))))) @ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) & (Y3 @ Y4)))) @ (repl @ Y2 @ (^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (eps @ (^[Y8 : $i]: ((Y5 & (Y6 = Y8)) | ((~ Y5) & (Y7 = Y8)))))))))) @ (Y3 @ Y4) @ Y4 @ (eps @ (^[Y5 : $i]: ((Y3 @ Y5) & (in @ Y5 @ Y2))))))) @ emptyset)))) @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: ((^[Y4 : $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (eps @ (^[Y7 : $i]: ((Y4 & (Y5 = Y7)) | ((~ Y4) & (Y6 = Y7)))))))))) @ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) & (Y3 @ Y4)))) @ (repl @ Y2 @ (^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (eps @ (^[Y8 : $i]: ((Y5 & (Y6 = Y8)) | ((~ Y5) & (Y7 = Y8)))))))))) @ (Y3 @ Y4) @ Y4 @ (eps @ (^[Y5 : $i]: ((Y3 @ Y5) & (in @ Y5 @ Y2))))))) @ emptyset)))) @ (univof @ emptyset) @ nat_p) @ (^[Y2 : $i]: (~ (emptyset = Y2)))) @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: ((^[Y4 : $o]: ((^[Y5 : $o]: ((^[Y6 : $o]: (Y5 => Y6)))) @ Y4 @ $false)) @ (all_of @ (^[Y4 : $i]: (in @ Y4 @ Y2)) @ ((^[Y4 : $i]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $o]: ((^[Y9 : $o]: (Y8 => Y9)))) @ Y7 @ $false)) @ (Y5 @ Y6))))))) @ Y2 @ Y3)))))) @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: ((^[Y4 : $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (eps @ (^[Y7 : $i]: ((Y4 & (Y5 = Y7)) | ((~ Y4) & (Y6 = Y7)))))))))) @ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) & (Y3 @ Y4)))) @ (repl @ Y2 @ (^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (eps @ (^[Y8 : $i]: ((Y5 & (Y6 = Y8)) | ((~ Y5) & (Y7 = Y8)))))))))) @ (Y3 @ Y4) @ Y4 @ (eps @ (^[Y5 : $i]: ((Y3 @ Y5) & (in @ Y5 @ Y2))))))) @ emptyset)))) @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: ((^[Y4 : $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (eps @ (^[Y7 : $i]: ((Y4 & (Y5 = Y7)) | ((~ Y4) & (Y6 = Y7)))))))))) @ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) & (Y3 @ Y4)))) @ (repl @ Y2 @ (^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (eps @ (^[Y8 : $i]: ((Y5 & (Y6 = Y8)) | ((~ Y5) & (Y7 = Y8)))))))))) @ (Y3 @ Y4) @ Y4 @ (eps @ (^[Y5 : $i]: ((Y3 @ Y5) & (in @ Y5 @ Y2))))))) @ emptyset)))) @ (univof @ emptyset) @ nat_p) @ (^[Y2 : $i]: (~ (emptyset = Y2)))) @ ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (Y6 = Y7)))))) @ ((^[Y5 : $i]: ((^[Y6 : $i > $o]: ((^[Y7 : $o]: ((^[Y8 : $i]: ((^[Y9 : $i]: (eps @ (^[Y10 : $i]: ((Y7 & (Y8 = Y10)) | ((~ Y7) & (Y9 = Y10)))))))))) @ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ Y5) & (Y6 @ Y7)))) @ (repl @ Y5 @ (^[Y7 : $i]: ((^[Y8 : $o]: ((^[Y9 : $i]: ((^[Y10 : $i]: (eps @ (^[Y11 : $i]: ((Y8 & (Y9 = Y11)) | ((~ Y8) & (Y10 = Y11)))))))))) @ (Y6 @ Y7) @ Y7 @ (eps @ (^[Y8 : $i]: ((Y6 @ Y8) & (in @ Y8 @ Y5))))))) @ emptyset)))) @ ((^[Y5 : $i]: ((^[Y6 : $i > $o]: ((^[Y7 : $o]: ((^[Y8 : $i]: ((^[Y9 : $i]: (eps @ (^[Y10 : $i]: ((Y7 & (Y8 = Y10)) | ((~ Y7) & (Y9 = Y10)))))))))) @ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ Y5) & (Y6 @ Y7)))) @ (repl @ Y5 @ (^[Y7 : $i]: ((^[Y8 : $o]: ((^[Y9 : $i]: ((^[Y10 : $i]: (eps @ (^[Y11 : $i]: ((Y8 & (Y9 = Y11)) | ((~ Y8) & (Y10 = Y11)))))))))) @ (Y6 @ Y7) @ Y7 @ (eps @ (^[Y8 : $i]: ((Y6 @ Y8) & (in @ Y8 @ Y5))))))) @ emptyset)))) @ (univof @ emptyset) @ nat_p) @ (^[Y5 : $i]: (~ (emptyset = Y5)))) @ Y2 @ (n_pl @ Y3 @ Y4))))))) @ Y0 @ Y1)) @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: ((^[Y4 : $o]: ((^[Y5 : $o]: ((^[Y6 : $o]: (Y5 => Y6)))) @ Y4 @ $false)) @ (all_of @ (^[Y4 : $i]: (in @ Y4 @ Y2)) @ ((^[Y4 : $i]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $o]: ((^[Y9 : $o]: (Y8 => Y9)))) @ Y7 @ $false)) @ (Y5 @ Y6))))))) @ Y2 @ Y3)))))) @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: ((^[Y4 : $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (eps @ (^[Y7 : $i]: ((Y4 & (Y5 = Y7)) | ((~ Y4) & (Y6 = Y7)))))))))) @ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) & (Y3 @ Y4)))) @ (repl @ Y2 @ (^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (eps @ (^[Y8 : $i]: ((Y5 & (Y6 = Y8)) | ((~ Y5) & (Y7 = Y8)))))))))) @ (Y3 @ Y4) @ Y4 @ (eps @ (^[Y5 : $i]: ((Y3 @ Y5) & (in @ Y5 @ Y2))))))) @ emptyset)))) @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: ((^[Y4 : $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (eps @ (^[Y7 : $i]: ((Y4 & (Y5 = Y7)) | ((~ Y4) & (Y6 = Y7)))))))))) @ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) & (Y3 @ Y4)))) @ (repl @ Y2 @ (^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (eps @ (^[Y8 : $i]: ((Y5 & (Y6 = Y8)) | ((~ Y5) & (Y7 = Y8)))))))))) @ (Y3 @ Y4) @ Y4 @ (eps @ (^[Y5 : $i]: ((Y3 @ Y5) & (in @ Y5 @ Y2))))))) @ emptyset)))) @ (univof @ emptyset) @ nat_p) @ (^[Y2 : $i]: (~ (emptyset = Y2)))) @ ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (Y6 = Y7)))))) @ ((^[Y5 : $i]: ((^[Y6 : $i > $o]: ((^[Y7 : $o]: ((^[Y8 : $i]: ((^[Y9 : $i]: (eps @ (^[Y10 : $i]: ((Y7 & (Y8 = Y10)) | ((~ Y7) & (Y9 = Y10)))))))))) @ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ Y5) & (Y6 @ Y7)))) @ (repl @ Y5 @ (^[Y7 : $i]: ((^[Y8 : $o]: ((^[Y9 : $i]: ((^[Y10 : $i]: (eps @ (^[Y11 : $i]: ((Y8 & (Y9 = Y11)) | ((~ Y8) & (Y10 = Y11)))))))))) @ (Y6 @ Y7) @ Y7 @ (eps @ (^[Y8 : $i]: ((Y6 @ Y8) & (in @ Y8 @ Y5))))))) @ emptyset)))) @ ((^[Y5 : $i]: ((^[Y6 : $i > $o]: ((^[Y7 : $o]: ((^[Y8 : $i]: ((^[Y9 : $i]: (eps @ (^[Y10 : $i]: ((Y7 & (Y8 = Y10)) | ((~ Y7) & (Y9 = Y10)))))))))) @ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ Y5) & (Y6 @ Y7)))) @ (repl @ Y5 @ (^[Y7 : $i]: ((^[Y8 : $o]: ((^[Y9 : $i]: ((^[Y10 : $i]: (eps @ (^[Y11 : $i]: ((Y8 & (Y9 = Y11)) | ((~ Y8) & (Y10 = Y11)))))))))) @ (Y6 @ Y7) @ Y7 @ (eps @ (^[Y8 : $i]: ((Y6 @ Y8) & (in @ Y8 @ Y5))))))) @ emptyset)))) @ (univof @ emptyset) @ nat_p) @ (^[Y5 : $i]: (~ (emptyset = Y5)))) @ Y2 @ (n_pl @ Y3 @ Y4))))))) @ Y1 @ Y0))))))) = $true)), 420.49/60.61 inference(definition_unfolding,[],[f648,f677,f677,f698,f679,f678,f680,f678,f680])). 420.49/60.61 thf(f680,plain,( 420.49/60.61 (diffprop = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (Y4 = Y5)))))) @ ((^[Y3 : $i]: ((^[Y4 : $i > $o]: ((^[Y5 : $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (eps @ (^[Y8 : $i]: ((Y5 & (Y6 = Y8)) | ((~ Y5) & (Y7 = Y8)))))))))) @ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (Y4 @ Y5)))) @ (repl @ Y3 @ (^[Y5 : $i]: ((^[Y6 : $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: (eps @ (^[Y9 : $i]: ((Y6 & (Y7 = Y9)) | ((~ Y6) & (Y8 = Y9)))))))))) @ (Y4 @ Y5) @ Y5 @ (eps @ (^[Y6 : $i]: ((Y4 @ Y6) & (in @ Y6 @ Y3))))))) @ emptyset)))) @ ((^[Y3 : $i]: ((^[Y4 : $i > $o]: ((^[Y5 : $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (eps @ (^[Y8 : $i]: ((Y5 & (Y6 = Y8)) | ((~ Y5) & (Y7 = Y8)))))))))) @ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y3) & (Y4 @ Y5)))) @ (repl @ Y3 @ (^[Y5 : $i]: ((^[Y6 : $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: (eps @ (^[Y9 : $i]: ((Y6 & (Y7 = Y9)) | ((~ Y6) & (Y8 = Y9)))))))))) @ (Y4 @ Y5) @ Y5 @ (eps @ (^[Y6 : $i]: ((Y4 @ Y6) & (in @ Y6 @ Y3))))))) @ emptyset)))) @ (univof @ emptyset) @ nat_p) @ (^[Y3 : $i]: (~ (emptyset = Y3)))) @ Y0 @ (n_pl @ Y1 @ Y2))))))))), 420.49/60.61 inference(definition_unfolding,[],[f575,f679])). 420.49/60.61 thf(f575,plain,( 420.49/60.61 (diffprop = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (n_is @ Y0 @ (n_pl @ Y1 @ Y2))))))))), 420.49/60.61 inference(cnf_transformation,[],[f292])). 420.49/60.61 thf(f292,plain,( 420.49/60.61 (diffprop = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (n_is @ Y0 @ (n_pl @ Y1 @ Y2))))))))), 420.49/60.61 inference(fool_elimination,[],[f185])). 420.49/60.61 thf(f185,axiom,( 420.49/60.61 ((^[X0 : $i, X1 : $i, X2 : $i] : (n_is @ X0 @ (n_pl @ X1 @ X2))) = diffprop)), 420.49/60.61 file('/export/starexec/sandbox/tmp/tmp.2i9OyGfWTf/E---3.1_15619.p',def_diffprop)). 