0.05/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.05/0.11 % Command : run_vampire %s %d THM 0.09/0.32 % Computer : n021.cluster.edu 0.09/0.32 % Model : x86_64 x86_64 0.09/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.09/0.32 % Memory : 8042.1875MB 0.09/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.09/0.32 % CPULimit : 1920 0.09/0.32 % WCLimit : 240 0.09/0.32 % DateTime : Wed Jul 30 08:56:34 EDT 2025 0.09/0.32 % CPUTime : 0.09/0.33 This is a THF_ problem 0.09/0.33 Running higher-order theorem proving 0.17/0.41 Running /export/starexec/sandbox2/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/tmp/tmp.Wx2OXKe4bp/E---3.1_26322.p -m 16384 -t 240 0.25/0.47 % (26435)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on E---3.1_26322 for (2399ds/18Mi) 0.25/0.47 % (26434)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_26322 for (2399ds/275Mi) 0.25/0.48 % (26433)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_26322 for (2399ds/2Mi) 0.25/0.48 % (26433)Instruction limit reached! 0.25/0.48 % (26433)------------------------------ 0.25/0.48 % (26433)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.25/0.48 % (26433)Termination reason: Unknown 0.25/0.48 % (26433)Termination phase: shuffling 0.25/0.48 0.25/0.48 % (26433)Memory used [KB]: 1663 0.25/0.48 % (26433)Time elapsed: 0.003 s 0.25/0.48 % (26433)Instructions burned: 2 (million) 0.25/0.48 % (26433)------------------------------ 0.25/0.48 % (26433)------------------------------ 0.25/0.48 % (26435)Instruction limit reached! 0.25/0.48 % (26435)------------------------------ 0.25/0.48 % (26435)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.25/0.48 % (26435)Termination reason: Unknown 0.25/0.48 % (26435)Termination phase: shuffling 0.25/0.48 0.25/0.48 % (26435)Memory used [KB]: 1918 0.25/0.48 % (26435)Time elapsed: 0.011 s 0.25/0.48 % (26435)Instructions burned: 19 (million) 0.25/0.48 % (26435)------------------------------ 0.25/0.48 % (26435)------------------------------ 0.25/0.49 % (26432)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on E---3.1_26322 for (2399ds/2Mi) 0.25/0.49 % (26431)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_26322 for (2399ds/27Mi) 0.25/0.49 % (26432)Instruction limit reached! 0.25/0.49 % (26432)------------------------------ 0.25/0.49 % (26432)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.25/0.49 % (26432)Termination reason: Unknown 0.25/0.49 % (26432)Termination phase: shuffling 0.25/0.49 0.25/0.49 % (26432)Memory used [KB]: 1663 0.25/0.49 % (26432)Time elapsed: 0.004 s 0.25/0.49 % (26432)Instructions burned: 3 (million) 0.25/0.49 % (26432)------------------------------ 0.25/0.49 % (26432)------------------------------ 0.25/0.49 % (26430)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_26322 for (2399ds/4Mi) 0.25/0.49 % (26430)Instruction limit reached! 0.25/0.49 % (26430)------------------------------ 0.25/0.49 % (26430)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.25/0.49 % (26430)Termination reason: Unknown 0.25/0.49 % (26430)Termination phase: shuffling 0.25/0.49 0.25/0.49 % (26430)Memory used [KB]: 1791 0.25/0.49 % (26430)Time elapsed: 0.006 s 0.25/0.49 % (26430)Instructions burned: 5 (million) 0.25/0.49 % (26430)------------------------------ 0.25/0.49 % (26430)------------------------------ 0.25/0.50 % (26429)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on E---3.1_26322 for (2399ds/183Mi) 0.25/0.50 % (26437)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_26322 for (2399ds/37Mi) 0.25/0.52 % (26437)Instruction limit reached! 0.25/0.52 % (26437)------------------------------ 0.25/0.52 % (26437)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.25/0.52 % (26436)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_26322 for (2399ds/3Mi) 0.25/0.52 % (26437)Termination reason: Unknown 0.25/0.52 % (26437)Termination phase: shuffling 0.25/0.52 0.25/0.52 % (26437)Memory used [KB]: 2430 0.25/0.52 % (26437)Time elapsed: 0.019 s 0.25/0.52 % (26437)Instructions burned: 37 (million) 0.25/0.52 % (26437)------------------------------ 0.25/0.52 % (26437)------------------------------ 0.25/0.52 % (26431)Instruction limit reached! 0.25/0.52 % (26431)------------------------------ 0.25/0.52 % (26431)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.25/0.52 % (26431)Termination reason: Unknown 0.25/0.52 % (26431)Termination phase: shuffling 0.25/0.52 0.25/0.52 % (26431)Memory used [KB]: 2174 0.25/0.52 % (26431)Time elapsed: 0.017 s 0.25/0.52 % (26431)Instructions burned: 28 (million) 0.25/0.52 % (26431)------------------------------ 0.25/0.52 % (26431)------------------------------ 0.25/0.52 % (26436)Instruction limit reached! 0.25/0.52 % (26436)------------------------------ 0.25/0.52 % (26436)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.25/0.52 % (26436)Termination reason: Unknown 0.25/0.52 % (26436)Termination phase: shuffling 0.25/0.52 0.25/0.52 % (26436)Memory used [KB]: 1663 0.25/0.52 % (26436)Time elapsed: 0.004 s 0.25/0.52 % (26436)Instructions burned: 3 (million) 0.25/0.52 % (26436)------------------------------ 0.25/0.52 % (26436)------------------------------ 0.25/0.52 % (26438)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_26322 for (2399ds/15Mi) 0.25/0.53 % (26434)Refutation not found, incomplete strategy 0.25/0.53 % (26434)------------------------------ 0.25/0.53 % (26434)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.25/0.53 % (26434)Termination reason: Refutation not found, incomplete strategy 0.25/0.53 0.25/0.53 0.25/0.53 % (26434)Memory used [KB]: 7164 0.25/0.53 % (26434)Time elapsed: 0.056 s 0.25/0.53 % (26434)Instructions burned: 114 (million) 0.25/0.53 % (26434)------------------------------ 0.25/0.53 % (26434)------------------------------ 0.25/0.53 % (26438)Instruction limit reached! 0.25/0.53 % (26438)------------------------------ 0.25/0.53 % (26438)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.25/0.53 % (26438)Termination reason: Unknown 0.25/0.53 % (26438)Termination phase: shuffling 0.25/0.53 0.25/0.53 % (26438)Memory used [KB]: 1918 0.25/0.53 % (26438)Time elapsed: 0.010 s 0.25/0.53 % (26438)Instructions burned: 15 (million) 0.25/0.53 % (26438)------------------------------ 0.25/0.53 % (26438)------------------------------ 0.25/0.53 % (26441)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on E---3.1_26322 for (2399ds/7Mi) 0.25/0.53 % (26442)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on E---3.1_26322 for (2399ds/16Mi) 0.25/0.53 % (26439)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_26322 for (2399ds/3Mi) 0.25/0.54 % (26439)Instruction limit reached! 0.25/0.54 % (26439)------------------------------ 0.25/0.54 % (26439)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.25/0.54 % (26439)Termination reason: Unknown 0.25/0.54 % (26439)Termination phase: shuffling 0.25/0.54 0.25/0.54 % (26439)Memory used [KB]: 1791 0.25/0.54 % (26439)Time elapsed: 0.004 s 0.25/0.54 % (26439)Instructions burned: 4 (million) 0.25/0.54 % (26439)------------------------------ 0.25/0.54 % (26439)------------------------------ 0.25/0.54 % (26441)Instruction limit reached! 0.25/0.54 % (26441)------------------------------ 0.25/0.54 % (26441)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.25/0.54 % (26441)Termination reason: Unknown 0.25/0.54 % (26441)Termination phase: shuffling 0.25/0.54 0.25/0.54 % (26441)Memory used [KB]: 1791 0.25/0.54 % (26441)Time elapsed: 0.006 s 0.25/0.54 % (26441)Instructions burned: 8 (million) 0.25/0.54 % (26441)------------------------------ 0.25/0.54 % (26441)------------------------------ 0.25/0.54 % (26442)Instruction limit reached! 0.25/0.54 % (26442)------------------------------ 0.25/0.54 % (26442)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.25/0.54 % (26442)Termination reason: Unknown 0.25/0.54 % (26442)Termination phase: shuffling 0.25/0.54 0.25/0.54 % (26442)Memory used [KB]: 1918 0.25/0.54 % (26442)Time elapsed: 0.011 s 0.25/0.54 % (26442)Instructions burned: 17 (million) 0.25/0.54 % (26442)------------------------------ 0.25/0.54 % (26442)------------------------------ 0.62/0.54 % (26443)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_26322 for (2398ds/3Mi) 0.62/0.55 % (26443)Instruction limit reached! 0.62/0.55 % (26443)------------------------------ 0.62/0.55 % (26443)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.62/0.55 % (26443)Termination reason: Unknown 0.62/0.55 % (26443)Termination phase: shuffling 0.62/0.55 0.62/0.55 % (26443)Memory used [KB]: 1663 0.62/0.55 % (26443)Time elapsed: 0.003 s 0.62/0.55 % (26443)Instructions burned: 3 (million) 0.62/0.55 % (26443)------------------------------ 0.62/0.55 % (26443)------------------------------ 0.62/0.55 % (26445)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_26322 for (2398ds/7Mi) 0.62/0.55 % (26444)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_26322 for (2398ds/3Mi) 0.62/0.55 % (26444)Instruction limit reached! 0.62/0.55 % (26444)------------------------------ 0.62/0.55 % (26444)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.62/0.55 % (26444)Termination reason: Unknown 0.62/0.55 % (26444)Termination phase: shuffling 0.62/0.55 0.62/0.55 % (26444)Memory used [KB]: 1663 0.62/0.55 % (26444)Time elapsed: 0.003 s 0.62/0.55 % (26444)Instructions burned: 3 (million) 0.62/0.55 % (26444)------------------------------ 0.62/0.55 % (26444)------------------------------ 0.62/0.56 % (26445)Instruction limit reached! 0.62/0.56 % (26445)------------------------------ 0.62/0.56 % (26445)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.62/0.56 % (26445)Termination reason: Unknown 0.62/0.56 % (26445)Termination phase: shuffling 0.62/0.56 0.62/0.56 % (26445)Memory used [KB]: 1791 0.62/0.56 % (26445)Time elapsed: 0.007 s 0.62/0.56 % (26445)Instructions burned: 9 (million) 0.62/0.56 % (26445)------------------------------ 0.62/0.56 % (26445)------------------------------ 0.62/0.56 % (26447)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on E---3.1_26322 for (2398ds/4Mi) 0.62/0.56 % (26447)Instruction limit reached! 0.62/0.56 % (26447)------------------------------ 0.62/0.56 % (26447)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.62/0.56 % (26447)Termination reason: Unknown 0.62/0.56 % (26447)Termination phase: shuffling 0.62/0.56 0.62/0.56 % (26447)Memory used [KB]: 1791 0.62/0.56 % (26447)Time elapsed: 0.004 s 0.62/0.56 % (26447)Instructions burned: 4 (million) 0.62/0.56 % (26447)------------------------------ 0.62/0.56 % (26447)------------------------------ 0.66/0.56 % (26448)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_26322 for (2398ds/18Mi) 0.66/0.57 % (26446)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_26322 for (2398ds/3Mi) 0.66/0.57 % (26446)Instruction limit reached! 0.66/0.57 % (26446)------------------------------ 0.66/0.57 % (26446)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.66/0.57 % (26446)Termination reason: Unknown 0.66/0.57 % (26446)Termination phase: shuffling 0.66/0.57 0.66/0.57 % (26446)Memory used [KB]: 1663 0.66/0.57 % (26446)Time elapsed: 0.003 s 0.66/0.57 % (26446)Instructions burned: 3 (million) 0.66/0.57 % (26446)------------------------------ 0.66/0.57 % (26446)------------------------------ 0.66/0.57 % (26449)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on E---3.1_26322 for (2398ds/710Mi) 0.66/0.57 % (26448)Instruction limit reached! 0.66/0.57 % (26448)------------------------------ 0.66/0.57 % (26448)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.66/0.57 % (26448)Termination reason: Unknown 0.66/0.57 % (26448)Termination phase: shuffling 0.66/0.57 0.66/0.57 % (26448)Memory used [KB]: 1918 0.66/0.57 % (26448)Time elapsed: 0.012 s 0.66/0.57 % (26448)Instructions burned: 19 (million) 0.66/0.57 % (26448)------------------------------ 0.66/0.57 % (26448)------------------------------ 0.66/0.58 % (26450)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on E---3.1_26322 for (2398ds/6Mi) 0.66/0.58 % (26450)Instruction limit reached! 0.66/0.58 % (26450)------------------------------ 0.66/0.58 % (26450)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.66/0.58 % (26450)Termination reason: Unknown 0.66/0.58 % (26450)Termination phase: shuffling 0.66/0.58 0.66/0.58 % (26450)Memory used [KB]: 1791 0.66/0.58 % (26450)Time elapsed: 0.005 s 0.66/0.58 % (26450)Instructions burned: 6 (million) 0.66/0.58 % (26450)------------------------------ 0.66/0.58 % (26450)------------------------------ 0.66/0.58 % (26440)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_26322 for (2399ds/1041Mi) 0.66/0.59 % (26452)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_26322 for (2398ds/21Mi) 0.66/0.60 % (26454)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_26322 for (2398ds/6Mi) 0.66/0.60 % (26451)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_26322 for (2398ds/902Mi) 0.66/0.60 % (26454)Instruction limit reached! 0.66/0.60 % (26454)------------------------------ 0.66/0.60 % (26454)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.66/0.60 % (26454)Termination reason: Unknown 0.66/0.60 % (26454)Termination phase: shuffling 0.66/0.60 0.66/0.60 % (26454)Memory used [KB]: 1791 0.66/0.60 % (26454)Time elapsed: 0.006 s 0.66/0.60 % (26454)Instructions burned: 6 (million) 0.66/0.60 % (26454)------------------------------ 0.66/0.60 % (26454)------------------------------ 0.66/0.61 % (26452)Instruction limit reached! 0.66/0.61 % (26452)------------------------------ 0.66/0.61 % (26452)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.66/0.61 % (26452)Termination reason: Unknown 0.66/0.61 % (26452)Termination phase: shuffling 0.66/0.61 0.66/0.61 % (26452)Memory used [KB]: 2046 0.66/0.61 % (26452)Time elapsed: 0.013 s 0.66/0.61 % (26452)Instructions burned: 22 (million) 0.66/0.61 % (26452)------------------------------ 0.66/0.61 % (26452)------------------------------ 0.66/0.61 % (26453)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on E---3.1_26322 for (2398ds/5Mi) 0.66/0.61 % (26453)Instruction limit reached! 0.66/0.61 % (26453)------------------------------ 0.66/0.61 % (26453)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.66/0.61 % (26453)Termination reason: Unknown 0.66/0.61 % (26453)Termination phase: shuffling 0.66/0.61 0.66/0.61 % (26453)Memory used [KB]: 1791 0.66/0.61 % (26453)Time elapsed: 0.006 s 0.66/0.61 % (26453)Instructions burned: 6 (million) 0.66/0.61 % (26453)------------------------------ 0.66/0.61 % (26453)------------------------------ 0.66/0.63 % (26457)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_26322 for (2397ds/19Mi) 0.89/0.64 % (26455)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on E---3.1_26322 for (2398ds/377Mi) 0.89/0.64 % (26457)Instruction limit reached! 0.89/0.64 % (26457)------------------------------ 0.89/0.64 % (26457)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.89/0.64 % (26457)Termination reason: Unknown 0.89/0.64 % (26457)Termination phase: shuffling 0.89/0.64 0.89/0.64 % (26457)Memory used [KB]: 2046 0.89/0.64 % (26457)Time elapsed: 0.013 s 0.89/0.64 % (26457)Instructions burned: 20 (million) 0.89/0.64 % (26457)------------------------------ 0.89/0.64 % (26457)------------------------------ 0.89/0.65 % (26456)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_26322 for (2398ds/779Mi) 0.89/0.66 % (26458)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_26322 for (2397ds/879Mi) 0.95/0.69 % (26429)Instruction limit reached! 0.95/0.69 % (26429)------------------------------ 0.95/0.69 % (26429)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.95/0.69 % (26429)Termination reason: Unknown 0.95/0.69 % (26429)Termination phase: Function definition elimination 0.95/0.69 0.95/0.69 % (26429)Memory used [KB]: 2814 0.95/0.69 % (26429)Time elapsed: 0.107 s 0.95/0.69 % (26429)Instructions burned: 184 (million) 0.95/0.69 % (26429)------------------------------ 0.95/0.69 % (26429)------------------------------ 0.95/0.71 % (26451)Refutation not found, incomplete strategy 0.95/0.71 % (26451)------------------------------ 0.95/0.71 % (26451)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.95/0.71 % (26451)Termination reason: Refutation not found, incomplete strategy 0.95/0.71 0.95/0.71 0.95/0.71 % (26451)Memory used [KB]: 7547 0.95/0.71 % (26451)Time elapsed: 0.137 s 0.95/0.71 % (26451)Instructions burned: 215 (million) 0.95/0.71 % (26451)------------------------------ 0.95/0.71 % (26451)------------------------------ 1.13/0.74 % (26458)Refutation not found, incomplete strategy 1.13/0.74 % (26458)------------------------------ 1.13/0.74 % (26458)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.13/0.74 % (26458)Termination reason: Refutation not found, incomplete strategy 1.13/0.74 1.13/0.74 1.13/0.74 % (26458)Memory used [KB]: 7291 1.13/0.74 % (26458)Time elapsed: 0.084 s 1.13/0.74 % (26458)Instructions burned: 168 (million) 1.13/0.74 % (26458)------------------------------ 1.13/0.74 % (26458)------------------------------ 1.13/0.75 % (26459)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on E---3.1_26322 for (2397ds/17Mi) 1.25/0.75 % (26462)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on E---3.1_26322 for (2396ds/30Mi) 1.25/0.77 % (26459)Instruction limit reached! 1.25/0.77 % (26459)------------------------------ 1.25/0.77 % (26459)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.25/0.77 % (26459)Termination reason: Unknown 1.25/0.77 % (26459)Termination phase: shuffling 1.25/0.77 1.25/0.77 % (26459)Memory used [KB]: 1918 1.25/0.77 % (26459)Time elapsed: 0.012 s 1.25/0.77 % (26459)Instructions burned: 18 (million) 1.25/0.77 % (26459)------------------------------ 1.25/0.77 % (26459)------------------------------ 1.25/0.77 % (26462)Instruction limit reached! 1.25/0.77 % (26462)------------------------------ 1.25/0.77 % (26462)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.25/0.77 % (26462)Termination reason: Unknown 1.25/0.77 % (26462)Termination phase: shuffling 1.25/0.77 1.25/0.77 % (26462)Memory used [KB]: 2174 1.25/0.77 % (26462)Time elapsed: 0.018 s 1.25/0.77 % (26462)Instructions burned: 30 (million) 1.25/0.77 % (26462)------------------------------ 1.25/0.77 % (26462)------------------------------ 1.25/0.78 % (26461)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on E---3.1_26322 for (2397ds/3Mi) 1.25/0.78 % (26461)Instruction limit reached! 1.25/0.78 % (26461)------------------------------ 1.25/0.78 % (26461)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.25/0.78 % (26461)Termination reason: Unknown 1.25/0.78 % (26461)Termination phase: shuffling 1.25/0.78 1.25/0.78 % (26461)Memory used [KB]: 1791 1.25/0.78 % (26461)Time elapsed: 0.004 s 1.25/0.78 % (26461)Instructions burned: 4 (million) 1.25/0.78 % (26461)------------------------------ 1.25/0.78 % (26461)------------------------------ 1.25/0.79 % (26464)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_26322 for (2396ds/100Mi) 1.25/0.81 % (26463)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_26322 for (2396ds/127Mi) 1.36/0.83 % (26464)Instruction limit reached! 1.36/0.83 % (26464)------------------------------ 1.36/0.83 % (26464)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.36/0.83 % (26464)Termination reason: Unknown 1.36/0.83 % (26464)Termination phase: Property scanning 1.36/0.83 1.36/0.83 % (26464)Memory used [KB]: 2686 1.36/0.83 % (26464)Time elapsed: 0.051 s 1.36/0.83 % (26464)Instructions burned: 101 (million) 1.36/0.83 % (26464)------------------------------ 1.36/0.83 % (26464)------------------------------ 1.36/0.85 % (26465)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_26322 for (2396ds/3Mi) 1.36/0.85 % (26465)Instruction limit reached! 1.36/0.85 % (26465)------------------------------ 1.36/0.85 % (26465)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.36/0.85 % (26465)Termination reason: Unknown 1.36/0.85 % (26465)Termination phase: shuffling 1.36/0.85 1.36/0.85 % (26465)Memory used [KB]: 1791 1.36/0.85 % (26465)Time elapsed: 0.004 s 1.36/0.85 % (26465)Instructions burned: 3 (million) 1.36/0.85 % (26465)------------------------------ 1.36/0.85 % (26465)------------------------------ 1.36/0.85 % (26466)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_26322 for (2395ds/20Mi) 1.47/0.86 % (26466)Instruction limit reached! 1.47/0.86 % (26466)------------------------------ 1.47/0.86 % (26466)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.47/0.86 % (26466)Termination reason: Unknown 1.47/0.86 % (26466)Termination phase: shuffling 1.47/0.86 1.47/0.86 % (26466)Memory used [KB]: 2046 1.47/0.86 % (26466)Time elapsed: 0.012 s 1.47/0.86 % (26466)Instructions burned: 21 (million) 1.47/0.86 % (26466)------------------------------ 1.47/0.86 % (26466)------------------------------ 1.47/0.88 % (26468)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_26322 for (2395ds/107Mi) 1.47/0.92 % (26467)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_26322 for (2395ds/86Mi) 1.47/0.92 % (26449)Instruction limit reached! 1.47/0.92 % (26449)------------------------------ 1.47/0.92 % (26449)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.47/0.92 % (26449)Termination reason: Unknown 1.47/0.92 % (26449)Termination phase: Saturation 1.47/0.92 1.47/0.92 % (26449)Memory used [KB]: 8827 1.47/0.92 % (26449)Time elapsed: 0.355 s 1.47/0.92 % (26449)Instructions burned: 710 (million) 1.47/0.92 % (26449)------------------------------ 1.47/0.92 % (26449)------------------------------ 1.47/0.93 % (26468)Instruction limit reached! 1.47/0.93 % (26468)------------------------------ 1.47/0.93 % (26468)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.47/0.93 % (26468)Termination reason: Unknown 1.47/0.93 % (26468)Termination phase: SInE selection 1.47/0.93 1.47/0.93 % (26468)Memory used [KB]: 2558 1.47/0.93 % (26468)Time elapsed: 0.055 s 1.47/0.93 % (26468)Instructions burned: 107 (million) 1.47/0.93 % (26468)------------------------------ 1.47/0.93 % (26468)------------------------------ 1.97/0.94 % (26463)Instruction limit reached! 1.97/0.94 % (26463)------------------------------ 1.97/0.94 % (26463)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.97/0.94 % (26463)Termination reason: Unknown 1.97/0.94 % (26463)Termination phase: Property scanning 1.97/0.94 1.97/0.94 % (26463)Memory used [KB]: 2686 1.97/0.94 % (26463)Time elapsed: 0.069 s 1.97/0.94 % (26463)Instructions burned: 129 (million) 1.97/0.94 % (26463)------------------------------ 1.97/0.94 % (26463)------------------------------ 1.97/0.95 % (26469)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_26322 for (2394ds/39Mi) 1.97/0.95 % (26470)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_26322 for (2394ds/448Mi) 1.97/0.96 % (26455)Instruction limit reached! 1.97/0.96 % (26455)------------------------------ 1.97/0.96 % (26455)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.97/0.96 % (26455)Termination reason: Unknown 1.97/0.96 % (26455)Termination phase: Function definition elimination 1.97/0.96 1.97/0.96 % (26455)Memory used [KB]: 2814 1.97/0.96 % (26455)Time elapsed: 0.150 s 1.97/0.96 % (26455)Instructions burned: 377 (million) 1.97/0.96 % (26455)------------------------------ 1.97/0.96 % (26455)------------------------------ 1.97/0.97 % (26469)Instruction limit reached! 