420.49/60.61 thf(f678,plain,( 420.49/60.61 (n_some = ((^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $o]: ((^[Y3 : $o]: ((^[Y4 : $o]: (Y3 => Y4)))) @ Y2 @ $false)) @ (all_of @ (^[Y2 : $i]: (in @ Y2 @ Y0)) @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $o]: ((^[Y7 : $o]: (Y6 => Y7)))) @ Y5 @ $false)) @ (Y3 @ Y4))))))) @ Y0 @ Y1)))))) @ ((^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $o]: ((^[Y3 : $i]: ((^[Y4 : $i]: (eps @ (^[Y5 : $i]: ((Y2 & (Y3 = Y5)) | ((~ Y2) & (Y4 = Y5)))))))))) @ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) @ (repl @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: (eps @ (^[Y6 : $i]: ((Y3 & (Y4 = Y6)) | ((~ Y3) & (Y5 = Y6)))))))))) @ (Y1 @ Y2) @ Y2 @ (eps @ (^[Y3 : $i]: ((Y1 @ Y3) & (in @ Y3 @ Y0))))))) @ emptyset)))) @ ((^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $o]: ((^[Y3 : $i]: ((^[Y4 : $i]: (eps @ (^[Y5 : $i]: ((Y2 & (Y3 = Y5)) | ((~ Y2) & (Y4 = Y5)))))))))) @ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) @ (repl @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: (eps @ (^[Y6 : $i]: ((Y3 & (Y4 = Y6)) | ((~ Y3) & (Y5 = Y6)))))))))) @ (Y1 @ Y2) @ Y2 @ (eps @ (^[Y3 : $i]: ((Y1 @ Y3) & (in @ Y3 @ Y0))))))) @ emptyset)))) @ (univof @ emptyset) @ nat_p) @ (^[Y0 : $i]: (~ (emptyset = Y0))))))), 420.49/60.61 inference(definition_unfolding,[],[f594,f674,f677])). 420.49/60.61 thf(f674,plain,( 420.49/60.61 (l_some = (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $o]: ((^[Y3 : $o]: ((^[Y4 : $o]: (Y3 => Y4)))) @ Y2 @ $false)) @ (all_of @ (^[Y2 : $i]: (in @ Y2 @ Y0)) @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $o]: ((^[Y7 : $o]: (Y6 => Y7)))) @ Y5 @ $false)) @ (Y3 @ Y4))))))) @ Y0 @ Y1)))))))), 420.49/60.61 inference(definition_unfolding,[],[f618,f672,f673])). 420.49/60.61 thf(f673,plain,( 420.49/60.61 (non = (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((^[Y3 : $o]: ((^[Y4 : $o]: ((^[Y5 : $o]: (Y4 => Y5)))) @ Y3 @ $false)) @ (Y1 @ Y2))))))))), 420.49/60.61 inference(definition_unfolding,[],[f659,f672])). 420.49/60.61 thf(f659,plain,( 420.49/60.61 (non = (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (d_not @ (Y1 @ Y2))))))))), 420.49/60.61 inference(cnf_transformation,[],[f493])). 420.49/60.61 thf(f493,plain,( 420.49/60.61 (non = (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (d_not @ (Y1 @ Y2))))))))), 420.49/60.61 inference(fool_elimination,[],[f43])). 420.49/60.61 thf(f43,axiom,( 420.49/60.61 (non = (^[X0 : $i, X1 : $i > $o, X2 : $i] : (d_not @ (X1 @ X2))))), 420.49/60.61 file('/export/starexec/sandbox/tmp/tmp.2i9OyGfWTf/E---3.1_15619.p',def_non)). 420.49/60.61 thf(f672,plain,( 420.49/60.61 (d_not = (^[Y0 : $o]: ((^[Y1 : $o]: ((^[Y2 : $o]: (Y1 => Y2)))) @ Y0 @ $false)))), 420.49/60.61 inference(definition_unfolding,[],[f609,f663])). 420.49/60.61 thf(f663,plain,( 420.49/60.61 (imp = (^[Y0 : $o]: ((^[Y1 : $o]: (Y0 => Y1)))))), 420.49/60.61 inference(cnf_transformation,[],[f502])). 420.49/60.61 thf(f502,plain,( 420.49/60.61 (imp = (^[Y0 : $o]: ((^[Y1 : $o]: (Y0 => Y1)))))), 420.49/60.61 inference(fool_elimination,[],[f501])). 420.49/60.61 thf(f501,plain,( 420.49/60.61 ((^[X0 : $o, X1 : $o] : (X0 => X1)) = imp)), 420.49/60.61 inference(rectify,[],[f33])). 420.49/60.61 thf(f33,axiom,( 420.49/60.61 ((^[X0 : $o, X1 : $o] : (X0 => X1)) = imp)), 420.49/60.61 file('/export/starexec/sandbox/tmp/tmp.2i9OyGfWTf/E---3.1_15619.p',def_imp)). 420.49/60.61 thf(f609,plain,( 420.49/60.61 (d_not = (^[Y0 : $o]: (imp @ Y0 @ $false)))), 420.49/60.61 inference(cnf_transformation,[],[f509])). 420.49/60.61 thf(f509,plain,( 420.49/60.61 (d_not = (^[Y0 : $o]: (imp @ Y0 @ $false)))), 420.49/60.61 inference(fool_elimination,[],[f34])). 420.49/60.61 thf(f34,axiom,( 420.49/60.61 (d_not = (^[X0 : $o] : (imp @ X0 @ $false)))), 420.49/60.61 file('/export/starexec/sandbox/tmp/tmp.2i9OyGfWTf/E---3.1_15619.p',def_d_not)). 420.49/60.61 thf(f618,plain,( 420.49/60.61 (l_some = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (d_not @ (all_of @ (^[Y2 : $i]: (in @ Y2 @ Y0)) @ (non @ Y0 @ Y1)))))))), 420.49/60.61 inference(cnf_transformation,[],[f541])). 420.49/60.61 thf(f541,plain,( 420.49/60.61 (l_some = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (d_not @ (all_of @ (^[Y2 : $i]: (in @ Y2 @ Y0)) @ (non @ Y0 @ Y1)))))))), 420.49/60.61 inference(fool_elimination,[],[f44])). 420.49/60.61 thf(f44,axiom,( 420.49/60.61 ((^[X0 : $i, X1 : $i > $o] : (d_not @ (all_of @ (^[X2 : $i] : (in @ X2 @ X0)) @ (non @ X0 @ X1)))) = l_some)), 420.49/60.61 file('/export/starexec/sandbox/tmp/tmp.2i9OyGfWTf/E---3.1_15619.p',def_l_some)). 420.49/60.61 thf(f594,plain,( 420.49/60.61 (n_some = (l_some @ nat))), 420.49/60.61 inference(cnf_transformation,[],[f274])). 420.49/60.61 thf(f274,plain,( 420.49/60.61 (n_some = (l_some @ nat))), 420.49/60.61 inference(fool_elimination,[],[f99])). 420.49/60.61 thf(f99,axiom,( 420.49/60.61 (n_some = (l_some @ nat))), 420.49/60.61 file('/export/starexec/sandbox/tmp/tmp.2i9OyGfWTf/E---3.1_15619.p',def_n_some)). 420.49/60.61 thf(f679,plain,( 420.49/60.61 (n_is = ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y1 = Y2)))))) @ ((^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $o]: ((^[Y3 : $i]: ((^[Y4 : $i]: (eps @ (^[Y5 : $i]: ((Y2 & (Y3 = Y5)) | ((~ Y2) & (Y4 = Y5)))))))))) @ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) @ (repl @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: (eps @ (^[Y6 : $i]: ((Y3 & (Y4 = Y6)) | ((~ Y3) & (Y5 = Y6)))))))))) @ (Y1 @ Y2) @ Y2 @ (eps @ (^[Y3 : $i]: ((Y1 @ Y3) & (in @ Y3 @ Y0))))))) @ emptyset)))) @ ((^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $o]: ((^[Y3 : $i]: ((^[Y4 : $i]: (eps @ (^[Y5 : $i]: ((Y2 & (Y3 = Y5)) | ((~ Y2) & (Y4 = Y5)))))))))) @ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) @ (repl @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: (eps @ (^[Y6 : $i]: ((Y3 & (Y4 = Y6)) | ((~ Y3) & (Y5 = Y6)))))))))) @ (Y1 @ Y2) @ Y2 @ (eps @ (^[Y3 : $i]: ((Y1 @ Y3) & (in @ Y3 @ Y0))))))) @ emptyset)))) @ (univof @ emptyset) @ nat_p) @ (^[Y0 : $i]: (~ (emptyset = Y0))))))), 420.49/60.61 inference(definition_unfolding,[],[f555,f584,f677])). 420.49/60.61 thf(f584,plain,( 420.49/60.61 (e_is = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y1 = Y2)))))))), 420.49/60.61 inference(cnf_transformation,[],[f238])). 420.49/60.61 thf(f238,plain,( 420.49/60.61 (e_is = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y1 = Y2)))))))), 420.49/60.61 inference(fool_elimination,[],[f237])). 420.49/60.61 thf(f237,plain,( 420.49/60.61 ((^[X0 : $i, X1 : $i, X2 : $i] : ((X1 = X2))) = e_is)), 420.49/60.61 inference(rectify,[],[f49])). 420.49/60.61 thf(f49,axiom,( 420.49/60.61 ((^[X0 : $i, X7 : $i, X8 : $i] : ((X7 = X8))) = e_is)), 420.49/60.61 file('/export/starexec/sandbox/tmp/tmp.2i9OyGfWTf/E---3.1_15619.p',def_e_is)). 420.49/60.61 thf(f555,plain,( 420.49/60.61 (n_is = (e_is @ nat))), 420.49/60.61 inference(cnf_transformation,[],[f409])). 420.49/60.61 thf(f409,plain,( 420.49/60.61 (n_is = (e_is @ nat))), 420.49/60.61 inference(fool_elimination,[],[f96])). 420.49/60.61 thf(f96,axiom,( 420.49/60.61 (n_is = (e_is @ nat))), 420.49/60.61 file('/export/starexec/sandbox/tmp/tmp.2i9OyGfWTf/E---3.1_15619.p',def_n_is)). 420.49/60.61 thf(f698,plain,( 420.49/60.61 (ec3 = (^[Y0 : $o]: ((^[Y1 : $o]: ((^[Y2 : $o]: ((^[Y3 : $o]: ((^[Y4 : $o]: ((^[Y5 : $o]: ((^[Y6 : $o]: ((^[Y7 : $o]: ((^[Y8 : $o]: ((^[Y9 : $o]: ((^[Y10 : $o]: (Y9 => Y10)))) @ Y8 @ $false)) @ ((^[Y8 : $o]: ((^[Y9 : $o]: ((^[Y10 : $o]: ((^[Y11 : $o]: (Y10 => Y11)))) @ Y8 @ ((^[Y10 : $o]: ((^[Y11 : $o]: ((^[Y12 : $o]: (Y11 => Y12)))) @ Y10 @ $false)) @ Y9))))) @ Y6 @ Y7))))) @ Y3 @ ((^[Y6 : $o]: ((^[Y7 : $o]: ((^[Y8 : $o]: ((^[Y9 : $o]: ((^[Y10 : $o]: (Y9 => Y10)))) @ Y8 @ $false)) @ ((^[Y8 : $o]: ((^[Y9 : $o]: ((^[Y10 : $o]: ((^[Y11 : $o]: (Y10 => Y11)))) @ Y8 @ ((^[Y10 : $o]: ((^[Y11 : $o]: ((^[Y12 : $o]: (Y11 => Y12)))) @ Y10 @ $false)) @ Y9))))) @ Y6 @ Y7))))) @ Y4 @ Y5))))))) @ ((^[Y3 : $o]: ((^[Y4 : $o]: ((^[Y5 : $o]: ((^[Y6 : $o]: (Y5 => Y6)))) @ Y3 @ ((^[Y5 : $o]: ((^[Y6 : $o]: ((^[Y7 : $o]: (Y6 => Y7)))) @ Y5 @ $false)) @ Y4))))) @ Y0 @ Y1) @ ((^[Y3 : $o]: ((^[Y4 : $o]: ((^[Y5 : $o]: ((^[Y6 : $o]: (Y5 => Y6)))) @ Y3 @ ((^[Y5 : $o]: ((^[Y6 : $o]: ((^[Y7 : $o]: (Y6 => Y7)))) @ Y5 @ $false)) @ Y4))))) @ Y1 @ Y2) @ ((^[Y3 : $o]: ((^[Y4 : $o]: ((^[Y5 : $o]: ((^[Y6 : $o]: (Y5 => Y6)))) @ Y3 @ ((^[Y5 : $o]: ((^[Y6 : $o]: ((^[Y7 : $o]: (Y6 => Y7)))) @ Y5 @ $false)) @ Y4))))) @ Y2 @ Y0))))))))), 420.49/60.61 inference(definition_unfolding,[],[f595,f697,f693,f693,f693])). 420.49/60.61 thf(f693,plain,( 420.49/60.61 (l_ec = (^[Y0 : $o]: ((^[Y1 : $o]: ((^[Y2 : $o]: ((^[Y3 : $o]: (Y2 => Y3)))) @ Y0 @ ((^[Y2 : $o]: ((^[Y3 : $o]: ((^[Y4 : $o]: (Y3 => Y4)))) @ Y2 @ $false)) @ Y1))))))), 420.49/60.61 inference(definition_unfolding,[],[f656,f663,f672])). 420.49/60.61 thf(f656,plain,( 420.49/60.61 (l_ec = (^[Y0 : $o]: ((^[Y1 : $o]: (imp @ Y0 @ (d_not @ Y1))))))), 420.49/60.61 inference(cnf_transformation,[],[f387])). 420.49/60.61 thf(f387,plain,( 420.49/60.61 (l_ec = (^[Y0 : $o]: ((^[Y1 : $o]: (imp @ Y0 @ (d_not @ Y1))))))), 420.49/60.61 inference(fool_elimination,[],[f37])). 420.49/60.61 thf(f37,axiom,( 420.49/60.61 ((^[X0 : $o, X1 : $o] : (imp @ X0 @ (d_not @ X1))) = l_ec)), 420.49/60.61 file('/export/starexec/sandbox/tmp/tmp.2i9OyGfWTf/E---3.1_15619.p',def_l_ec)). 420.49/60.61 thf(f697,plain,( 420.49/60.61 (and3 = (^[Y0 : $o]: ((^[Y1 : $o]: ((^[Y2 : $o]: ((^[Y3 : $o]: ((^[Y4 : $o]: ((^[Y5 : $o]: ((^[Y6 : $o]: ((^[Y7 : $o]: (Y6 => Y7)))) @ Y5 @ $false)) @ ((^[Y5 : $o]: ((^[Y6 : $o]: ((^[Y7 : $o]: ((^[Y8 : $o]: (Y7 => Y8)))) @ Y5 @ ((^[Y7 : $o]: ((^[Y8 : $o]: ((^[Y9 : $o]: (Y8 => Y9)))) @ Y7 @ $false)) @ Y6))))) @ Y3 @ Y4))))) @ Y0 @ ((^[Y3 : $o]: ((^[Y4 : $o]: ((^[Y5 : $o]: ((^[Y6 : $o]: ((^[Y7 : $o]: (Y6 => Y7)))) @ Y5 @ $false)) @ ((^[Y5 : $o]: ((^[Y6 : $o]: ((^[Y7 : $o]: ((^[Y8 : $o]: (Y7 => Y8)))) @ Y5 @ ((^[Y7 : $o]: ((^[Y8 : $o]: ((^[Y9 : $o]: (Y8 => Y9)))) @ Y7 @ $false)) @ Y6))))) @ Y3 @ Y4))))) @ Y1 @ Y2))))))))), 420.49/60.61 inference(definition_unfolding,[],[f613,f694,f694])). 420.49/60.61 thf(f694,plain,( 420.49/60.61 (d_and = (^[Y0 : $o]: ((^[Y1 : $o]: ((^[Y2 : $o]: ((^[Y3 : $o]: ((^[Y4 : $o]: (Y3 => Y4)))) @ Y2 @ $false)) @ ((^[Y2 : $o]: ((^[Y3 : $o]: ((^[Y4 : $o]: ((^[Y5 : $o]: (Y4 => Y5)))) @ Y2 @ ((^[Y4 : $o]: ((^[Y5 : $o]: ((^[Y6 : $o]: (Y5 => Y6)))) @ Y4 @ $false)) @ Y3))))) @ Y0 @ Y1))))))), 420.49/60.61 inference(definition_unfolding,[],[f603,f672,f693])). 420.49/60.61 thf(f603,plain,( 420.49/60.61 (d_and = (^[Y0 : $o]: ((^[Y1 : $o]: (d_not @ (l_ec @ Y0 @ Y1))))))), 420.49/60.61 inference(cnf_transformation,[],[f256])). 420.49/60.61 thf(f256,plain,( 420.49/60.61 (d_and = (^[Y0 : $o]: ((^[Y1 : $o]: (d_not @ (l_ec @ Y0 @ Y1))))))), 420.49/60.61 inference(fool_elimination,[],[f38])). 420.49/60.61 thf(f38,axiom,( 420.49/60.61 (d_and = (^[X0 : $o, X1 : $o] : (d_not @ (l_ec @ X0 @ X1))))), 420.49/60.61 file('/export/starexec/sandbox/tmp/tmp.2i9OyGfWTf/E---3.1_15619.p',def_d_and)). 420.49/60.61 thf(f613,plain,( 420.49/60.61 (and3 = (^[Y0 : $o]: ((^[Y1 : $o]: ((^[Y2 : $o]: (d_and @ Y0 @ (d_and @ Y1 @ Y2))))))))), 420.49/60.61 inference(cnf_transformation,[],[f521])). 420.49/60.61 thf(f521,plain,( 420.49/60.61 (and3 = (^[Y0 : $o]: ((^[Y1 : $o]: ((^[Y2 : $o]: (d_and @ Y0 @ (d_and @ Y1 @ Y2))))))))), 420.49/60.61 inference(fool_elimination,[],[f46])). 420.49/60.61 thf(f46,axiom,( 420.49/60.61 ((^[X0 : $o, X1 : $o, X2 : $o] : (d_and @ X0 @ (d_and @ X1 @ X2))) = and3)), 420.49/60.61 file('/export/starexec/sandbox/tmp/tmp.2i9OyGfWTf/E---3.1_15619.p',def_and3)). 420.49/60.61 thf(f595,plain,( 420.49/60.61 (ec3 = (^[Y0 : $o]: ((^[Y1 : $o]: ((^[Y2 : $o]: (and3 @ (l_ec @ Y0 @ Y1) @ (l_ec @ Y1 @ Y2) @ (l_ec @ Y2 @ Y0))))))))), 420.49/60.61 inference(cnf_transformation,[],[f428])). 420.49/60.61 thf(f428,plain,( 420.49/60.61 (ec3 = (^[Y0 : $o]: ((^[Y1 : $o]: ((^[Y2 : $o]: (and3 @ (l_ec @ Y0 @ Y1) @ (l_ec @ Y1 @ Y2) @ (l_ec @ Y2 @ Y0))))))))), 420.49/60.61 inference(fool_elimination,[],[f47])). 420.49/60.61 thf(f47,axiom,( 420.49/60.61 (ec3 = (^[X0 : $o, X1 : $o, X2 : $o] : (and3 @ (l_ec @ X0 @ X1) @ (l_ec @ X1 @ X2) @ (l_ec @ X2 @ X0))))), 420.49/60.61 file('/export/starexec/sandbox/tmp/tmp.2i9OyGfWTf/E---3.1_15619.p',def_ec3)). 420.49/60.61 thf(f677,plain,( 420.49/60.61 (nat = ((^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $o]: ((^[Y3 : $i]: ((^[Y4 : $i]: (eps @ (^[Y5 : $i]: ((Y2 & (Y3 = Y5)) | ((~ Y2) & (Y4 = Y5)))))))))) @ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) @ (repl @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: (eps @ (^[Y6 : $i]: ((Y3 & (Y4 = Y6)) | ((~ Y3) & (Y5 = Y6)))))))))) @ (Y1 @ Y2) @ Y2 @ (eps @ (^[Y3 : $i]: ((Y1 @ Y3) & (in @ Y3 @ Y0))))))) @ emptyset)))) @ ((^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $o]: ((^[Y3 : $i]: ((^[Y4 : $i]: (eps @ (^[Y5 : $i]: ((Y2 & (Y3 = Y5)) | ((~ Y2) & (Y4 = Y5)))))))))) @ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) @ (repl @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: (eps @ (^[Y6 : $i]: ((Y3 & (Y4 = Y6)) | ((~ Y3) & (Y5 = Y6)))))))))) @ (Y1 @ Y2) @ Y2 @ (eps @ (^[Y3 : $i]: ((Y1 @ Y3) & (in @ Y3 @ Y0))))))) @ emptyset)))) @ (univof @ emptyset) @ nat_p) @ (^[Y0 : $i]: (~ (emptyset = Y0)))))), 420.49/60.61 inference(definition_unfolding,[],[f671,f675,f676])). 420.49/60.61 thf(f676,plain,( 420.49/60.61 (omega = ((^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $o]: ((^[Y3 : $i]: ((^[Y4 : $i]: (eps @ (^[Y5 : $i]: ((Y2 & (Y3 = Y5)) | ((~ Y2) & (Y4 = Y5)))))))))) @ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) @ (repl @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: (eps @ (^[Y6 : $i]: ((Y3 & (Y4 = Y6)) | ((~ Y3) & (Y5 = Y6)))))))))) @ (Y1 @ Y2) @ Y2 @ (eps @ (^[Y3 : $i]: ((Y1 @ Y3) & (in @ Y3 @ Y0))))))) @ emptyset)))) @ (univof @ emptyset) @ nat_p))), 420.49/60.61 inference(definition_unfolding,[],[f650,f675])). 420.49/60.61 thf(f650,plain,( 420.49/60.61 (omega = (d_Sep @ (univof @ emptyset) @ nat_p))), 420.49/60.61 inference(cnf_transformation,[],[f257])). 420.49/60.61 thf(f257,plain,( 420.49/60.61 (omega = (d_Sep @ (univof @ emptyset) @ nat_p))), 420.49/60.61 inference(fool_elimination,[],[f21])). 420.49/60.61 thf(f21,axiom,( 420.49/60.61 (omega = (d_Sep @ (univof @ emptyset) @ nat_p))), 420.49/60.61 file('/export/starexec/sandbox/tmp/tmp.2i9OyGfWTf/E---3.1_15619.p',def_omega)). 420.49/60.61 thf(f675,plain,( 420.49/60.61 (d_Sep = (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $o]: ((^[Y3 : $i]: ((^[Y4 : $i]: (eps @ (^[Y5 : $i]: ((Y2 & (Y3 = Y5)) | ((~ Y2) & (Y4 = Y5)))))))))) @ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) @ (repl @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: (eps @ (^[Y6 : $i]: ((Y3 & (Y4 = Y6)) | ((~ Y3) & (Y5 = Y6)))))))))) @ (Y1 @ Y2) @ Y2 @ (eps @ (^[Y3 : $i]: ((Y1 @ Y3) & (in @ Y3 @ Y0))))))) @ emptyset)))))), 420.49/60.61 inference(definition_unfolding,[],[f578,f666,f666])). 420.49/60.61 thf(f666,plain,( 420.49/60.61 (if = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps @ (^[Y3 : $i]: ((Y0 & (Y1 = Y3)) | ((~ Y0) & (Y2 = Y3)))))))))))), 420.49/60.61 inference(cnf_transformation,[],[f404])). 420.49/60.61 thf(f404,plain,( 420.49/60.61 (if = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps @ (^[Y3 : $i]: ((Y0 & (Y1 = Y3)) | ((~ Y0) & (Y2 = Y3)))))))))))), 420.49/60.61 inference(fool_elimination,[],[f403])). 420.49/60.61 thf(f403,plain,( 420.49/60.61 (if = (^[X0 : $o, X1 : $i, X2 : $i] : (eps @ (^[X3 : $i] : (((X2 = X3) & ~X0) | ((X1 = X3) & X0))))))), 420.49/60.61 inference(rectify,[],[f8])). 