1.97/0.97 % (26469)------------------------------ 1.97/0.97 % (26469)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.97/0.97 % (26469)Termination reason: Unknown 1.97/0.97 % (26469)Termination phase: shuffling 1.97/0.97 1.97/0.97 % (26469)Memory used [KB]: 2430 1.97/0.97 % (26469)Time elapsed: 0.022 s 1.97/0.97 % (26469)Instructions burned: 40 (million) 1.97/0.97 % (26469)------------------------------ 1.97/0.97 % (26469)------------------------------ 2.26/0.98 % (26471)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_26322 for (2394ds/46Mi) 2.26/0.99 % (26473)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_26322 for (2394ds/507Mi) 2.26/1.01 % (26472)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_26322 for (2394ds/98Mi) 2.26/1.03 % (26471)Instruction limit reached! 2.26/1.03 % (26471)------------------------------ 2.26/1.03 % (26471)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 2.26/1.03 % (26471)Termination reason: Unknown 2.26/1.03 % (26471)Termination phase: shuffling 2.26/1.03 2.26/1.03 % (26471)Memory used [KB]: 2430 2.26/1.03 % (26471)Time elapsed: 0.029 s 2.26/1.03 % (26471)Instructions burned: 47 (million) 2.26/1.03 % (26471)------------------------------ 2.26/1.03 % (26471)------------------------------ 2.33/1.05 % (26467)Instruction limit reached! 2.33/1.05 % (26467)------------------------------ 2.33/1.05 % (26467)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 2.33/1.05 % (26467)Termination reason: Unknown 2.33/1.05 % (26467)Termination phase: Property scanning 2.33/1.05 2.33/1.05 % (26467)Memory used [KB]: 2558 2.33/1.05 % (26467)Time elapsed: 0.048 s 2.33/1.05 % (26467)Instructions burned: 86 (million) 2.33/1.05 % (26467)------------------------------ 2.33/1.05 % (26467)------------------------------ 2.85/1.09 % (26474)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_26322 for (2393ds/149Mi) 2.85/1.10 % (26475)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on E---3.1_26322 for (2393ds/39Mi) 2.85/1.14 % (26472)Instruction limit reached! 2.85/1.14 % (26472)------------------------------ 2.85/1.14 % (26472)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 2.85/1.14 % (26472)Termination reason: Unknown 2.85/1.14 % (26472)Termination phase: Property scanning 2.85/1.14 2.85/1.14 % (26472)Memory used [KB]: 2686 2.85/1.14 % (26472)Time elapsed: 0.053 s 2.85/1.14 % (26472)Instructions burned: 100 (million) 2.85/1.14 % (26472)------------------------------ 2.85/1.14 % (26472)------------------------------ 3.12/1.15 % (26475)Instruction limit reached! 3.12/1.15 % (26475)------------------------------ 3.12/1.15 % (26475)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.12/1.15 % (26475)Termination reason: Unknown 3.12/1.15 % (26475)Termination phase: shuffling 3.12/1.15 3.12/1.15 % (26475)Memory used [KB]: 2302 3.12/1.15 % (26475)Time elapsed: 0.024 s 3.12/1.15 % (26475)Instructions burned: 40 (million) 3.12/1.15 % (26475)------------------------------ 3.12/1.15 % (26475)------------------------------ 3.12/1.17 % (26470)Instruction limit reached! 3.12/1.17 % (26470)------------------------------ 3.12/1.17 % (26470)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.12/1.17 % (26470)Termination reason: Unknown 3.12/1.17 % (26470)Termination phase: Saturation 3.12/1.17 3.12/1.17 % (26470)Memory used [KB]: 8699 3.12/1.17 % (26470)Time elapsed: 0.222 s 3.12/1.17 % (26470)Instructions burned: 449 (million) 3.12/1.17 % (26470)------------------------------ 3.12/1.17 % (26470)------------------------------ 3.12/1.18 % (26473)Instruction limit reached! 3.12/1.18 % (26473)------------------------------ 3.12/1.18 % (26473)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.12/1.18 % (26473)Termination reason: Unknown 3.12/1.18 % (26473)Termination phase: Function definition elimination 3.12/1.18 3.12/1.18 % (26473)Memory used [KB]: 2814 3.12/1.18 % (26473)Time elapsed: 0.192 s 3.12/1.18 % (26473)Instructions burned: 507 (million) 3.12/1.18 % (26473)------------------------------ 3.12/1.18 % (26473)------------------------------ 3.12/1.19 % (26478)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on E---3.1_26322 for (2392ds/47Mi) 3.12/1.19 % (26476)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_26322 for (2392ds/6Mi) 3.26/1.19 % (26479)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_26322 for (2392ds/44Mi) 3.26/1.20 % (26477)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_26322 for (2392ds/1087Mi) 3.26/1.21 % (26476)Instruction limit reached! 3.26/1.21 % (26476)------------------------------ 3.26/1.21 % (26476)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.26/1.21 % (26476)Termination reason: Unknown 3.26/1.21 % (26476)Termination phase: shuffling 3.26/1.21 3.26/1.21 % (26476)Memory used [KB]: 1791 3.26/1.21 % (26476)Time elapsed: 0.005 s 3.26/1.21 % (26476)Instructions burned: 6 (million) 3.26/1.21 % (26476)------------------------------ 3.26/1.21 % (26476)------------------------------ 3.26/1.21 % (26478)Instruction limit reached! 3.26/1.21 % (26478)------------------------------ 3.26/1.21 % (26478)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.26/1.21 % (26478)Termination reason: Unknown 3.26/1.21 % (26478)Termination phase: shuffling 3.26/1.21 3.26/1.21 % (26478)Memory used [KB]: 2430 3.26/1.21 % (26478)Time elapsed: 0.026 s 3.26/1.21 % (26478)Instructions burned: 47 (million) 3.26/1.21 % (26478)------------------------------ 3.26/1.21 % (26478)------------------------------ 3.26/1.21 % (26479)Instruction limit reached! 3.26/1.21 % (26479)------------------------------ 3.26/1.21 % (26479)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.26/1.21 % (26479)Termination reason: Unknown 3.26/1.21 % (26479)Termination phase: shuffling 3.26/1.21 3.26/1.21 % (26479)Memory used [KB]: 2430 3.26/1.21 % (26479)Time elapsed: 0.025 s 3.26/1.21 % (26479)Instructions burned: 45 (million) 3.26/1.21 % (26479)------------------------------ 3.26/1.21 % (26479)------------------------------ 3.26/1.23 % (26481)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_26322 for (2392ds/62Mi) 3.26/1.23 % (26482)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_26322 for (2392ds/31Mi) 3.26/1.23 % (26474)Instruction limit reached! 3.26/1.23 % (26474)------------------------------ 3.26/1.23 % (26474)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.26/1.23 % (26474)Termination reason: Unknown 3.26/1.23 % (26474)Termination phase: Function definition elimination 3.26/1.23 3.26/1.23 % (26474)Memory used [KB]: 2814 3.26/1.23 % (26474)Time elapsed: 0.121 s 3.26/1.23 % (26474)Instructions burned: 151 (million) 3.26/1.23 % (26474)------------------------------ 3.26/1.23 % (26474)------------------------------ 3.46/1.25 % (26482)Instruction limit reached! 3.46/1.25 % (26482)------------------------------ 3.46/1.25 % (26482)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.46/1.25 % (26482)Termination reason: Unknown 3.46/1.25 % (26482)Termination phase: shuffling 3.46/1.25 3.46/1.25 % (26482)Memory used [KB]: 2302 3.46/1.25 % (26482)Time elapsed: 0.018 s 3.46/1.25 % (26482)Instructions burned: 33 (million) 3.46/1.25 % (26482)------------------------------ 3.46/1.25 % (26482)------------------------------ 3.46/1.26 % (26480)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_26322 for (2392ds/432Mi) 3.46/1.26 % (26481)Instruction limit reached! 3.46/1.26 % (26481)------------------------------ 3.46/1.26 % (26481)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.46/1.26 % (26481)Termination reason: Unknown 3.46/1.26 % (26481)Termination phase: Property scanning 3.46/1.26 3.46/1.26 % (26481)Memory used [KB]: 2686 3.46/1.26 % (26481)Time elapsed: 0.033 s 3.46/1.26 % (26481)Instructions burned: 62 (million) 3.46/1.26 % (26481)------------------------------ 3.46/1.26 % (26481)------------------------------ 3.46/1.27 % (26485)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_26322 for (2391ds/71Mi) 3.46/1.29 % (26484)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_26322 for (2391ds/453Mi) 3.57/1.31 % (26485)Instruction limit reached! 3.57/1.31 % (26485)------------------------------ 3.57/1.31 % (26485)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.57/1.31 % (26485)Termination reason: Unknown 3.57/1.31 % (26485)Termination phase: Property scanning 3.57/1.31 3.57/1.31 % (26485)Memory used [KB]: 2558 3.57/1.31 % (26485)Time elapsed: 0.037 s 3.57/1.31 % (26485)Instructions burned: 72 (million) 3.57/1.31 % (26485)------------------------------ 3.57/1.31 % (26485)------------------------------ 3.57/1.32 % (26483)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on E---3.1_26322 for (2391ds/96Mi) 3.57/1.33 % (26486)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_26322 for (2391ds/83Mi) 3.67/1.36 % (26440)Instruction limit reached! 3.67/1.36 % (26440)------------------------------ 3.67/1.36 % (26440)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.67/1.36 % (26440)Termination reason: Unknown 3.67/1.36 % (26440)Termination phase: Function definition elimination 3.67/1.36 3.67/1.36 % (26440)Memory used [KB]: 3070 3.67/1.36 % (26440)Time elapsed: 0.504 s 3.67/1.36 % (26440)Instructions burned: 1043 (million) 3.67/1.36 % (26440)------------------------------ 3.67/1.36 % (26440)------------------------------ 3.67/1.37 % (26486)Instruction limit reached! 3.67/1.37 % (26486)------------------------------ 3.67/1.37 % (26486)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.67/1.37 % (26486)Termination reason: Unknown 3.67/1.37 % (26486)Termination phase: Property scanning 3.67/1.37 3.67/1.37 % (26486)Memory used [KB]: 2558 3.67/1.37 % (26486)Time elapsed: 0.043 s 3.67/1.37 % (26486)Instructions burned: 84 (million) 3.67/1.37 % (26486)------------------------------ 3.67/1.37 % (26486)------------------------------ 3.67/1.38 % (26487)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_26322 for (2390ds/11Mi) 3.67/1.39 % (26487)Instruction limit reached! 3.67/1.39 % (26487)------------------------------ 3.67/1.39 % (26487)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.67/1.39 % (26487)Termination reason: Unknown 3.67/1.39 % (26487)Termination phase: shuffling 3.67/1.39 3.67/1.39 % (26487)Memory used [KB]: 1918 3.67/1.39 % (26487)Time elapsed: 0.008 s 3.67/1.39 % (26487)Instructions burned: 13 (million) 3.67/1.39 % (26487)------------------------------ 3.67/1.39 % (26487)------------------------------ 3.67/1.40 % (26483)Instruction limit reached! 3.67/1.40 % (26483)------------------------------ 3.67/1.40 % (26483)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.67/1.40 % (26483)Termination reason: Unknown 3.67/1.40 % (26483)Termination phase: Property scanning 3.67/1.40 3.67/1.40 % (26483)Memory used [KB]: 2558 3.67/1.40 % (26483)Time elapsed: 0.050 s 3.67/1.40 % (26483)Instructions burned: 97 (million) 3.67/1.40 % (26483)------------------------------ 3.67/1.40 % (26483)------------------------------ 3.67/1.41 % (26489)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on E---3.1_26322 for (2390ds/6Mi) 3.67/1.41 % (26488)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_26322 for (2390ds/41Mi) 3.67/1.41 % (26489)Instruction limit reached! 3.67/1.41 % (26489)------------------------------ 3.67/1.41 % (26489)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.67/1.41 % (26489)Termination reason: Unknown 3.67/1.41 % (26489)Termination phase: shuffling 3.67/1.41 3.67/1.41 % (26489)Memory used [KB]: 1791 3.67/1.41 % (26489)Time elapsed: 0.007 s 3.67/1.41 % (26489)Instructions burned: 7 (million) 3.67/1.41 % (26489)------------------------------ 3.67/1.41 % (26489)------------------------------ 3.67/1.43 % (26491)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_26322 for (2390ds/343Mi) 3.67/1.44 % (26488)Instruction limit reached! 3.67/1.44 % (26488)------------------------------ 3.67/1.44 % (26488)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.67/1.44 % (26488)Termination reason: Unknown 3.67/1.44 % (26488)Termination phase: shuffling 3.67/1.44 3.67/1.44 % (26488)Memory used [KB]: 2430 3.67/1.44 % (26488)Time elapsed: 0.023 s 3.67/1.44 % (26488)Instructions burned: 42 (million) 3.67/1.44 % (26488)------------------------------ 3.67/1.44 % (26488)------------------------------ 3.92/1.46 % (26477)Refutation not found, incomplete strategy 3.92/1.46 % (26477)------------------------------ 3.92/1.46 % (26477)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 3.92/1.46 % (26477)Termination reason: Refutation not found, incomplete strategy 3.92/1.46 3.92/1.46 3.92/1.46 % (26477)Memory used [KB]: 7291 3.92/1.46 % (26477)Time elapsed: 0.305 s 3.92/1.46 % (26477)Instructions burned: 154 (million) 3.92/1.46 % (26477)------------------------------ 3.92/1.46 % (26477)------------------------------ 3.92/1.48 % (26490)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on E---3.1_26322 for (2390ds/150Mi) 3.92/1.49 % (26492)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_26322 for (2389ds/109Mi) 4.02/1.51 % (26493)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_26322 for (2389ds/253Mi) 4.04/1.59 % (26492)Instruction limit reached! 4.04/1.59 % (26492)------------------------------ 4.04/1.59 % (26492)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 4.04/1.59 % (26484)Instruction limit reached! 4.04/1.59 % (26484)------------------------------ 4.04/1.59 % (26484)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 4.04/1.59 % (26492)Termination reason: Unknown 4.04/1.59 % (26492)Termination phase: SInE selection 4.04/1.59 4.04/1.59 % (26492)Memory used [KB]: 2558 4.04/1.59 % (26492)Time elapsed: 0.059 s 4.04/1.59 % (26492)Instructions burned: 110 (million) 4.04/1.59 % (26492)------------------------------ 4.04/1.59 % (26492)------------------------------ 4.04/1.59 % (26484)Termination reason: Unknown 4.04/1.59 % (26484)Termination phase: Function definition elimination 4.04/1.59 4.04/1.59 % (26484)Memory used [KB]: 3070 4.04/1.59 % (26484)Time elapsed: 0.181 s 4.04/1.59 % (26484)Instructions burned: 453 (million) 4.04/1.59 % (26484)------------------------------ 4.04/1.59 % (26484)------------------------------ 4.67/1.64 % (26494)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_26322 for (2388ds/140Mi) 4.67/1.66 % (26495)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_26322 for (2388ds/614Mi) 4.83/1.68 % (26456)Instruction limit reached! 4.83/1.68 % (26456)------------------------------ 4.83/1.68 % (26456)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 4.83/1.68 % (26456)Termination reason: Unknown 4.83/1.68 % (26456)Termination phase: Saturation 4.83/1.68 4.83/1.68 % (26456)Memory used [KB]: 11257 4.83/1.68 % (26456)Time elapsed: 1.042 s 4.83/1.68 % (26456)Instructions burned: 779 (million) 4.83/1.68 % (26456)------------------------------ 4.83/1.68 % (26456)------------------------------ 4.83/1.69 % (26490)Instruction limit reached! 4.83/1.69 % (26490)------------------------------ 4.83/1.69 % (26490)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 4.83/1.69 % (26490)Termination reason: Unknown 4.83/1.69 % (26490)Termination phase: Function definition elimination 4.83/1.69 4.83/1.69 % (26490)Memory used [KB]: 2814 4.83/1.69 % (26490)Time elapsed: 0.078 s 4.83/1.69 % (26490)Instructions burned: 152 (million) 4.83/1.69 % (26490)------------------------------ 4.83/1.69 % (26490)------------------------------ 4.83/1.69 % (26491)Instruction limit reached! 4.83/1.69 % (26491)------------------------------ 4.83/1.69 % (26491)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 4.83/1.70 % (26491)Termination reason: Unknown 4.83/1.70 % (26491)Termination phase: Saturation 4.83/1.70 4.83/1.70 % (26491)Memory used [KB]: 7803 4.83/1.70 % (26491)Time elapsed: 0.166 s 4.83/1.70 % (26491)Instructions burned: 343 (million) 4.83/1.70 % (26491)------------------------------ 4.83/1.70 % (26491)------------------------------ 4.83/1.72 % (26493)Refutation not found, incomplete strategy 4.83/1.72 % (26493)------------------------------ 4.83/1.72 % (26493)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 4.83/1.72 % (26493)Termination reason: Refutation not found, incomplete strategy 4.83/1.72 4.83/1.72 4.83/1.72 % (26493)Memory used [KB]: 7675 4.83/1.72 % (26493)Time elapsed: 0.247 s 4.83/1.72 % (26493)Instructions burned: 226 (million) 4.83/1.72 % (26493)------------------------------ 4.83/1.72 % (26493)------------------------------ 4.83/1.73 % (26480)Instruction limit reached! 4.83/1.73 % (26480)------------------------------ 4.83/1.73 % (26480)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 4.83/1.73 % (26480)Termination reason: Unknown 4.83/1.73 % (26480)Termination phase: Function definition elimination 4.83/1.73 4.83/1.73 % (26480)Memory used [KB]: 3070 4.83/1.73 % (26480)Time elapsed: 0.173 s 4.83/1.73 % (26480)Instructions burned: 434 (million) 4.83/1.73 % (26480)------------------------------ 4.83/1.73 % (26480)------------------------------ 4.83/1.74 % (26499)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_26322 for (2387ds/134Mi) 4.83/1.74 % (26497)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_26322 for (2387ds/339Mi) 4.83/1.74 % (26496)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_26322 for (2387ds/202Mi) 4.83/1.77 % (26494)Refutation not found, incomplete strategy 4.83/1.77 % (26494)------------------------------ 4.83/1.77 % (26494)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 4.83/1.77 % (26494)Termination reason: Refutation not found, incomplete strategy 4.83/1.77 4.83/1.77 4.83/1.77 % (26494)Memory used [KB]: 7164 4.83/1.77 % (26494)Time elapsed: 0.153 s 4.83/1.77 % (26494)Instructions burned: 121 (million) 4.83/1.77 % (26494)------------------------------ 4.83/1.77 % (26494)------------------------------ 5.04/1.78 % (26498)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_26322 for (2387ds/283Mi) 5.04/1.78 % (26500)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on E---3.1_26322 for (2386ds/298Mi) 5.06/1.81 % (26501)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on E---3.1_26322 for (2386ds/192Mi) 5.07/1.85 % (26499)Instruction limit reached! 5.07/1.85 % (26499)------------------------------ 5.07/1.85 % (26499)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 5.07/1.86 % (26499)Termination reason: Unknown 5.07/1.86 % (26499)Termination phase: Property scanning 5.07/1.86 5.07/1.86 % (26499)Memory used [KB]: 2686 5.07/1.86 % (26499)Time elapsed: 0.068 s 5.07/1.86 % (26499)Instructions burned: 134 (million) 5.07/1.86 % (26499)------------------------------ 5.07/1.86 % (26499)------------------------------ 5.20/1.93 % (26496)Refutation not found, incomplete strategy 5.20/1.93 % (26496)------------------------------ 5.20/1.93 % (26496)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 5.20/1.93 % (26496)Termination reason: Refutation not found, incomplete strategy 5.20/1.93 5.20/1.93 5.20/1.93 % (26496)Memory used [KB]: 7164 5.20/1.93 % (26496)Time elapsed: 0.229 s 5.20/1.93 % (26496)Instructions burned: 125 (million) 5.20/1.93 % (26496)------------------------------ 5.20/1.93 % (26496)------------------------------ 5.20/1.93 % (26500)Instruction limit reached! 5.20/1.93 % (26500)------------------------------ 5.20/1.93 % (26500)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 5.20/1.94 % (26500)Termination reason: Unknown 5.20/1.94 % (26500)Termination phase: Function definition elimination 5.20/1.94 5.20/1.94 % (26500)Memory used [KB]: 3070 5.20/1.94 % (26500)Time elapsed: 0.127 s 5.20/1.94 % (26500)Instructions burned: 300 (million) 5.20/1.94 % (26500)------------------------------ 5.20/1.94 % (26500)------------------------------ 5.20/1.95 % (26502)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_26322 for (2385ds/258Mi) 5.20/1.95 % (26503)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_26322 for (2384ds/90Mi) 5.45/1.99 % (26503)Instruction limit reached! 5.45/1.99 % (26503)------------------------------ 5.45/1.99 % (26503)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 5.45/1.99 % (26501)Instruction limit reached! 5.45/1.99 % (26501)------------------------------ 5.45/1.99 % (26501)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 5.45/1.99 % (26501)Termination reason: Unknown 5.45/1.99 % (26501)Termination phase: Function definition elimination 5.45/1.99 5.45/1.99 % (26501)Memory used [KB]: 2814 5.45/1.99 % (26501)Time elapsed: 0.098 s 5.45/1.99 % (26501)Instructions burned: 192 (million) 5.45/1.99 % (26501)------------------------------ 5.45/1.99 % (26501)------------------------------ 5.45/1.99 % (26503)Termination reason: Unknown 5.45/1.99 % (26503)Termination phase: Property scanning 5.45/1.99 5.45/1.99 % (26503)Memory used [KB]: 2558 5.45/1.99 % (26503)Time elapsed: 0.043 s 5.45/1.99 % (26503)Instructions burned: 92 (million) 5.45/1.99 % (26503)------------------------------ 5.45/1.99 % (26503)------------------------------ 5.45/2.01 % (26505)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_26322 for (2384ds/458Mi) 5.45/2.04 % (26504)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_26322 for (2384ds/231Mi) 5.45/2.04 % (26506)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_26322 for (2384ds/31Mi) 5.45/2.06 % (26506)Instruction limit reached! 5.45/2.06 % (26506)------------------------------ 5.45/2.06 % (26506)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 5.45/2.06 % (26506)Termination reason: Unknown 5.45/2.06 % (26506)Termination phase: shuffling 5.45/2.06 5.45/2.06 % (26506)Memory used [KB]: 2174 5.45/2.06 % (26506)Time elapsed: 0.018 s 5.45/2.06 % (26506)Instructions burned: 31 (million) 5.45/2.06 % (26506)------------------------------ 5.45/2.06 % (26506)------------------------------ 5.45/2.07 % (26495)Instruction limit reached! 5.45/2.07 % (26495)------------------------------ 5.45/2.07 % (26495)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 5.45/2.07 % (26495)Termination reason: Unknown 5.45/2.07 % (26495)Termination phase: Function definition elimination 5.45/2.07 5.45/2.07 % (26495)Memory used [KB]: 3070 5.45/2.07 % (26495)Time elapsed: 0.243 s 5.45/2.07 % (26495)Instructions burned: 614 (million) 5.45/2.07 % (26495)------------------------------ 5.45/2.07 % (26495)------------------------------ 5.70/2.10 % (26508)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_26322 for (2383ds/987Mi) 5.70/2.10 % (26507)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_26322 for (2383ds/297Mi) 6.20/2.16 % (26498)Instruction limit reached! 6.20/2.16 % (26498)------------------------------ 6.20/2.16 % (26498)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 6.20/2.16 % (26498)Termination reason: Unknown 6.20/2.16 % (26498)Termination phase: Function definition elimination 6.20/2.16 6.20/2.17 % (26498)Memory used [KB]: 3070 6.20/2.17 % (26498)Time elapsed: 0.126 s 6.20/2.17 % (26498)Instructions burned: 284 (million) 6.20/2.17 % (26498)------------------------------ 6.20/2.17 % (26498)------------------------------ 6.20/2.20 % (26505)Instruction limit reached! 6.20/2.20 % (26505)------------------------------ 6.20/2.20 % (26505)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 6.20/2.20 % (26505)Termination reason: Unknown 6.20/2.20 % (26505)Termination phase: Function definition elimination 6.20/2.20 6.20/2.20 % (26505)Memory used [KB]: 2814 6.20/2.20 % (26505)Time elapsed: 0.177 s 6.20/2.20 % (26505)Instructions burned: 458 (million) 6.20/2.20 % (26505)------------------------------ 6.20/2.20 % (26505)------------------------------ 6.20/2.20 % (26509)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_26322 for (2382ds/182Mi) 6.20/2.21 % (26497)Instruction limit reached! 