420.49/60.61 thf(f8,axiom,( 420.49/60.61 (if = (^[X0 : $o, X1 : $i, X2 : $i] : (eps @ (^[X3 : $i] : (((X2 = X3) & ~X0) | ((X1 = X3) & X0))))))), 420.49/60.61 file('/export/starexec/sandbox/tmp/tmp.2i9OyGfWTf/E---3.1_15619.p',def_if)). 420.49/60.61 thf(f578,plain,( 420.49/60.61 (d_Sep = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (if @ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) @ (repl @ Y0 @ (^[Y2 : $i]: (if @ (Y1 @ Y2) @ Y2 @ (eps @ (^[Y3 : $i]: ((Y1 @ Y3) & (in @ Y3 @ Y0))))))) @ emptyset)))))), 420.49/60.61 inference(cnf_transformation,[],[f339])). 420.49/60.61 thf(f339,plain,( 420.49/60.61 (d_Sep = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (if @ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (Y1 @ Y2)))) @ (repl @ Y0 @ (^[Y2 : $i]: (if @ (Y1 @ Y2) @ Y2 @ (eps @ (^[Y3 : $i]: ((Y1 @ Y3) & (in @ Y3 @ Y0))))))) @ emptyset)))))), 420.49/60.61 inference(fool_elimination,[],[f338])). 420.49/60.61 thf(f338,plain,( 420.49/60.61 (d_Sep = (^[X0 : $i, X1 : $i > $o] : (if @ ? [X2] : ((X1 @ X2) & (in @ X2 @ X0)) @ (repl @ X0 @ (^[X3 : $i] : (if @ (X1 @ X3) @ X3 @ (eps @ (^[X4 : $i] : ((in @ X4 @ X0) & (X1 @ X4))))))) @ emptyset)))), 420.49/60.61 inference(rectify,[],[f14])). 420.49/60.61 thf(f14,axiom,( 420.49/60.61 (d_Sep = (^[X0 : $i, X1 : $i > $o] : (if @ ? [X2] : ((X1 @ X2) & (in @ X2 @ X0)) @ (repl @ X0 @ (^[X2 : $i] : (if @ (X1 @ X2) @ X2 @ (eps @ (^[X3 : $i] : ((in @ X3 @ X0) & (X1 @ X3))))))) @ emptyset)))), 420.49/60.61 file('/export/starexec/sandbox/tmp/tmp.2i9OyGfWTf/E---3.1_15619.p',def_d_Sep)). 420.49/60.61 thf(f671,plain,( 420.49/60.61 (nat = (d_Sep @ omega @ (^[Y0 : $i]: (~ (emptyset = Y0)))))), 420.49/60.61 inference(cnf_transformation,[],[f311])). 420.49/60.61 thf(f311,plain,( 420.49/60.61 (nat = (d_Sep @ omega @ (^[Y0 : $i]: (~ (emptyset = Y0)))))), 420.49/60.61 inference(fool_elimination,[],[f95])). 420.49/60.61 thf(f95,axiom,( 420.49/60.61 (nat = (d_Sep @ omega @ (^[X0 : $i] : ((emptyset != X0)))))), 420.49/60.61 file('/export/starexec/sandbox/tmp/tmp.2i9OyGfWTf/E---3.1_15619.p',def_nat)). 420.49/60.61 thf(f648,plain,( 420.49/60.61 ((all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: (ec3 @ (n_is @ Y0 @ Y1) @ (n_some @ (diffprop @ Y0 @ Y1)) @ (n_some @ (diffprop @ Y1 @ Y0))))))) = $true)), 420.49/60.61 inference(cnf_transformation,[],[f469])). 420.49/60.61 thf(f469,plain,( 420.49/60.61 ((all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: (ec3 @ (n_is @ Y0 @ Y1) @ (n_some @ (diffprop @ Y0 @ Y1)) @ (n_some @ (diffprop @ Y1 @ Y0))))))) = $true)), 420.49/60.61 inference(fool_elimination,[],[f468])). 420.49/60.61 thf(f468,plain,( 420.49/60.61 (all_of @ (^[X0 : $i] : (in @ X0 @ nat)) @ (^[X1 : $i] : (all_of @ (^[X2 : $i] : (in @ X2 @ nat)) @ (^[X3 : $i] : (ec3 @ (n_is @ X1 @ X3) @ (n_some @ (diffprop @ X1 @ X3)) @ (n_some @ (diffprop @ X3 @ X1)))))))), 420.49/60.61 inference(rectify,[],[f204])). 420.49/60.61 thf(f204,axiom,( 420.49/60.61 (all_of @ (^[X0 : $i] : (in @ X0 @ nat)) @ (^[X0 : $i] : (all_of @ (^[X1 : $i] : (in @ X1 @ nat)) @ (^[X1 : $i] : (ec3 @ (n_is @ X0 @ X1) @ (n_some @ (diffprop @ X0 @ X1)) @ (n_some @ (diffprop @ X1 @ X0)))))))), 420.49/60.61 file('/export/starexec/sandbox/tmp/tmp.2i9OyGfWTf/E---3.1_15619.p',satz9b)). 420.49/60.61 thf(f946,plain,( 420.49/60.61 ($true = (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((emptyset = Y3) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y0 = (n_pl @ Y1 @ Y2))))) => (Y0 = Y1)) => (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y1 = (n_pl @ Y0 @ Y2))))))))))))), 420.49/60.61 inference(boolean_simplification,[],[f945])). 420.49/60.61 thf(f945,plain,( 420.49/60.61 ((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((emptyset = Y3) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y0 = (n_pl @ Y1 @ Y2)) => $false))) => (Y0 = Y1)) => (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y1 = (n_pl @ Y0 @ Y2))))))))))) = $true)), 420.49/60.61 inference(boolean_simplification,[],[f944])). 420.49/60.61 thf(f944,plain,( 420.49/60.61 ($true = (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((emptyset = Y3) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (((~ (~ (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y0 = (n_pl @ Y1 @ Y2)) => $false))))) => (Y0 = Y1)) => (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y1 = (n_pl @ Y0 @ Y2))))))))))))), 420.49/60.61 inference(boolean_simplification,[],[f943])). 420.49/60.61 thf(f943,plain,( 420.49/60.61 ((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((emptyset = Y3) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (((~ ((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y0 = (n_pl @ Y1 @ Y2)) => $false))) => $false)) => (Y0 = Y1)) => (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y1 = (n_pl @ Y0 @ Y2))))))))))) = $true)), 420.49/60.61 inference(boolean_simplification,[],[f942])). 420.49/60.61 thf(f942,plain,( 420.49/60.61 ($true = (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((emptyset = Y3) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (((((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y0 = (n_pl @ Y1 @ Y2)) => $false))) => $false) => $false) => (Y0 = Y1)) => (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((emptyset = Y4) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y1 = (n_pl @ Y0 @ Y2))))))))))))), 420.49/60.61 inference(boolean_simplification,[],[f941])). 420.49/60.61 thf(f941,plain,( 420.49/60.61 ((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((~ (~ (emptyset = Y2))) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((~ (~ (emptyset = Y3))) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (((((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y0 = (n_pl @ Y1 @ Y2)) => $false))) => $false) => $false) => (Y0 = Y1)) => (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: (~ (Y1 = (n_pl @ Y0 @ Y2))))))))))) = $true)), 420.49/60.61 inference(boolean_simplification,[],[f940])). 420.49/60.61 thf(f940,plain,( 420.49/60.61 ((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((~ (~ (emptyset = Y2))) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((~ (~ (emptyset = Y3))) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (((((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y0 = (n_pl @ Y1 @ Y2)) => $false))) => $false) => $false) => (Y0 = Y1)) => (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y1 = (n_pl @ Y0 @ Y2)) => $false))))))))) = $true)), 420.49/60.61 inference(boolean_simplification,[],[f939])). 420.49/60.61 thf(f939,plain,( 420.49/60.61 ($true = (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((~ (~ (emptyset = Y2))) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((~ (~ (emptyset = Y3))) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (((((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y0 = (n_pl @ Y1 @ Y2)) => $false))) => $false) => $false) => (Y0 = Y1)) => (~ (~ (all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y1 = (n_pl @ Y0 @ Y2)) => $false))))))))))))), 420.49/60.61 inference(boolean_simplification,[],[f938])). 420.49/60.61 thf(f938,plain,( 420.49/60.61 ($true = (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((~ (~ (emptyset = Y2))) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((~ (~ (emptyset = Y3))) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (((((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y0 = (n_pl @ Y1 @ Y2)) => $false))) => $false) => $false) => (Y0 = Y1)) => (~ ((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y1 = (n_pl @ Y0 @ Y2)) => $false))) => $false)))))))))), 420.49/60.61 inference(boolean_simplification,[],[f937])). 