6.20/2.21 % (26497)------------------------------ 6.20/2.21 % (26497)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 6.20/2.21 % (26497)Termination reason: Unknown 6.20/2.21 % (26497)Termination phase: Function definition elimination 6.20/2.21 6.20/2.21 % (26497)Memory used [KB]: 2814 6.20/2.21 % (26497)Time elapsed: 0.149 s 6.20/2.21 % (26497)Instructions burned: 339 (million) 6.20/2.21 % (26497)------------------------------ 6.20/2.21 % (26497)------------------------------ 6.44/2.25 % (26511)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_26322 for (2382ds/154Mi) 6.44/2.26 % (26510)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_26322 for (2382ds/182Mi) 6.57/2.33 % (26504)Instruction limit reached! 6.57/2.33 % (26504)------------------------------ 6.57/2.33 % (26504)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 6.57/2.33 % (26504)Termination reason: Unknown 6.57/2.33 % (26504)Termination phase: Function definition elimination 6.57/2.33 6.57/2.33 % (26504)Memory used [KB]: 3070 6.57/2.33 % (26504)Time elapsed: 0.106 s 6.57/2.33 % (26504)Instructions burned: 232 (million) 6.57/2.33 % (26504)------------------------------ 6.57/2.33 % (26504)------------------------------ 6.57/2.34 % (26509)Instruction limit reached! 6.57/2.34 % (26509)------------------------------ 6.57/2.34 % (26509)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 6.57/2.34 % (26502)Instruction limit reached! 6.57/2.34 % (26502)------------------------------ 6.57/2.34 % (26502)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 6.57/2.34 % (26502)Termination reason: Unknown 6.57/2.34 % (26502)Termination phase: Saturation 6.57/2.34 6.57/2.34 % (26502)Memory used [KB]: 3198 6.57/2.34 % (26502)Time elapsed: 0.134 s 6.57/2.34 % (26502)Instructions burned: 258 (million) 6.57/2.34 % (26502)------------------------------ 6.57/2.34 % (26502)------------------------------ 6.57/2.35 % (26509)Termination reason: Unknown 6.57/2.35 % (26509)Termination phase: Function definition elimination 6.57/2.35 6.57/2.35 % (26509)Memory used [KB]: 2814 6.57/2.35 % (26509)Time elapsed: 0.089 s 6.57/2.35 % (26509)Instructions burned: 182 (million) 6.57/2.35 % (26509)------------------------------ 6.57/2.35 % (26509)------------------------------ 6.77/2.37 % (26511)Instruction limit reached! 6.77/2.37 % (26511)------------------------------ 6.77/2.37 % (26511)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 6.77/2.37 % (26511)Termination reason: Unknown 6.77/2.37 % (26511)Termination phase: Function definition elimination 6.77/2.37 6.77/2.37 % (26511)Memory used [KB]: 3070 6.77/2.37 % (26511)Time elapsed: 0.078 s 6.77/2.37 % (26511)Instructions burned: 155 (million) 6.77/2.37 % (26511)------------------------------ 6.77/2.37 % (26511)------------------------------ 6.77/2.38 % (26507)Instruction limit reached! 6.77/2.38 % (26507)------------------------------ 6.77/2.38 % (26507)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 6.77/2.38 % (26507)Termination reason: Unknown 6.77/2.38 % (26507)Termination phase: Saturation 6.77/2.38 6.77/2.38 % (26507)Memory used [KB]: 7931 6.77/2.38 % (26507)Time elapsed: 0.318 s 6.77/2.38 % (26507)Instructions burned: 297 (million) 6.77/2.38 % (26507)------------------------------ 6.77/2.38 % (26507)------------------------------ 6.77/2.39 % (26512)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_26322 for (2380ds/79Mi) 6.77/2.39 % (26515)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_26322 for (2380ds/922Mi) 6.77/2.42 % (26513)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_26322 for (2380ds/216Mi) 6.77/2.44 % (26516)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_26322 for (2380ds/182Mi) 6.77/2.46 % (26514)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_26322 for (2380ds/114Mi) 6.97/2.52 % (26510)Instruction limit reached! 6.97/2.52 % (26510)------------------------------ 6.97/2.52 % (26510)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 6.97/2.52 % (26510)Termination reason: Unknown 6.97/2.52 % (26510)Termination phase: Property scanning 6.97/2.52 6.97/2.52 % (26510)Memory used [KB]: 2686 6.97/2.52 % (26510)Time elapsed: 0.096 s 6.97/2.52 % (26510)Instructions burned: 183 (million) 6.97/2.52 % (26510)------------------------------ 6.97/2.52 % (26510)------------------------------ 7.07/2.53 % (26512)Instruction limit reached! 7.07/2.53 % (26512)------------------------------ 7.07/2.53 % (26512)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 7.07/2.53 % (26512)Termination reason: Unknown 7.07/2.53 % (26512)Termination phase: Property scanning 7.07/2.53 7.07/2.53 % (26512)Memory used [KB]: 2558 7.07/2.53 % (26512)Time elapsed: 0.046 s 7.07/2.53 % (26512)Instructions burned: 79 (million) 7.07/2.53 % (26512)------------------------------ 7.07/2.53 % (26512)------------------------------ 7.07/2.57 % (26517)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_26322 for (2379ds/164Mi) 7.07/2.60 % (26518)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_26322 for (2379ds/50Mi) 7.16/2.60 % (26516)Instruction limit reached! 7.16/2.60 % (26516)------------------------------ 7.16/2.60 % (26516)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 7.16/2.61 % (26514)Instruction limit reached! 7.16/2.61 % (26514)------------------------------ 7.16/2.61 % (26514)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 7.16/2.61 % (26514)Termination reason: Unknown 7.16/2.61 % (26514)Termination phase: Property scanning 7.16/2.61 7.16/2.61 % (26514)Memory used [KB]: 2686 7.16/2.61 % (26514)Time elapsed: 0.061 s 7.16/2.61 % (26514)Instructions burned: 115 (million) 7.16/2.61 % (26514)------------------------------ 7.16/2.61 % (26514)------------------------------ 7.16/2.61 % (26516)Termination reason: Unknown 7.16/2.61 % (26516)Termination phase: Function definition elimination 7.16/2.61 7.16/2.61 % (26516)Memory used [KB]: 3070 7.16/2.61 % (26516)Time elapsed: 0.092 s 7.16/2.61 % (26516)Instructions burned: 185 (million) 7.16/2.61 % (26516)------------------------------ 7.16/2.61 % (26516)------------------------------ 7.16/2.66 % (26520)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_26322 for (2378ds/1021Mi) 7.16/2.66 % (26518)Instruction limit reached! 7.16/2.66 % (26518)------------------------------ 7.16/2.66 % (26518)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 7.16/2.66 % (26518)Termination reason: Unknown 7.16/2.66 % (26518)Termination phase: shuffling 7.16/2.66 7.16/2.66 % (26518)Memory used [KB]: 2558 7.16/2.66 % (26518)Time elapsed: 0.029 s 7.16/2.66 % (26518)Instructions burned: 50 (million) 7.16/2.66 % (26518)------------------------------ 7.16/2.66 % (26518)------------------------------ 7.41/2.67 % (26519)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_26322 for (2378ds/368Mi) 7.41/2.70 % (26513)Instruction limit reached! 7.41/2.70 % (26513)------------------------------ 7.41/2.70 % (26513)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 7.41/2.70 % (26513)Termination reason: Unknown 7.41/2.70 % (26513)Termination phase: Property scanning 7.41/2.70 7.41/2.70 % (26513)Memory used [KB]: 3070 7.41/2.70 % (26513)Time elapsed: 0.109 s 7.41/2.70 % (26513)Instructions burned: 218 (million) 7.41/2.70 % (26513)------------------------------ 7.41/2.70 % (26513)------------------------------ 7.41/2.72 % (26521)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_26322 for (2377ds/267Mi) 7.41/2.73 % (26517)Instruction limit reached! 7.41/2.73 % (26517)------------------------------ 7.41/2.73 % (26517)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 7.41/2.74 % (26517)Termination reason: Unknown 7.41/2.74 % (26517)Termination phase: Function definition elimination 7.41/2.74 7.41/2.74 % (26517)Memory used [KB]: 2942 7.41/2.74 % (26517)Time elapsed: 0.091 s 7.41/2.74 % (26517)Instructions burned: 165 (million) 7.41/2.74 % (26517)------------------------------ 7.41/2.74 % (26517)------------------------------ 7.41/2.76 % (26522)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_26322 for (2377ds/204Mi) 7.41/2.76 % (26508)Instruction limit reached! 7.41/2.76 % (26508)------------------------------ 7.41/2.76 % (26508)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 7.41/2.76 % (26508)Termination reason: Unknown 7.41/2.76 % (26508)Termination phase: Function definition elimination 7.41/2.76 7.41/2.77 % (26508)Memory used [KB]: 3070 7.41/2.77 % (26508)Time elapsed: 0.359 s 7.41/2.77 % (26508)Instructions burned: 989 (million) 7.41/2.77 % (26508)------------------------------ 7.41/2.77 % (26508)------------------------------ 7.68/2.80 % (26515)Instruction limit reached! 7.68/2.80 % (26515)------------------------------ 7.68/2.80 % (26515)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 7.68/2.80 % (26515)Termination reason: Unknown 7.68/2.80 % (26515)Termination phase: Function definition elimination 7.68/2.80 7.68/2.80 % (26515)Memory used [KB]: 2814 7.68/2.80 % (26515)Time elapsed: 0.321 s 7.68/2.80 % (26515)Instructions burned: 922 (million) 7.68/2.80 % (26515)------------------------------ 7.68/2.80 % (26515)------------------------------ 8.21/2.82 % (26525)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_26322 for (2376ds/4436Mi) 8.21/2.82 % (26524)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_26322 for (2376ds/53Mi) 8.21/2.84 % (26523)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_26322 for (2376ds/26Mi) 8.28/2.87 % (26524)Instruction limit reached! 8.28/2.87 % (26524)------------------------------ 8.28/2.87 % (26524)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 8.28/2.87 % (26524)Termination reason: Unknown 8.28/2.87 % (26524)Termination phase: shuffling 8.28/2.87 8.28/2.87 % (26524)Memory used [KB]: 2558 8.28/2.87 % (26524)Time elapsed: 0.029 s 8.28/2.87 % (26524)Instructions burned: 53 (million) 8.28/2.87 % (26524)------------------------------ 8.28/2.87 % (26524)------------------------------ 8.28/2.89 % (26523)Instruction limit reached! 8.28/2.89 % (26523)------------------------------ 8.28/2.89 % (26523)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 8.28/2.89 % (26523)Termination reason: Unknown 8.28/2.89 % (26523)Termination phase: shuffling 8.28/2.89 8.28/2.89 % (26523)Memory used [KB]: 2174 8.28/2.89 % (26523)Time elapsed: 0.017 s 8.28/2.89 % (26523)Instructions burned: 26 (million) 8.28/2.89 % (26523)------------------------------ 8.28/2.89 % (26523)------------------------------ 8.28/2.89 % (26525)Refutation not found, incomplete strategy 8.28/2.89 % (26525)------------------------------ 8.28/2.89 % (26525)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 8.28/2.89 % (26525)Termination reason: Refutation not found, incomplete strategy 8.28/2.89 8.28/2.89 8.28/2.89 % (26525)Memory used [KB]: 7291 8.28/2.89 % (26525)Time elapsed: 0.078 s 8.28/2.89 % (26525)Instructions burned: 155 (million) 8.28/2.89 % (26525)------------------------------ 8.28/2.89 % (26525)------------------------------ 8.48/2.91 % (26526)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_26322 for (2375ds/1539Mi) 8.48/2.94 % (26528)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_26322 for (2375ds/5205Mi) 8.55/2.98 % (26527)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_26322 for (2375ds/408Mi) 8.79/3.16 % (26522)Instruction limit reached! 8.79/3.16 % (26522)------------------------------ 8.79/3.16 % (26522)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 8.79/3.16 % (26522)Termination reason: Unknown 8.79/3.16 % (26522)Termination phase: Function definition elimination 8.79/3.16 8.79/3.16 % (26522)Memory used [KB]: 2814 8.79/3.16 % (26522)Time elapsed: 0.117 s 8.79/3.16 % (26522)Instructions burned: 205 (million) 8.79/3.16 % (26522)------------------------------ 8.79/3.16 % (26522)------------------------------ 8.79/3.17 % (26521)Instruction limit reached! 8.79/3.17 % (26521)------------------------------ 8.79/3.17 % (26521)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 8.79/3.17 % (26521)Termination reason: Unknown 8.79/3.17 % (26521)Termination phase: Function definition elimination 8.79/3.17 8.79/3.17 % (26521)Memory used [KB]: 3070 8.79/3.17 % (26521)Time elapsed: 0.138 s 8.79/3.17 % (26521)Instructions burned: 267 (million) 8.79/3.17 % (26521)------------------------------ 8.79/3.17 % (26521)------------------------------ 8.79/3.20 % (26529)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_26322 for (2372ds/1913Mi) 8.86/3.21 % (26519)Instruction limit reached! 8.86/3.21 % (26519)------------------------------ 8.86/3.21 % (26519)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 8.86/3.21 % (26519)Termination reason: Unknown 8.86/3.21 % (26519)Termination phase: Function definition elimination 8.86/3.21 8.86/3.21 % (26519)Memory used [KB]: 2814 8.86/3.21 % (26519)Time elapsed: 0.178 s 8.86/3.21 % (26519)Instructions burned: 369 (million) 8.86/3.21 % (26519)------------------------------ 8.86/3.21 % (26519)------------------------------ 8.86/3.24 % (26530)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_26322 for (2372ds/4350Mi) 8.89/3.28 % (26531)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_26322 for (2372ds/68Mi) 9.79/3.38 % (26520)Instruction limit reached! 9.79/3.38 % (26520)------------------------------ 9.79/3.38 % (26520)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 9.79/3.38 % (26520)Termination reason: Unknown 9.79/3.38 % (26520)Termination phase: Function definition elimination 9.79/3.38 9.79/3.38 % (26520)Memory used [KB]: 3070 9.79/3.38 % (26520)Time elapsed: 0.354 s 9.79/3.38 % (26520)Instructions burned: 1023 (million) 9.79/3.38 % (26520)------------------------------ 9.79/3.38 % (26520)------------------------------ 9.79/3.39 % (26531)Instruction limit reached! 9.79/3.39 % (26531)------------------------------ 9.79/3.39 % (26531)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 9.79/3.39 % (26531)Termination reason: Unknown 9.79/3.39 % (26531)Termination phase: Property scanning 9.79/3.39 9.79/3.39 % (26531)Memory used [KB]: 2558 9.79/3.39 % (26531)Time elapsed: 0.045 s 9.79/3.39 % (26531)Instructions burned: 68 (million) 9.79/3.39 % (26531)------------------------------ 9.79/3.39 % (26531)------------------------------ 9.79/3.40 % (26526)Instruction limit reached! 9.79/3.40 % (26526)------------------------------ 9.79/3.40 % (26526)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 9.79/3.40 % (26526)Termination reason: Unknown 9.79/3.40 % (26526)Termination phase: Function definition elimination 9.79/3.40 9.79/3.40 % (26526)Memory used [KB]: 3070 9.79/3.40 % (26526)Time elapsed: 0.488 s 9.79/3.40 % (26526)Instructions burned: 1539 (million) 9.79/3.40 % (26526)------------------------------ 9.79/3.40 % (26526)------------------------------ 9.99/3.42 % (26532)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_26322 for (2370ds/358Mi) 9.99/3.44 % (26533)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_26322 for (2370ds/31Mi) 10.10/3.47 % (26534)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on E---3.1_26322 for (2370ds/279Mi) 10.10/3.50 % (26533)Instruction limit reached! 10.10/3.50 % (26533)------------------------------ 10.10/3.50 % (26533)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 10.10/3.50 % (26533)Termination reason: Unknown 10.10/3.50 % (26533)Termination phase: shuffling 10.10/3.50 10.10/3.50 % (26533)Memory used [KB]: 2302 10.10/3.50 % (26533)Time elapsed: 0.020 s 10.10/3.50 % (26533)Instructions burned: 32 (million) 10.10/3.50 % (26533)------------------------------ 10.10/3.50 % (26533)------------------------------ 10.10/3.54 % (26535)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on E---3.1_26322 for (2369ds/258Mi) 10.47/3.68 % (26527)Instruction limit reached! 10.47/3.68 % (26527)------------------------------ 10.47/3.68 % (26527)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 10.47/3.68 % (26527)Termination reason: Unknown 10.47/3.68 % (26527)Termination phase: Saturation 10.47/3.68 10.47/3.68 % (26527)Memory used [KB]: 8443 10.47/3.68 % (26527)Time elapsed: 0.622 s 10.47/3.68 % (26527)Instructions burned: 409 (million) 10.47/3.68 % (26527)------------------------------ 10.47/3.68 % (26527)------------------------------ 10.58/3.75 % (26536)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_26322 for (2367ds/26Mi) 10.64/3.78 % (26535)Instruction limit reached! 10.64/3.78 % (26535)------------------------------ 10.64/3.78 % (26535)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 10.64/3.78 % (26535)Termination reason: Unknown 10.64/3.78 % (26535)Termination phase: Saturation 10.64/3.78 10.64/3.78 % (26535)Memory used [KB]: 7547 10.64/3.78 % (26535)Time elapsed: 0.136 s 10.64/3.78 % (26535)Instructions burned: 259 (million) 10.64/3.78 % (26535)------------------------------ 10.64/3.78 % (26535)------------------------------ 10.64/3.79 % (26532)Instruction limit reached! 10.64/3.79 % (26532)------------------------------ 10.64/3.79 % (26532)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 10.64/3.79 % (26532)Termination reason: Unknown 10.64/3.79 % (26532)Termination phase: Saturation 10.64/3.79 10.64/3.79 % (26532)Memory used [KB]: 7931 10.64/3.79 % (26532)Time elapsed: 0.171 s 10.64/3.79 % (26532)Instructions burned: 359 (million) 10.64/3.79 % (26532)------------------------------ 10.64/3.79 % (26532)------------------------------ 10.64/3.79 % (26536)Instruction limit reached! 10.64/3.79 % (26536)------------------------------ 10.64/3.79 % (26536)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 10.64/3.79 % (26536)Termination reason: Unknown 10.64/3.79 % (26536)Termination phase: shuffling 10.64/3.79 10.64/3.79 % (26536)Memory used [KB]: 2174 10.64/3.79 % (26536)Time elapsed: 0.017 s 10.64/3.79 % (26536)Instructions burned: 26 (million) 10.64/3.79 % (26536)------------------------------ 10.64/3.79 % (26536)------------------------------ 10.64/3.81 % (26534)Instruction limit reached! 10.64/3.81 % (26534)------------------------------ 10.64/3.81 % (26534)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 10.64/3.81 % (26534)Termination reason: Unknown 10.64/3.81 % (26534)Termination phase: Saturation 10.64/3.81 10.64/3.81 % (26534)Memory used [KB]: 7803 10.64/3.81 % (26534)Time elapsed: 0.149 s 10.64/3.81 % (26534)Instructions burned: 279 (million) 10.64/3.81 % (26534)------------------------------ 10.64/3.81 % (26534)------------------------------ 10.64/3.83 % (26539)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_26322 for (2366ds/253Mi) 10.64/3.84 % (26538)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_26322 for (2366ds/373Mi) 10.64/3.85 % (26537)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_26322 for (2366ds/995Mi) 11.27/3.88 % (26540)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_26322 for (2366ds/832Mi) 11.92/4.11 % (26538)Instruction limit reached! 11.92/4.11 % (26538)------------------------------ 11.92/4.11 % (26538)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 11.92/4.11 % (26538)Termination reason: Unknown 11.92/4.11 % (26538)Termination phase: Function definition elimination 11.92/4.11 11.92/4.11 % (26538)Memory used [KB]: 2814 11.92/4.11 % (26538)Time elapsed: 0.154 s 11.92/4.11 % (26538)Instructions burned: 374 (million) 11.92/4.11 % (26538)------------------------------ 11.92/4.11 % (26538)------------------------------ 11.92/4.11 % (26540)Refutation not found, incomplete strategy 11.92/4.11 % (26540)------------------------------ 11.92/4.11 % (26540)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 11.92/4.11 % (26540)Termination reason: Refutation not found, incomplete strategy 11.92/4.11 11.92/4.11 11.92/4.11 % (26540)Memory used [KB]: 7547 11.92/4.11 % (26540)Time elapsed: 0.280 s 11.92/4.11 % (26540)Instructions burned: 215 (million) 11.92/4.11 % (26540)------------------------------ 11.92/4.11 % (26540)------------------------------ 12.11/4.15 % (26542)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_26322 for (2363ds/40Mi) 12.19/4.16 % (26541)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_26322 for (2363ds/668Mi) 12.19/4.18 % (26542)Instruction limit reached! 12.19/4.18 % (26542)------------------------------ 12.19/4.18 % (26542)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 12.19/4.18 % (26542)Termination reason: Unknown 12.19/4.18 % (26542)Termination phase: shuffling 12.19/4.18 12.19/4.18 % (26542)Memory used [KB]: 2430 12.19/4.18 % (26542)Time elapsed: 0.022 s 12.19/4.18 % (26542)Instructions burned: 40 (million) 12.19/4.18 % (26542)------------------------------ 12.19/4.18 % (26542)------------------------------ 12.19/4.22 % (26539)Instruction limit reached! 12.19/4.22 % (26539)------------------------------ 12.19/4.22 % (26539)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 12.19/4.22 % (26539)Termination reason: Unknown 12.19/4.22 % (26539)Termination phase: Function definition elimination 12.19/4.22 12.19/4.22 % (26539)Memory used [KB]: 3070 12.19/4.22 % (26539)Time elapsed: 0.141 s 12.19/4.22 % (26539)Instructions burned: 254 (million) 12.19/4.22 % (26539)------------------------------ 12.19/4.22 % (26539)------------------------------ 12.39/4.23 % (26543)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_26322 for (2362ds/294Mi) 12.47/4.29 % (26544)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_26322 for (2362ds/187Mi) 13.15/4.49 % (26544)Instruction limit reached! 13.15/4.49 % (26544)------------------------------ 13.15/4.49 % (26544)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 13.15/4.49 % (26544)Termination reason: Unknown 13.15/4.49 % (26544)Termination phase: Function definition elimination 13.15/4.49 13.15/4.49 % (26544)Memory used [KB]: 2814 13.15/4.49 % (26544)Time elapsed: 0.089 s 13.15/4.49 % (26544)Instructions burned: 187 (million) 13.15/4.49 % (26544)------------------------------ 13.15/4.49 % (26544)------------------------------ 13.15/4.50 % (26545)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_26322 for (2359ds/371Mi) 13.54/4.60 % (26543)Instruction limit reached! 13.54/4.60 % (26543)------------------------------ 13.54/4.60 % (26543)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 13.54/4.60 % (26543)Termination reason: Unknown 13.54/4.60 % (26543)Termination phase: Saturation 13.54/4.60 13.54/4.60 % (26543)Memory used [KB]: 7675 13.54/4.60 % (26543)Time elapsed: 0.416 s 13.54/4.60 % (26543)Instructions burned: 294 (million) 13.54/4.60 % (26543)------------------------------ 13.54/4.60 % (26543)------------------------------ 13.67/4.64 % (26541)Instruction limit reached! 13.67/4.64 % (26541)------------------------------ 13.67/4.64 % (26541)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 13.67/4.64 % (26541)Termination reason: Unknown 13.67/4.64 % (26541)Termination phase: Function definition elimination 13.67/4.64 13.67/4.64 % (26541)Memory used [KB]: 3070 13.67/4.64 % (26541)Time elapsed: 0.263 s 13.67/4.64 % (26541)Instructions burned: 670 (million) 13.67/4.64 % (26541)------------------------------ 13.67/4.64 % (26541)------------------------------ 13.67/4.64 % (26546)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_26322 for (2358ds/1827Mi) 13.69/4.67 % (26545)Instruction limit reached! 13.69/4.67 % (26545)------------------------------ 13.69/4.67 % (26545)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 13.69/4.67 % (26545)Termination reason: Unknown 13.69/4.67 % (26545)Termination phase: Saturation 13.69/4.67 13.69/4.67 % (26545)Memory used [KB]: 7931 13.69/4.67 % (26545)Time elapsed: 0.192 s 13.69/4.67 % (26545)Instructions burned: 371 (million) 13.69/4.67 % (26545)------------------------------ 13.69/4.67 % (26545)------------------------------ 13.69/4.69 % (26548)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_26322 for (2357ds/316Mi) 13.69/4.69 % (26547)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_26322 for (2357ds/70Mi) 13.69/4.70 % (26537)Instruction limit reached! 