420.49/60.61 thf(f937,plain,( 420.49/60.61 ((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((~ (~ (emptyset = Y2))) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3))))) & ((repl @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3))))) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((~ (emptyset = Y3)) & (Y3 = Y4)) | ((~ (~ (emptyset = Y3))) & ((eps @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ (eps @ (^[Y6 : $i]: (((?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7)))) & ((repl @ (univof @ emptyset) @ (^[Y7 : $i]: (eps @ (^[Y8 : $i]: (((nat_p @ Y7) & (Y7 = Y8)) | ((~ (nat_p @ Y7)) & ((eps @ (^[Y9 : $i]: ((nat_p @ Y9) & (in @ Y9 @ (univof @ emptyset))))) = Y8))))))) = Y6)) | ((~ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ (univof @ emptyset)) & (nat_p @ Y7))))) & (emptyset = Y6))))))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4)))))) & (~ (emptyset = Y3)))))) & (emptyset = Y2))))))) @ (^[Y1 : $i]: (((((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y0 = (n_pl @ Y1 @ Y2)) => $false))) => $false) => $false) => (Y0 = Y1)) => (((all_of @ (^[Y2 : $i]: (in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4))))) & ((repl @ (eps @ (^[Y4 : $i]: (((?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5)))) & ((repl @ (univof @ emptyset) @ (^[Y5 : $i]: (eps @ (^[Y6 : $i]: (((nat_p @ Y5) & (Y5 = Y6)) | ((~ (nat_p @ Y5)) & ((eps @ (^[Y7 : $i]: ((nat_p @ Y7) & (in @ Y7 @ (univof @ emptyset))))) = Y6))))))) = Y4)) | ((~ (?? @ $i @ (^[Y5 : $i]: ((in @ Y5 @ (univof @ emptyset)) & (nat_p @ Y5))))) & (emptyset = Y4))))) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((~ (emptyset = Y4)) & (Y4 = Y5)) | ((~ (~ (emptyset = Y4))) & ((eps @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ (eps @ (^[Y7 : $i]: (((?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8)))) & ((repl @ (univof @ emptyset) @ (^[Y8 : $i]: (eps @ (^[Y9 : $i]: (((nat_p @ Y8) & (Y8 = Y9)) | ((~ (nat_p @ Y8)) & ((eps @ (^[Y10 : $i]: ((nat_p @ Y10) & (in @ Y10 @ (univof @ emptyset))))) = Y9))))))) = Y7)) | ((~ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ (univof @ emptyset)) & (nat_p @ Y8))))) & (emptyset = Y7))))))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5)))))) & (~ (emptyset = Y4)))))) & (emptyset = Y3))))))) @ (^[Y2 : $i]: ((Y1 = (n_pl @ Y0 @ Y2)) => $false))) => $false) => $false))))))) = $true)), 420.49/60.61 inference(beta_eta_normalization,[],[f732])). 420.49/60.61 thf(f732,plain,( 420.49/60.61 ($true = (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ ((^[Y1 : $i]: ((^[Y2 : $i > $o]: ((^[Y3 : $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: (eps @ (^[Y6 : $i]: ((Y3 & (Y4 = Y6)) | ((~ Y3) & (Y5 = Y6)))))))))) @ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (Y2 @ Y3)))) @ (repl @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (eps @ (^[Y7 : $i]: ((Y4 & (Y5 = Y7)) | ((~ Y4) & (Y6 = Y7)))))))))) @ (Y2 @ Y3) @ Y3 @ (eps @ (^[Y4 : $i]: ((Y2 @ Y4) & (in @ Y4 @ Y1))))))) @ emptyset)))) @ ((^[Y1 : $i]: ((^[Y2 : $i > $o]: ((^[Y3 : $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: (eps @ (^[Y6 : $i]: ((Y3 & (Y4 = Y6)) | ((~ Y3) & (Y5 = Y6)))))))))) @ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) & (Y2 @ Y3)))) @ (repl @ Y1 @ (^[Y3 : $i]: ((^[Y4 : $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (eps @ (^[Y7 : $i]: ((Y4 & (Y5 = Y7)) | ((~ Y4) & (Y6 = Y7)))))))))) @ (Y2 @ Y3) @ Y3 @ (eps @ (^[Y4 : $i]: ((Y2 @ Y4) & (in @ Y4 @ Y1))))))) @ emptyset)))) @ (univof @ emptyset) @ nat_p) @ (^[Y1 : $i]: (~ (emptyset = Y1)))))) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: ((^[Y4 : $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (eps @ (^[Y7 : $i]: ((Y4 & (Y5 = Y7)) | ((~ Y4) & (Y6 = Y7)))))))))) @ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) & (Y3 @ Y4)))) @ (repl @ Y2 @ (^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (eps @ (^[Y8 : $i]: ((Y5 & (Y6 = Y8)) | ((~ Y5) & (Y7 = Y8)))))))))) @ (Y3 @ Y4) @ Y4 @ (eps @ (^[Y5 : $i]: ((Y3 @ Y5) & (in @ Y5 @ Y2))))))) @ emptyset)))) @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: ((^[Y4 : $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (eps @ (^[Y7 : $i]: ((Y4 & (Y5 = Y7)) | ((~ Y4) & (Y6 = Y7)))))))))) @ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) & (Y3 @ Y4)))) @ (repl @ Y2 @ (^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (eps @ (^[Y8 : $i]: ((Y5 & (Y6 = Y8)) | ((~ Y5) & (Y7 = Y8)))))))))) @ (Y3 @ Y4) @ Y4 @ (eps @ (^[Y5 : $i]: ((Y3 @ Y5) & (in @ Y5 @ Y2))))))) @ emptyset)))) @ (univof @ emptyset) @ nat_p) @ (^[Y2 : $i]: (~ (emptyset = Y2)))))) @ (^[Y1 : $i]: (((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $o]: ((^[Y5 : $o]: ((^[Y6 : $o]: (Y5 => Y6)))) @ ((^[Y5 : $o]: ((^[Y6 : $o]: ((^[Y7 : $o]: (Y6 => Y7)))) @ Y5 @ $false)) @ Y4))) @ ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i > $o]: ((^[Y8 : $o]: ((^[Y9 : $o]: ((^[Y10 : $o]: (Y9 => Y10)))) @ Y8 @ $false)) @ (all_of @ (^[Y8 : $i]: (in @ Y8 @ Y6)) @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: ((^[Y10 : $i]: ((^[Y11 : $o]: ((^[Y12 : $o]: ((^[Y13 : $o]: (Y12 => Y13)))) @ Y11 @ $false)) @ (Y9 @ Y10))))))) @ Y6 @ Y7)))))) @ ((^[Y6 : $i]: ((^[Y7 : $i > $o]: ((^[Y8 : $o]: ((^[Y9 : $i]: ((^[Y10 : $i]: (eps @ (^[Y11 : $i]: ((Y8 & (Y9 = Y11)) | ((~ Y8) & (Y10 = Y11)))))))))) @ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ Y6) & (Y7 @ Y8)))) @ (repl @ Y6 @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (eps @ (^[Y12 : $i]: ((Y9 & (Y10 = Y12)) | ((~ Y9) & (Y11 = Y12)))))))))) @ (Y7 @ Y8) @ Y8 @ (eps @ (^[Y9 : $i]: ((Y7 @ Y9) & (in @ Y9 @ Y6))))))) @ emptyset)))) @ ((^[Y6 : $i]: ((^[Y7 : $i > $o]: ((^[Y8 : $o]: ((^[Y9 : $i]: ((^[Y10 : $i]: (eps @ (^[Y11 : $i]: ((Y8 & (Y9 = Y11)) | ((~ Y8) & (Y10 = Y11)))))))))) @ (?? @ $i @ (^[Y8 : $i]: ((in @ Y8 @ Y6) & (Y7 @ Y8)))) @ (repl @ Y6 @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (eps @ (^[Y12 : $i]: ((Y9 & (Y10 = Y12)) | ((~ Y9) & (Y11 = Y12)))))))))) @ (Y7 @ Y8) @ Y8 @ (eps @ (^[Y9 : $i]: ((Y7 @ Y9) & (in @ Y9 @ Y6))))))) @ emptyset)))) @ (univof @ emptyset) @ nat_p) @ (^[Y6 : $i]: (~ (emptyset = Y6)))) @ ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: ((^[Y11 : $i]: (Y10 = Y11)))))) @ ((^[Y9 : $i]: ((^[Y10 : $i > $o]: ((^[Y11 : $o]: ((^[Y12 : $i]: ((^[Y13 : $i]: (eps @ (^[Y14 : $i]: ((Y11 & (Y12 = Y14)) | ((~ Y11) & (Y13 = Y14)))))))))) @ (?? @ $i @ (^[Y11 : $i]: ((in @ Y11 @ Y9) & (Y10 @ Y11)))) @ (repl @ Y9 @ (^[Y11 : $i]: ((^[Y12 : $o]: ((^[Y13 : $i]: ((^[Y14 : $i]: (eps @ (^[Y15 : $i]: ((Y12 & (Y13 = Y15)) | ((~ Y12) & (Y14 = Y15)))))))))) @ (Y10 @ Y11) @ Y11 @ (eps @ (^[Y12 : $i]: ((Y10 @ Y12) & (in @ Y12 @ Y9))))))) @ emptyset)))) @ ((^[Y9 : $i]: ((^[Y10 : $i > $o]: ((^[Y11 : $o]: ((^[Y12 : $i]: ((^[Y13 : $i]: (eps @ (^[Y14 : $i]: ((Y11 & (Y12 = Y14)) | ((~ Y11) & (Y13 = Y14)))))))))) @ (?? @ $i @ (^[Y11 : $i]: ((in @ Y11 @ Y9) & (Y10 @ Y11)))) @ (repl @ Y9 @ (^[Y11 : $i]: ((^[Y12 : $o]: ((^[Y13 : $i]: ((^[Y14 : $i]: (eps @ (^[Y15 : $i]: ((Y12 & (Y13 = Y15)) | ((~ Y12) & (Y14 = Y15)))))))))) @ (Y10 @ Y11) @ Y11 @ (eps @ (^[Y12 : $i]: ((Y10 @ Y12) & (in @ Y12 @ Y9))))))) @ emptyset)))) @ (univof @ emptyset) @ nat_p) @ (^[Y9 : $i]: (~ (emptyset = Y9)))) @ Y6 @ (n_pl @ Y7 @ Y8))))))) @ Y4 @ Y5))))) @ Y2 @ Y3) @ ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (Y5 = Y6)))))) @ ((^[Y4 : $i]: ((^[Y5 : $i > $o]: ((^[Y6 : $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: (eps @ (^[Y9 : $i]: ((Y6 & (Y7 = Y9)) | ((~ Y6) & (Y8 = Y9)))))))))) @ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y4) & (Y5 @ Y6)))) @ (repl @ Y4 @ (^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $i]: ((^[Y9 : $i]: (eps @ (^[Y10 : $i]: ((Y7 & (Y8 = Y10)) | ((~ Y7) & (Y9 = Y10)))))))))) @ (Y5 @ Y6) @ Y6 @ (eps @ (^[Y7 : $i]: ((Y5 @ Y7) & (in @ Y7 @ Y4))))))) @ emptyset)))) @ ((^[Y4 : $i]: ((^[Y5 : $i > $o]: ((^[Y6 : $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: (eps @ (^[Y9 : $i]: ((Y6 & (Y7 = Y9)) | ((~ Y6) & (Y8 = Y9)))))))))) @ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y4) & (Y5 @ Y6)))) @ (repl @ Y4 @ (^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $i]: ((^[Y9 : $i]: (eps @ (^[Y10 : $i]: ((Y7 & (Y8 = Y10)) | ((~ Y7) & (Y9 = Y10)))))))))) @ (Y5 @ Y6) @ Y6 @ (eps @ (^[Y7 : $i]: ((Y5 @ Y7) & (in @ Y7 @ Y4))))))) @ emptyset)))) @ (univof @ emptyset) @ nat_p) @ (^[Y4 : $i]: (~ (emptyset = Y4)))) @ Y2 @ Y3))))) @ Y0 @ Y1) => ((^[Y2 : $o]: ((^[Y3 : $o]: ((^[Y4 : $o]: (Y3 => Y4)))) @ Y2 @ $false)) @ ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i > $o]: ((^[Y6 : $o]: ((^[Y7 : $o]: ((^[Y8 : $o]: (Y7 => Y8)))) @ Y6 @ $false)) @ (all_of @ (^[Y6 : $i]: (in @ Y6 @ Y4)) @ ((^[Y6 : $i]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $o]: ((^[Y11 : $o]: (Y10 => Y11)))) @ Y9 @ $false)) @ (Y7 @ Y8))))))) @ Y4 @ Y5)))))) @ ((^[Y4 : $i]: ((^[Y5 : $i > $o]: ((^[Y6 : $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: (eps @ (^[Y9 : $i]: ((Y6 & (Y7 = Y9)) | ((~ Y6) & (Y8 = Y9)))))))))) @ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y4) & (Y5 @ Y6)))) @ (repl @ Y4 @ (^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $i]: ((^[Y9 : $i]: (eps @ (^[Y10 : $i]: ((Y7 & (Y8 = Y10)) | ((~ Y7) & (Y9 = Y10)))))))))) @ (Y5 @ Y6) @ Y6 @ (eps @ (^[Y7 : $i]: ((Y5 @ Y7) & (in @ Y7 @ Y4))))))) @ emptyset)))) @ ((^[Y4 : $i]: ((^[Y5 : $i > $o]: ((^[Y6 : $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: (eps @ (^[Y9 : $i]: ((Y6 & (Y7 = Y9)) | ((~ Y6) & (Y8 = Y9)))))))))) @ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y4) & (Y5 @ Y6)))) @ (repl @ Y4 @ (^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $i]: ((^[Y9 : $i]: (eps @ (^[Y10 : $i]: ((Y7 & (Y8 = Y10)) | ((~ Y7) & (Y9 = Y10)))))))))) @ (Y5 @ Y6) @ Y6 @ (eps @ (^[Y7 : $i]: ((Y5 @ Y7) & (in @ Y7 @ Y4))))))) @ emptyset)))) @ (univof @ emptyset) @ nat_p) @ (^[Y4 : $i]: (~ (emptyset = Y4)))) @ ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: (Y8 = Y9)))))) @ ((^[Y7 : $i]: ((^[Y8 : $i > $o]: ((^[Y9 : $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (eps @ (^[Y12 : $i]: ((Y9 & (Y10 = Y12)) | ((~ Y9) & (Y11 = Y12)))))))))) @ (?? @ $i @ (^[Y9 : $i]: ((in @ Y9 @ Y7) & (Y8 @ Y9)))) @ (repl @ Y7 @ (^[Y9 : $i]: ((^[Y10 : $o]: ((^[Y11 : $i]: ((^[Y12 : $i]: (eps @ (^[Y13 : $i]: ((Y10 & (Y11 = Y13)) | ((~ Y10) & (Y12 = Y13)))))))))) @ (Y8 @ Y9) @ Y9 @ (eps @ (^[Y10 : $i]: ((Y8 @ Y10) & (in @ Y10 @ Y7))))))) @ emptyset)))) @ ((^[Y7 : $i]: ((^[Y8 : $i > $o]: ((^[Y9 : $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (eps @ (^[Y12 : $i]: ((Y9 & (Y10 = Y12)) | ((~ Y9) & (Y11 = Y12)))))))))) @ (?? @ $i @ (^[Y9 : $i]: ((in @ Y9 @ Y7) & (Y8 @ Y9)))) @ (repl @ Y7 @ (^[Y9 : $i]: ((^[Y10 : $o]: ((^[Y11 : $i]: ((^[Y12 : $i]: (eps @ (^[Y13 : $i]: ((Y10 & (Y11 = Y13)) | ((~ Y10) & (Y12 = Y13)))))))))) @ (Y8 @ Y9) @ Y9 @ (eps @ (^[Y10 : $i]: ((Y8 @ Y10) & (in @ Y10 @ Y7))))))) @ emptyset)))) @ (univof @ emptyset) @ nat_p) @ (^[Y7 : $i]: (~ (emptyset = Y7)))) @ Y4 @ (n_pl @ Y5 @ Y6))))))) @ Y3 @ Y2))))) @ Y0 @ Y1)))))))))), 420.49/60.61 inference(definition_unfolding,[],[f558,f677,f677,f686,f672,f682])). 420.49/60.61 thf(f682,plain,( 420.49/60.61 (iii = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $o]: ((^[Y4 : $o]: ((^[Y5 : $o]: ((^[Y6 : $o]: (Y5 => Y6)))) @ Y4 @ $false)) @ (all_of @ (^[Y4 : $i]: (in @ Y4 @ Y2)) @ ((^[Y4 : $i]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $o]: ((^[Y9 : $o]: (Y8 => Y9)))) @ Y7 @ $false)) @ (Y5 @ Y6))))))) @ Y2 @ Y3)))))) @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: ((^[Y4 : $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (eps @ (^[Y7 : $i]: ((Y4 & (Y5 = Y7)) | ((~ Y4) & (Y6 = Y7)))))))))) @ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) & (Y3 @ Y4)))) @ (repl @ Y2 @ (^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (eps @ (^[Y8 : $i]: ((Y5 & (Y6 = Y8)) | ((~ Y5) & (Y7 = Y8)))))))))) @ (Y3 @ Y4) @ Y4 @ (eps @ (^[Y5 : $i]: ((Y3 @ Y5) & (in @ Y5 @ Y2))))))) @ emptyset)))) @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: ((^[Y4 : $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (eps @ (^[Y7 : $i]: ((Y4 & (Y5 = Y7)) | ((~ Y4) & (Y6 = Y7)))))))))) @ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) & (Y3 @ Y4)))) @ (repl @ Y2 @ (^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (eps @ (^[Y8 : $i]: ((Y5 & (Y6 = Y8)) | ((~ Y5) & (Y7 = Y8)))))))))) @ (Y3 @ Y4) @ Y4 @ (eps @ (^[Y5 : $i]: ((Y3 @ Y5) & (in @ Y5 @ Y2))))))) @ emptyset)))) @ (univof @ emptyset) @ nat_p) @ (^[Y2 : $i]: (~ (emptyset = Y2)))) @ ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (Y6 = Y7)))))) @ ((^[Y5 : $i]: ((^[Y6 : $i > $o]: ((^[Y7 : $o]: ((^[Y8 : $i]: ((^[Y9 : $i]: (eps @ (^[Y10 : $i]: ((Y7 & (Y8 = Y10)) | ((~ Y7) & (Y9 = Y10)))))))))) @ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ Y5) & (Y6 @ Y7)))) @ (repl @ Y5 @ (^[Y7 : $i]: ((^[Y8 : $o]: ((^[Y9 : $i]: ((^[Y10 : $i]: (eps @ (^[Y11 : $i]: ((Y8 & (Y9 = Y11)) | ((~ Y8) & (Y10 = Y11)))))))))) @ (Y6 @ Y7) @ Y7 @ (eps @ (^[Y8 : $i]: ((Y6 @ Y8) & (in @ Y8 @ Y5))))))) @ emptyset)))) @ ((^[Y5 : $i]: ((^[Y6 : $i > $o]: ((^[Y7 : $o]: ((^[Y8 : $i]: ((^[Y9 : $i]: (eps @ (^[Y10 : $i]: ((Y7 & (Y8 = Y10)) | ((~ Y7) & (Y9 = Y10)))))))))) @ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ Y5) & (Y6 @ Y7)))) @ (repl @ Y5 @ (^[Y7 : $i]: ((^[Y8 : $o]: ((^[Y9 : $i]: ((^[Y10 : $i]: (eps @ (^[Y11 : $i]: ((Y8 & (Y9 = Y11)) | ((~ Y8) & (Y10 = Y11)))))))))) @ (Y6 @ Y7) @ Y7 @ (eps @ (^[Y8 : $i]: ((Y6 @ Y8) & (in @ Y8 @ Y5))))))) @ emptyset)))) @ (univof @ emptyset) @ nat_p) @ (^[Y5 : $i]: (~ (emptyset = Y5)))) @ Y2 @ (n_pl @ Y3 @ Y4))))))) @ Y1 @ Y0))))))), 420.49/60.61 inference(definition_unfolding,[],[f571,f678,f680])). 420.49/60.61 thf(f571,plain,( 420.49/60.61 (iii = (^[Y0 : $i]: ((^[Y1 : $i]: (n_some @ (diffprop @ Y1 @ Y0))))))), 420.49/60.61 inference(cnf_transformation,[],[f391])). 420.49/60.61 thf(f391,plain,( 420.49/60.61 (iii = (^[Y0 : $i]: ((^[Y1 : $i]: (n_some @ (diffprop @ Y1 @ Y0))))))), 420.49/60.61 inference(fool_elimination,[],[f187])). 420.49/60.61 thf(f187,axiom,( 420.49/60.61 ((^[X0 : $i, X1 : $i] : (n_some @ (diffprop @ X1 @ X0))) = iii)), 420.49/60.61 file('/export/starexec/sandbox/tmp/tmp.2i9OyGfWTf/E---3.1_15619.p',def_iii)). 420.49/60.61 thf(f686,plain,( 420.49/60.61 (moreis = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $o]: ((^[Y3 : $o]: ((^[Y4 : $o]: (Y3 => Y4)))) @ ((^[Y3 : $o]: ((^[Y4 : $o]: ((^[Y5 : $o]: (Y4 => Y5)))) @ Y3 @ $false)) @ Y2))) @ ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i > $o]: ((^[Y6 : $o]: ((^[Y7 : $o]: ((^[Y8 : $o]: (Y7 => Y8)))) @ Y6 @ $false)) @ (all_of @ (^[Y6 : $i]: (in @ Y6 @ Y4)) @ ((^[Y6 : $i]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $o]: ((^[Y11 : $o]: (Y10 => Y11)))) @ Y9 @ $false)) @ (Y7 @ Y8))))))) @ Y4 @ Y5)))))) @ ((^[Y4 : $i]: ((^[Y5 : $i > $o]: ((^[Y6 : $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: (eps @ (^[Y9 : $i]: ((Y6 & (Y7 = Y9)) | ((~ Y6) & (Y8 = Y9)))))))))) @ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y4) & (Y5 @ Y6)))) @ (repl @ Y4 @ (^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $i]: ((^[Y9 : $i]: (eps @ (^[Y10 : $i]: ((Y7 & (Y8 = Y10)) | ((~ Y7) & (Y9 = Y10)))))))))) @ (Y5 @ Y6) @ Y6 @ (eps @ (^[Y7 : $i]: ((Y5 @ Y7) & (in @ Y7 @ Y4))))))) @ emptyset)))) @ ((^[Y4 : $i]: ((^[Y5 : $i > $o]: ((^[Y6 : $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: (eps @ (^[Y9 : $i]: ((Y6 & (Y7 = Y9)) | ((~ Y6) & (Y8 = Y9)))))))))) @ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y4) & (Y5 @ Y6)))) @ (repl @ Y4 @ (^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $i]: ((^[Y9 : $i]: (eps @ (^[Y10 : $i]: ((Y7 & (Y8 = Y10)) | ((~ Y7) & (Y9 = Y10)))))))))) @ (Y5 @ Y6) @ Y6 @ (eps @ (^[Y7 : $i]: ((Y5 @ Y7) & (in @ Y7 @ Y4))))))) @ emptyset)))) @ (univof @ emptyset) @ nat_p) @ (^[Y4 : $i]: (~ (emptyset = Y4)))) @ ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: (Y8 = Y9)))))) @ ((^[Y7 : $i]: ((^[Y8 : $i > $o]: ((^[Y9 : $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (eps @ (^[Y12 : $i]: ((Y9 & (Y10 = Y12)) | ((~ Y9) & (Y11 = Y12)))))))))) @ (?? @ $i @ (^[Y9 : $i]: ((in @ Y9 @ Y7) & (Y8 @ Y9)))) @ (repl @ Y7 @ (^[Y9 : $i]: ((^[Y10 : $o]: ((^[Y11 : $i]: ((^[Y12 : $i]: (eps @ (^[Y13 : $i]: ((Y10 & (Y11 = Y13)) | ((~ Y10) & (Y12 = Y13)))))))))) @ (Y8 @ Y9) @ Y9 @ (eps @ (^[Y10 : $i]: ((Y8 @ Y10) & (in @ Y10 @ Y7))))))) @ emptyset)))) @ ((^[Y7 : $i]: ((^[Y8 : $i > $o]: ((^[Y9 : $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (eps @ (^[Y12 : $i]: ((Y9 & (Y10 = Y12)) | ((~ Y9) & (Y11 = Y12)))))))))) @ (?? @ $i @ (^[Y9 : $i]: ((in @ Y9 @ Y7) & (Y8 @ Y9)))) @ (repl @ Y7 @ (^[Y9 : $i]: ((^[Y10 : $o]: ((^[Y11 : $i]: ((^[Y12 : $i]: (eps @ (^[Y13 : $i]: ((Y10 & (Y11 = Y13)) | ((~ Y10) & (Y12 = Y13)))))))))) @ (Y8 @ Y9) @ Y9 @ (eps @ (^[Y10 : $i]: ((Y8 @ Y10) & (in @ Y10 @ Y7))))))) @ emptyset)))) @ (univof @ emptyset) @ nat_p) @ (^[Y7 : $i]: (~ (emptyset = Y7)))) @ Y4 @ (n_pl @ Y5 @ Y6))))))) @ Y2 @ Y3))))) @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (Y3 = Y4)))))) @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: ((^[Y4 : $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (eps @ (^[Y7 : $i]: ((Y4 & (Y5 = Y7)) | ((~ Y4) & (Y6 = Y7)))))))))) @ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) & (Y3 @ Y4)))) @ (repl @ Y2 @ (^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (eps @ (^[Y8 : $i]: ((Y5 & (Y6 = Y8)) | ((~ Y5) & (Y7 = Y8)))))))))) @ (Y3 @ Y4) @ Y4 @ (eps @ (^[Y5 : $i]: ((Y3 @ Y5) & (in @ Y5 @ Y2))))))) @ emptyset)))) @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: ((^[Y4 : $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (eps @ (^[Y7 : $i]: ((Y4 & (Y5 = Y7)) | ((~ Y4) & (Y6 = Y7)))))))))) @ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) & (Y3 @ Y4)))) @ (repl @ Y2 @ (^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (eps @ (^[Y8 : $i]: ((Y5 & (Y6 = Y8)) | ((~ Y5) & (Y7 = Y8)))))))))) @ (Y3 @ Y4) @ Y4 @ (eps @ (^[Y5 : $i]: ((Y3 @ Y5) & (in @ Y5 @ Y2))))))) @ emptyset)))) @ (univof @ emptyset) @ nat_p) @ (^[Y2 : $i]: (~ (emptyset = Y2)))) @ Y0 @ Y1))))))), 420.49/60.61 inference(definition_unfolding,[],[f649,f683,f681,f679])). 420.49/60.61 thf(f681,plain,( 420.49/60.61 (d_29_ii = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i > $o]: ((^[Y4 : $o]: ((^[Y5 : $o]: ((^[Y6 : $o]: (Y5 => Y6)))) @ Y4 @ $false)) @ (all_of @ (^[Y4 : $i]: (in @ Y4 @ Y2)) @ ((^[Y4 : $i]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $o]: ((^[Y9 : $o]: (Y8 => Y9)))) @ Y7 @ $false)) @ (Y5 @ Y6))))))) @ Y2 @ Y3)))))) @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: ((^[Y4 : $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (eps @ (^[Y7 : $i]: ((Y4 & (Y5 = Y7)) | ((~ Y4) & (Y6 = Y7)))))))))) @ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) & (Y3 @ Y4)))) @ (repl @ Y2 @ (^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (eps @ (^[Y8 : $i]: ((Y5 & (Y6 = Y8)) | ((~ Y5) & (Y7 = Y8)))))))))) @ (Y3 @ Y4) @ Y4 @ (eps @ (^[Y5 : $i]: ((Y3 @ Y5) & (in @ Y5 @ Y2))))))) @ emptyset)))) @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: ((^[Y4 : $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (eps @ (^[Y7 : $i]: ((Y4 & (Y5 = Y7)) | ((~ Y4) & (Y6 = Y7)))))))))) @ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) & (Y3 @ Y4)))) @ (repl @ Y2 @ (^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (eps @ (^[Y8 : $i]: ((Y5 & (Y6 = Y8)) | ((~ Y5) & (Y7 = Y8)))))))))) @ (Y3 @ Y4) @ Y4 @ (eps @ (^[Y5 : $i]: ((Y3 @ Y5) & (in @ Y5 @ Y2))))))) @ emptyset)))) @ (univof @ emptyset) @ nat_p) @ (^[Y2 : $i]: (~ (emptyset = Y2)))) @ ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (Y6 = Y7)))))) @ ((^[Y5 : $i]: ((^[Y6 : $i > $o]: ((^[Y7 : $o]: ((^[Y8 : $i]: ((^[Y9 : $i]: (eps @ (^[Y10 : $i]: ((Y7 & (Y8 = Y10)) | ((~ Y7) & (Y9 = Y10)))))))))) @ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ Y5) & (Y6 @ Y7)))) @ (repl @ Y5 @ (^[Y7 : $i]: ((^[Y8 : $o]: ((^[Y9 : $i]: ((^[Y10 : $i]: (eps @ (^[Y11 : $i]: ((Y8 & (Y9 = Y11)) | ((~ Y8) & (Y10 = Y11)))))))))) @ (Y6 @ Y7) @ Y7 @ (eps @ (^[Y8 : $i]: ((Y6 @ Y8) & (in @ Y8 @ Y5))))))) @ emptyset)))) @ ((^[Y5 : $i]: ((^[Y6 : $i > $o]: ((^[Y7 : $o]: ((^[Y8 : $i]: ((^[Y9 : $i]: (eps @ (^[Y10 : $i]: ((Y7 & (Y8 = Y10)) | ((~ Y7) & (Y9 = Y10)))))))))) @ (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ Y5) & (Y6 @ Y7)))) @ (repl @ Y5 @ (^[Y7 : $i]: ((^[Y8 : $o]: ((^[Y9 : $i]: ((^[Y10 : $i]: (eps @ (^[Y11 : $i]: ((Y8 & (Y9 = Y11)) | ((~ Y8) & (Y10 = Y11)))))))))) @ (Y6 @ Y7) @ Y7 @ (eps @ (^[Y8 : $i]: ((Y6 @ Y8) & (in @ Y8 @ Y5))))))) @ emptyset)))) @ (univof @ emptyset) @ nat_p) @ (^[Y5 : $i]: (~ (emptyset = Y5)))) @ Y2 @ (n_pl @ Y3 @ Y4))))))) @ Y0 @ Y1))))))), 420.49/60.61 inference(definition_unfolding,[],[f626,f678,f680])). 420.49/60.61 thf(f626,plain,( 420.49/60.61 (d_29_ii = (^[Y0 : $i]: ((^[Y1 : $i]: (n_some @ (diffprop @ Y0 @ Y1))))))), 420.49/60.61 inference(cnf_transformation,[],[f245])). 420.49/60.61 thf(f245,plain,( 420.49/60.61 (d_29_ii = (^[Y0 : $i]: ((^[Y1 : $i]: (n_some @ (diffprop @ Y0 @ Y1))))))), 420.49/60.61 inference(fool_elimination,[],[f186])). 420.49/60.61 thf(f186,axiom,( 420.49/60.61 ((^[X0 : $i, X1 : $i] : (n_some @ (diffprop @ X0 @ X1))) = d_29_ii)), 420.49/60.61 file('/export/starexec/sandbox/tmp/tmp.2i9OyGfWTf/E---3.1_15619.p',def_d_29_ii)). 420.49/60.61 thf(f683,plain,( 420.49/60.61 (l_or = (^[Y0 : $o]: ((^[Y1 : $o]: ((^[Y2 : $o]: (Y1 => Y2)))) @ ((^[Y1 : $o]: ((^[Y2 : $o]: ((^[Y3 : $o]: (Y2 => Y3)))) @ Y1 @ $false)) @ Y0))))), 420.49/60.61 inference(definition_unfolding,[],[f651,f663,f672])). 420.49/60.61 thf(f651,plain,( 420.49/60.61 (l_or = (^[Y0 : $o]: (imp @ (d_not @ Y0))))), 420.49/60.61 inference(cnf_transformation,[],[f437])). 420.49/60.61 thf(f437,plain,( 420.49/60.61 (l_or = (^[Y0 : $o]: (imp @ (d_not @ Y0))))), 420.49/60.61 inference(fool_elimination,[],[f39])). 420.49/60.61 thf(f39,axiom,( 420.49/60.61 (l_or = (^[X0 : $o] : (imp @ (d_not @ X0))))), 420.49/60.61 file('/export/starexec/sandbox/tmp/tmp.2i9OyGfWTf/E---3.1_15619.p',def_l_or)). 420.49/60.61 thf(f649,plain,( 420.49/60.61 (moreis = (^[Y0 : $i]: ((^[Y1 : $i]: (l_or @ (d_29_ii @ Y0 @ Y1) @ (n_is @ Y0 @ Y1))))))), 420.49/60.61 inference(cnf_transformation,[],[f306])). 420.49/60.61 thf(f306,plain,( 420.49/60.61 (moreis = (^[Y0 : $i]: ((^[Y1 : $i]: (l_or @ (d_29_ii @ Y0 @ Y1) @ (n_is @ Y0 @ Y1))))))), 420.49/60.61 inference(fool_elimination,[],[f189])). 420.49/60.61 thf(f189,axiom,( 420.49/60.61 (moreis = (^[X0 : $i, X1 : $i] : (l_or @ (d_29_ii @ X0 @ X1) @ (n_is @ X0 @ X1))))), 420.49/60.61 file('/export/starexec/sandbox/tmp/tmp.2i9OyGfWTf/E---3.1_15619.p',def_moreis)). 420.49/60.61 thf(f558,plain,( 420.49/60.61 ((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: ((moreis @ Y0 @ Y1) => (d_not @ (iii @ Y0 @ Y1)))))))) = $true)), 420.49/60.61 inference(cnf_transformation,[],[f276])). 420.49/60.61 thf(f276,plain,( 420.49/60.61 ((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ nat)) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ nat)) @ (^[Y1 : $i]: ((moreis @ Y0 @ Y1) => (d_not @ (iii @ Y0 @ Y1)))))))) = $true)), 420.49/60.61 inference(fool_elimination,[],[f275])). 420.49/60.61 thf(f275,plain,( 420.49/60.61 ~(all_of @ (^[X0 : $i] : (in @ X0 @ nat)) @ (^[X1 : $i] : (all_of @ (^[X2 : $i] : (in @ X2 @ nat)) @ (^[X3 : $i] : ((moreis @ X1 @ X3) => (d_not @ (iii @ X1 @ X3)))))))), 420.49/60.61 inference(rectify,[],[f214])). 420.49/60.61 thf(f214,negated_conjecture,( 420.49/60.61 ~(all_of @ (^[X0 : $i] : (in @ X0 @ nat)) @ (^[X0 : $i] : (all_of @ (^[X1 : $i] : (in @ X1 @ nat)) @ (^[X1 : $i] : ((moreis @ X0 @ X1) => (d_not @ (iii @ X0 @ X1)))))))), 420.49/60.61 inference(negated_conjecture,[],[f213])). 