13.69/4.70 % (26537)------------------------------ 13.69/4.70 % (26537)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 13.69/4.70 % (26537)Termination reason: Unknown 13.69/4.70 % (26537)Termination phase: Function definition elimination 13.69/4.70 13.69/4.70 % (26537)Memory used [KB]: 3070 13.69/4.70 % (26537)Time elapsed: 0.416 s 13.69/4.70 % (26537)Instructions burned: 996 (million) 13.69/4.70 % (26537)------------------------------ 13.69/4.70 % (26537)------------------------------ 14.01/4.72 % (26529)Instruction limit reached! 14.01/4.72 % (26529)------------------------------ 14.01/4.72 % (26529)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 14.01/4.72 % (26529)Termination reason: Unknown 14.01/4.72 % (26529)Termination phase: Saturation 14.01/4.72 14.01/4.72 % (26529)Memory used [KB]: 5373 14.01/4.72 % (26529)Time elapsed: 1.554 s 14.01/4.72 % (26529)Instructions burned: 1913 (million) 14.01/4.72 % (26529)------------------------------ 14.01/4.72 % (26529)------------------------------ 14.01/4.74 % (26550)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_26322 for (2356ds/4714Mi) 14.12/4.76 % (26549)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_26322 for (2356ds/932Mi) 14.12/4.80 % (26547)Instruction limit reached! 14.12/4.80 % (26547)------------------------------ 14.12/4.80 % (26547)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 14.12/4.80 % (26547)Termination reason: Unknown 14.12/4.80 % (26547)Termination phase: Property scanning 14.12/4.80 14.12/4.81 % (26547)Memory used [KB]: 2686 14.12/4.81 % (26547)Time elapsed: 0.041 s 14.12/4.81 % (26547)Instructions burned: 71 (million) 14.12/4.81 % (26547)------------------------------ 14.12/4.81 % (26547)------------------------------ 14.12/4.85 % (26551)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_26322 for (2356ds/8250Mi) 14.29/4.87 % (26548)Instruction limit reached! 14.29/4.87 % (26548)------------------------------ 14.29/4.87 % (26548)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 14.29/4.87 % (26548)Termination reason: Unknown 14.29/4.87 % (26548)Termination phase: Function definition elimination 14.29/4.87 14.29/4.87 % (26548)Memory used [KB]: 3070 14.29/4.87 % (26548)Time elapsed: 0.131 s 14.29/4.87 % (26548)Instructions burned: 316 (million) 14.29/4.87 % (26548)------------------------------ 14.29/4.87 % (26548)------------------------------ 14.51/4.94 % (26552)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_26322 for (2355ds/770Mi) 14.51/5.00 % (26552)Refutation not found, incomplete strategy 14.51/5.00 % (26552)------------------------------ 14.51/5.00 % (26552)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 14.51/5.00 % (26552)Termination reason: Refutation not found, incomplete strategy 14.51/5.00 14.51/5.00 14.51/5.00 % (26552)Memory used [KB]: 7291 14.51/5.00 % (26552)Time elapsed: 0.098 s 14.51/5.00 % (26552)Instructions burned: 124 (million) 14.51/5.00 % (26552)------------------------------ 14.51/5.00 % (26552)------------------------------ 14.51/5.02 % (26553)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_26322 for (2354ds/794Mi) 15.68/5.12 % (26549)Instruction limit reached! 15.68/5.12 % (26549)------------------------------ 15.68/5.12 % (26549)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 15.68/5.12 % (26549)Termination reason: Unknown 15.68/5.12 % (26549)Termination phase: Function definition elimination 15.68/5.12 15.68/5.12 % (26549)Memory used [KB]: 3070 15.68/5.12 % (26549)Time elapsed: 0.316 s 15.68/5.12 % (26549)Instructions burned: 934 (million) 15.68/5.12 % (26549)------------------------------ 15.68/5.12 % (26549)------------------------------ 15.68/5.17 % (26554)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_26322 for (2352ds/464Mi) 16.84/5.40 % (26553)Instruction limit reached! 16.84/5.40 % (26553)------------------------------ 16.84/5.40 % (26553)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 16.84/5.40 % (26553)Termination reason: Unknown 16.84/5.40 % (26553)Termination phase: Function definition elimination 16.84/5.40 16.84/5.40 % (26553)Memory used [KB]: 3070 16.84/5.40 % (26553)Time elapsed: 0.265 s 16.84/5.40 % (26553)Instructions burned: 795 (million) 16.84/5.40 % (26553)------------------------------ 16.84/5.40 % (26553)------------------------------ 16.84/5.44 % (26554)Instruction limit reached! 16.84/5.44 % (26554)------------------------------ 16.84/5.44 % (26554)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 16.84/5.44 % (26554)Termination reason: Unknown 16.84/5.44 % (26554)Termination phase: Function definition elimination 16.84/5.44 16.84/5.44 % (26554)Memory used [KB]: 2814 16.84/5.44 % (26554)Time elapsed: 0.169 s 16.84/5.44 % (26554)Instructions burned: 466 (million) 16.84/5.44 % (26554)------------------------------ 16.84/5.44 % (26554)------------------------------ 16.84/5.46 % (26555)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_26322 for (2350ds/1376Mi) 16.84/5.46 % (26556)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on E---3.1_26322 for (2349ds/906Mi) 18.26/5.74 % (26556)Instruction limit reached! 18.26/5.74 % (26556)------------------------------ 18.26/5.74 % (26556)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 18.26/5.74 % (26556)Termination reason: Unknown 18.26/5.74 % (26556)Termination phase: Function definition elimination 18.26/5.74 18.26/5.74 % (26556)Memory used [KB]: 3070 18.26/5.74 % (26556)Time elapsed: 0.285 s 18.26/5.74 % (26556)Instructions burned: 906 (million) 18.26/5.74 % (26556)------------------------------ 18.26/5.74 % (26556)------------------------------ 18.26/5.76 % (26557)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_26322 for (2346ds/434Mi) 18.97/5.96 % (26557)Instruction limit reached! 18.97/5.96 % (26557)------------------------------ 18.97/5.96 % (26557)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 18.97/5.96 % (26557)Termination reason: Unknown 18.97/5.96 % (26557)Termination phase: Saturation 18.97/5.96 18.97/5.96 % (26557)Memory used [KB]: 7547 18.97/5.96 % (26557)Time elapsed: 0.199 s 18.97/5.96 % (26557)Instructions burned: 434 (million) 18.97/5.96 % (26557)------------------------------ 18.97/5.96 % (26557)------------------------------ 18.97/5.97 % (26558)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_26322 for (2344ds/865Mi) 20.49/6.28 % (26550)Instruction limit reached! 20.49/6.28 % (26550)------------------------------ 20.49/6.28 % (26550)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 20.49/6.28 % (26550)Termination reason: Unknown 20.49/6.28 % (26550)Termination phase: Function definition elimination 20.49/6.28 20.49/6.28 % (26550)Memory used [KB]: 3070 20.49/6.28 % (26550)Time elapsed: 1.543 s 20.49/6.28 % (26550)Instructions burned: 4714 (million) 20.49/6.28 % (26550)------------------------------ 20.49/6.28 % (26550)------------------------------ 20.49/6.30 % (26559)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_26322 for (2341ds/593Mi) 20.92/6.36 % (26528)Instruction limit reached! 20.92/6.36 % (26528)------------------------------ 20.92/6.36 % (26528)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 20.92/6.36 % (26528)Termination reason: Unknown 20.92/6.36 % (26528)Termination phase: Function definition elimination 20.92/6.36 20.92/6.36 % (26528)Memory used [KB]: 3070 20.92/6.36 % (26528)Time elapsed: 1.752 s 20.92/6.36 % (26528)Instructions burned: 5206 (million) 20.92/6.36 % (26528)------------------------------ 20.92/6.36 % (26528)------------------------------ 20.92/6.37 % (26558)Instruction limit reached! 20.92/6.37 % (26558)------------------------------ 20.92/6.37 % (26558)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 20.92/6.37 % (26558)Termination reason: Unknown 20.92/6.37 % (26558)Termination phase: Saturation 20.92/6.37 20.92/6.37 % (26558)Memory used [KB]: 9594 20.92/6.37 % (26558)Time elapsed: 0.398 s 20.92/6.37 % (26558)Instructions burned: 866 (million) 20.92/6.37 % (26558)------------------------------ 20.92/6.37 % (26558)------------------------------ 20.92/6.41 % (26560)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_26322 for (2340ds/443Mi) 21.14/6.44 % (26561)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_26322 for (2340ds/594Mi) 21.14/6.45 % (26546)Instruction limit reached! 21.14/6.45 % (26546)------------------------------ 21.14/6.45 % (26546)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 21.14/6.45 % (26546)Termination reason: Unknown 21.14/6.45 % (26546)Termination phase: Saturation 21.14/6.45 21.14/6.45 % (26546)Memory used [KB]: 10362 21.14/6.45 % (26546)Time elapsed: 1.845 s 21.14/6.45 % (26546)Instructions burned: 1828 (million) 21.14/6.45 % (26546)------------------------------ 21.14/6.45 % (26546)------------------------------ 21.14/6.47 % (26562)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_26322 for (2339ds/327Mi) 21.22/6.53 % (26559)Instruction limit reached! 21.22/6.53 % (26559)------------------------------ 21.22/6.53 % (26559)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 21.22/6.53 % (26559)Termination reason: Unknown 21.22/6.53 % (26559)Termination phase: Function definition elimination 21.22/6.53 21.22/6.53 % (26559)Memory used [KB]: 3070 21.22/6.53 % (26559)Time elapsed: 0.235 s 21.22/6.53 % (26559)Instructions burned: 593 (million) 21.22/6.53 % (26559)------------------------------ 21.22/6.53 % (26559)------------------------------ 21.53/6.55 % (26563)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_26322 for (2338ds/5411Mi) 21.57/6.60 % (26563)Refutation not found, incomplete strategy 21.57/6.60 % (26563)------------------------------ 21.57/6.60 % (26563)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 21.57/6.60 % (26563)Termination reason: Refutation not found, incomplete strategy 21.57/6.60 21.57/6.60 21.57/6.60 % (26563)Memory used [KB]: 7164 21.57/6.60 % (26563)Time elapsed: 0.061 s 21.57/6.60 % (26563)Instructions burned: 114 (million) 21.57/6.60 % (26563)------------------------------ 21.57/6.60 % (26563)------------------------------ 21.70/6.62 % (26564)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_26322 for (2338ds/1762Mi) 21.70/6.63 % (26562)Instruction limit reached! 21.70/6.63 % (26562)------------------------------ 21.70/6.63 % (26562)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 21.70/6.63 % (26562)Termination reason: Unknown 21.70/6.63 % (26562)Termination phase: Saturation 21.70/6.63 21.70/6.63 % (26562)Memory used [KB]: 7675 21.70/6.63 % (26562)Time elapsed: 0.160 s 21.70/6.63 % (26562)Instructions burned: 327 (million) 21.70/6.63 % (26562)------------------------------ 21.70/6.63 % (26562)------------------------------ 21.70/6.64 % (26565)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_26322 for (2337ds/96Mi) 21.93/6.69 % (26565)Instruction limit reached! 21.93/6.69 % (26565)------------------------------ 21.93/6.69 % (26565)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 21.93/6.69 % (26565)Termination reason: Unknown 21.93/6.69 % (26565)Termination phase: shuffling 21.93/6.69 21.93/6.69 % (26565)Memory used [KB]: 2686 21.93/6.69 % (26565)Time elapsed: 0.049 s 21.93/6.69 % (26565)Instructions burned: 97 (million) 21.93/6.69 % (26565)------------------------------ 21.93/6.69 % (26565)------------------------------ 21.93/6.71 % (26566)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_26322 for (2337ds/503Mi) 22.74/6.82 % (26560)Instruction limit reached! 