420.49/60.61 thf(f213,conjecture,( 420.49/60.61 (all_of @ (^[X0 : $i] : (in @ X0 @ nat)) @ (^[X0 : $i] : (all_of @ (^[X1 : $i] : (in @ X1 @ nat)) @ (^[X1 : $i] : ((moreis @ X0 @ X1) => (d_not @ (iii @ X0 @ X1)))))))), 420.49/60.61 file('/export/starexec/sandbox/tmp/tmp.2i9OyGfWTf/E---3.1_15619.p',satz10c)). 420.49/60.61 thf(f16813,plain,( 420.49/60.61 spl0_897), 420.49/60.61 inference(avatar_contradiction_clause,[],[f16812])). 420.49/60.61 thf(f16812,plain,( 420.49/60.61 $false | spl0_897), 420.49/60.61 inference(trivial_inequality_removal,[],[f16811])). 420.49/60.61 thf(f16811,plain,( 420.49/60.61 ((all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0))))) != (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0)))))) | spl0_897), 420.49/60.61 inference(boolean_simplification,[],[f16810])). 420.49/60.61 thf(f16810,plain,( 420.49/60.61 ((all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0))))) != (~ (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0)))))))) | spl0_897), 420.49/60.61 inference(boolean_simplification,[],[f16809])). 420.49/60.61 thf(f16809,plain,( 420.49/60.61 ((~ ((all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0))))) => (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0)))))))) != (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0)))))) | spl0_897), 420.49/60.61 inference(boolean_simplification,[],[f16808])). 420.49/60.61 thf(f16808,plain,( 420.49/60.61 ((~ ((all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0))))) => ((all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0))))) => (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0))))))))) != (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0)))))) | spl0_897), 420.49/60.61 inference(boolean_simplification,[],[f16807])). 420.49/60.61 thf(f16807,plain,( 420.49/60.61 ((~ ((all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0))))) => (((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0)))))) => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0)))))) => (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0))))))))) != (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0)))))) | spl0_897), 420.49/60.61 inference(boolean_simplification,[],[f16806])). 420.49/60.61 thf(f16806,plain,( 420.49/60.61 ((~ ((all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0))))) => (((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0)))))) => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0)))))) => (~ (~ (~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0))))))))))) != (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0)))))) | spl0_897), 420.49/60.61 inference(boolean_simplification,[],[f16805])). 420.49/60.61 thf(f16805,plain,( 420.49/60.61 ((~ ((all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0))))) => (((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0)))))) => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0)))))) => (~ ((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0)))))) => $false))))) != (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0)))))) | spl0_897), 420.49/60.61 inference(boolean_simplification,[],[f16804])). 420.49/60.61 thf(f16804,plain,( 420.49/60.61 ((all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0))))) != (~ ((all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0))))) => (((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0)))))) => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0)))))) => (~ ((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0)))))) => (~ $true))))))) | spl0_897), 420.49/60.61 inference(boolean_simplification,[],[f16803])). 420.49/60.61 thf(f16803,plain,( 420.49/60.61 ((~ (($true => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0)))))) => (((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0)))))) => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0)))))) => (~ ((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0)))))) => (~ $true)))))) != ($true => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0))))))) | spl0_897), 420.49/60.61 inference(boolean_simplification,[],[f16802])). 420.49/60.61 thf(f16802,plain,( 420.49/60.61 ((~ (($true => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0)))))) => (((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0)))))) => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0)))))) => (~ ((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0)))))) => (~ $true)))))) != (((all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0))))) => $true) => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0))))))) | spl0_897), 420.49/60.61 inference(boolean_simplification,[],[f16801])). 420.49/60.61 thf(f16801,plain,( 420.49/60.61 ((~ (((sK38 = sK38) => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0)))))) => (((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0)))))) => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0)))))) => (~ ((~ (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0)))))) => (~ (sK38 = sK38))))))) != (((all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0))))) => (sK38 = sK38)) => (all_of @ (^[Y0 : $i]: (in @ Y0 @ (eps @ (^[Y1 : $i]: (((?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2))))) & ((repl @ (eps @ (^[Y2 : $i]: (((?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3)))) & ((repl @ (univof @ emptyset) @ (^[Y3 : $i]: (eps @ (^[Y4 : $i]: (((nat_p @ Y3) & (Y3 = Y4)) | ((~ (nat_p @ Y3)) & ((eps @ (^[Y5 : $i]: ((nat_p @ Y5) & (in @ Y5 @ (univof @ emptyset))))) = Y4))))))) = Y2)) | ((~ (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (univof @ emptyset)) & (nat_p @ Y3))))) & (emptyset = Y2))))) @ (^[Y2 : $i]: (eps @ (^[Y3 : $i]: (((~ (emptyset = Y2)) & (Y2 = Y3)) | ((emptyset = Y2) & ((eps @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ (eps @ (^[Y5 : $i]: (((?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6)))) & ((repl @ (univof @ emptyset) @ (^[Y6 : $i]: (eps @ (^[Y7 : $i]: (((nat_p @ Y6) & (Y6 = Y7)) | ((~ (nat_p @ Y6)) & ((eps @ (^[Y8 : $i]: ((nat_p @ Y8) & (in @ Y8 @ (univof @ emptyset))))) = Y7))))))) = Y5)) | ((~ (?? @ $i @ (^[Y6 : $i]: ((in @ Y6 @ (univof @ emptyset)) & (nat_p @ Y6))))) & (emptyset = Y5))))))))) = Y3))))))) = Y1)) | ((~ (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (eps @ (^[Y3 : $i]: (((?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4)))) & ((repl @ (univof @ emptyset) @ (^[Y4 : $i]: (eps @ (^[Y5 : $i]: (((nat_p @ Y4) & (Y4 = Y5)) | ((~ (nat_p @ Y4)) & ((eps @ (^[Y6 : $i]: ((nat_p @ Y6) & (in @ Y6 @ (univof @ emptyset))))) = Y5))))))) = Y3)) | ((~ (?? @ $i @ (^[Y4 : $i]: ((in @ Y4 @ (univof @ emptyset)) & (nat_p @ Y4))))) & (emptyset = Y3)))))) & (~ (emptyset = Y2)))))) & (emptyset = Y1))))))) @ (^[Y0 : $i]: (~ (sK38 = (n_pl @ sK38 @ Y0))))))) | spl0_897), 420.49/60.61 inference(superposition,[],[f8624,f16634])). 420.49/60.61 thf(f16634,plain,( 420.49/60.61 (sK38 = sK39) | spl0_897), 420.49/60.61 inference(equality_proxy_clausification,[],[f9256])). 420.49/60.61 thf(f9256,plain,( 420.49/60.61 ((sK38 = sK39) != $false) | spl0_897), 420.49/60.61 inference(avatar_component_clause,[],[f9254])). 420.49/60.61 % SZS output end Proof for E---3.1_15619 420.49/60.61 % (16381)------------------------------ 420.49/60.61 % (16381)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 420.49/60.61 % (16381)Termination reason: Refutation 420.49/60.61 420.49/60.61 % (16381)Memory used [KB]: 18677 420.49/60.61 % (16381)Time elapsed: 10.099 s 420.49/60.61 % (16381)Instructions burned: 40137 (million) 420.49/60.61 % (16381)------------------------------ 420.49/60.61 % (16381)------------------------------ 420.49/60.61 % (15728)Success in time 60.186 s 420.49/60.61 EOF