22.74/6.82 % (26560)------------------------------ 22.74/6.82 % (26560)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 22.74/6.82 % (26560)Termination reason: Unknown 22.74/6.82 % (26560)Termination phase: Saturation 22.74/6.82 22.74/6.82 % (26560)Memory used [KB]: 8571 22.74/6.82 % (26560)Time elapsed: 0.214 s 22.74/6.82 % (26560)Instructions burned: 443 (million) 22.74/6.82 % (26560)------------------------------ 22.74/6.82 % (26560)------------------------------ 22.74/6.86 % (26567)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_26322 for (2336ds/90Mi) 22.97/6.95 % (26566)Instruction limit reached! 22.97/6.95 % (26566)------------------------------ 22.97/6.95 % (26566)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 22.97/6.95 % (26566)Termination reason: Unknown 22.97/6.95 % (26566)Termination phase: Saturation 22.97/6.95 22.97/6.95 % (26566)Memory used [KB]: 8315 22.97/6.95 % (26566)Time elapsed: 0.243 s 22.97/6.95 % (26566)Instructions burned: 504 (million) 22.97/6.95 % (26566)------------------------------ 22.97/6.95 % (26566)------------------------------ 22.97/6.95 % (26567)Instruction limit reached! 22.97/6.95 % (26567)------------------------------ 22.97/6.95 % (26567)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 22.97/6.95 % (26567)Termination reason: Unknown 22.97/6.95 % (26567)Termination phase: Property scanning 22.97/6.95 22.97/6.95 % (26567)Memory used [KB]: 2558 22.97/6.95 % (26567)Time elapsed: 0.049 s 22.97/6.95 % (26567)Instructions burned: 92 (million) 22.97/6.95 % (26567)------------------------------ 22.97/6.95 % (26567)------------------------------ 23.39/6.97 % (26569)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_26322 for (2334ds/1512Mi) 23.39/6.98 % (26568)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on E---3.1_26322 for (2334ds/593Mi) 23.66/7.07 % (26569)Refutation not found, incomplete strategy 23.66/7.07 % (26569)------------------------------ 23.66/7.07 % (26569)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 23.66/7.07 % (26569)Termination reason: Refutation not found, incomplete strategy 23.66/7.07 23.66/7.07 23.66/7.07 % (26569)Memory used [KB]: 7675 23.66/7.07 % (26569)Time elapsed: 0.107 s 23.66/7.07 % (26569)Instructions burned: 226 (million) 23.66/7.07 % (26569)------------------------------ 23.66/7.07 % (26569)------------------------------ 23.66/7.09 % (26555)Instruction limit reached! 23.66/7.09 % (26555)------------------------------ 23.66/7.09 % (26555)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 23.66/7.09 % (26555)Termination reason: Unknown 23.66/7.09 % (26555)Termination phase: Function definition elimination 23.66/7.09 23.66/7.09 % (26555)Memory used [KB]: 3070 23.66/7.09 % (26555)Time elapsed: 0.632 s 23.66/7.09 % (26555)Instructions burned: 1377 (million) 23.66/7.09 % (26555)------------------------------ 23.66/7.09 % (26555)------------------------------ 24.00/7.11 % (26570)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_26322 for (2333ds/569Mi) 24.00/7.12 % (26561)Instruction limit reached! 24.00/7.12 % (26561)------------------------------ 24.00/7.12 % (26561)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 24.00/7.12 % (26561)Termination reason: Unknown 24.00/7.12 % (26561)Termination phase: Saturation 24.00/7.12 24.00/7.12 % (26561)Memory used [KB]: 7931 24.00/7.12 % (26561)Time elapsed: 0.725 s 24.00/7.12 % (26561)Instructions burned: 595 (million) 24.00/7.12 % (26561)------------------------------ 24.00/7.12 % (26561)------------------------------ 24.00/7.14 % (26571)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_26322 for (2333ds/501Mi) 24.17/7.18 % (26572)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_26322 for (2333ds/562Mi) 24.41/7.26 % (26564)Instruction limit reached! 24.41/7.26 % (26564)------------------------------ 24.41/7.26 % (26564)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 24.41/7.26 % (26564)Termination reason: Unknown 24.41/7.26 % (26564)Termination phase: Function definition elimination 24.41/7.26 24.41/7.26 % (26564)Memory used [KB]: 3070 24.41/7.26 % (26564)Time elapsed: 0.642 s 24.41/7.26 % (26564)Instructions burned: 1763 (million) 24.41/7.26 % (26564)------------------------------ 24.41/7.26 % (26564)------------------------------ 24.49/7.35 % (26573)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_26322 for (2331ds/406Mi) 25.06/7.40 % (26568)Instruction limit reached! 25.06/7.40 % (26568)------------------------------ 25.06/7.40 % (26568)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 25.06/7.40 % (26568)Termination reason: Unknown 25.06/7.40 % (26568)Termination phase: Function definition elimination 25.06/7.40 25.06/7.40 % (26568)Memory used [KB]: 3070 25.06/7.40 % (26568)Time elapsed: 0.216 s 25.06/7.40 % (26568)Instructions burned: 594 (million) 25.06/7.40 % (26568)------------------------------ 25.06/7.40 % (26568)------------------------------ 25.25/7.44 % (26574)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on E---3.1_26322 for (2330ds/582Mi) 25.84/7.70 % (26571)Instruction limit reached! 25.84/7.70 % (26571)------------------------------ 25.84/7.70 % (26571)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 25.84/7.70 % (26571)Termination reason: Unknown 25.84/7.70 % (26571)Termination phase: Function definition elimination 25.84/7.70 25.84/7.70 % (26571)Memory used [KB]: 3070 25.84/7.70 % (26571)Time elapsed: 0.205 s 25.84/7.70 % (26571)Instructions burned: 502 (million) 25.84/7.70 % (26571)------------------------------ 25.84/7.70 % (26571)------------------------------ 25.84/7.72 % (26570)Instruction limit reached! 25.84/7.72 % (26570)------------------------------ 25.84/7.72 % (26570)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 25.84/7.72 % (26570)Termination reason: Unknown 25.84/7.72 % (26570)Termination phase: Function definition elimination 25.84/7.72 25.84/7.72 % (26570)Memory used [KB]: 3070 25.84/7.72 % (26570)Time elapsed: 0.230 s 25.84/7.72 % (26570)Instructions burned: 571 (million) 25.84/7.72 % (26570)------------------------------ 25.84/7.72 % (26570)------------------------------ 26.00/7.75 % (26575)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_26322 for (2327ds/456Mi) 26.04/7.76 % (26573)Instruction limit reached! 26.04/7.76 % (26573)------------------------------ 26.04/7.76 % (26573)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 26.04/7.76 % (26573)Termination reason: Unknown 26.04/7.76 % (26573)Termination phase: Saturation 26.04/7.76 26.04/7.76 % (26573)Memory used [KB]: 8187 26.04/7.76 % (26573)Time elapsed: 0.481 s 26.04/7.76 % (26573)Instructions burned: 406 (million) 26.04/7.76 % (26573)------------------------------ 26.04/7.76 % (26573)------------------------------ 26.04/7.79 % (26576)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on E---3.1_26322 for (2327ds/393Mi) 26.04/7.80 % (26577)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_26322 for (2326ds/1335Mi) 26.58/7.91 % (26574)Instruction limit reached! 26.58/7.91 % (26574)------------------------------ 26.58/7.91 % (26574)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 26.58/7.91 % (26574)Termination reason: Unknown 26.58/7.91 % (26574)Termination phase: Function definition elimination 26.58/7.91 26.58/7.91 % (26574)Memory used [KB]: 3070 26.58/7.91 % (26574)Time elapsed: 0.258 s 26.58/7.91 % (26574)Instructions burned: 583 (million) 26.58/7.91 % (26574)------------------------------ 26.58/7.91 % (26574)------------------------------ 26.58/7.93 % (26572)Instruction limit reached! 26.58/7.93 % (26572)------------------------------ 26.58/7.93 % (26572)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 26.58/7.93 % (26572)Termination reason: Unknown 26.58/7.93 % (26572)Termination phase: Saturation 26.58/7.93 26.58/7.93 % (26572)Memory used [KB]: 8955 26.58/7.93 % (26572)Time elapsed: 0.799 s 26.58/7.93 % (26572)Instructions burned: 563 (million) 26.58/7.93 % (26572)------------------------------ 26.58/7.93 % (26572)------------------------------ 26.82/7.97 % (26578)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_26322 for (2324ds/3373Mi) 26.82/7.99 % (26579)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_26322 for (2324ds/474Mi) 27.22/8.13 % (26576)Instruction limit reached! 27.22/8.13 % (26576)------------------------------ 27.22/8.13 % (26576)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 27.22/8.13 % (26576)Termination reason: Unknown 27.22/8.13 % (26576)Termination phase: Function definition elimination 27.22/8.13 27.22/8.13 % (26576)Memory used [KB]: 3070 27.22/8.13 % (26576)Time elapsed: 0.155 s 27.22/8.13 % (26576)Instructions burned: 395 (million) 27.22/8.13 % (26576)------------------------------ 27.22/8.13 % (26576)------------------------------ 27.22/8.16 % (26580)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_26322 for (2322ds/157Mi) 27.34/8.21 % (26575)Instruction limit reached! 27.34/8.21 % (26575)------------------------------ 27.34/8.21 % (26575)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 27.34/8.21 % (26575)Termination reason: Unknown 27.34/8.21 % (26575)Termination phase: Saturation 27.34/8.21 27.34/8.21 % (26575)Memory used [KB]: 8827 27.34/8.21 % (26575)Time elapsed: 0.262 s 27.34/8.21 % (26575)Instructions burned: 456 (million) 27.34/8.21 % (26575)------------------------------ 27.34/8.21 % (26575)------------------------------ 27.34/8.22 % (26530)Instruction limit reached! 27.34/8.22 % (26530)------------------------------ 27.34/8.22 % (26530)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 27.34/8.22 % (26530)Termination reason: Unknown 27.34/8.22 % (26530)Termination phase: Saturation 27.34/8.22 27.34/8.22 % (26530)Memory used [KB]: 13688 27.34/8.22 % (26530)Time elapsed: 5.038 s 27.34/8.22 % (26530)Instructions burned: 4350 (million) 27.34/8.22 % (26530)------------------------------ 27.34/8.22 % (26530)------------------------------ 27.46/8.26 % (26581)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_26322 for (2321ds/590Mi) 27.48/8.27 % (26582)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_26322 for (2321ds/104Mi) 27.48/8.28 % (26579)Instruction limit reached! 27.48/8.28 % (26579)------------------------------ 27.48/8.28 % (26579)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 27.48/8.28 % (26579)Termination reason: Unknown 27.48/8.28 % (26579)Termination phase: Function definition elimination 27.48/8.28 27.48/8.28 % (26579)Memory used [KB]: 3070 27.48/8.28 % (26579)Time elapsed: 0.192 s 27.48/8.28 % (26579)Instructions burned: 474 (million) 27.48/8.28 % (26579)------------------------------ 27.48/8.28 % (26579)------------------------------ 27.48/8.30 % (26583)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_26322 for (2321ds/414Mi) 27.72/8.33 % (26580)Instruction limit reached! 27.72/8.33 % (26580)------------------------------ 27.72/8.33 % (26580)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 27.72/8.33 % (26580)Termination reason: Unknown 27.72/8.33 % (26580)Termination phase: Function definition elimination 27.72/8.33 27.72/8.33 % (26580)Memory used [KB]: 2814 27.72/8.33 % (26580)Time elapsed: 0.107 s 27.72/8.33 % (26580)Instructions burned: 159 (million) 27.72/8.33 % (26580)------------------------------ 27.72/8.33 % (26580)------------------------------ 27.83/8.39 % (26584)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_26322 for (2320ds/715Mi) 27.83/8.40 % (26582)Instruction limit reached! 27.83/8.40 % (26582)------------------------------ 27.83/8.40 % (26582)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 27.83/8.40 % (26582)Termination reason: Unknown 27.83/8.40 % (26582)Termination phase: Property scanning 27.83/8.40 27.83/8.40 % (26582)Memory used [KB]: 2686 27.83/8.40 % (26582)Time elapsed: 0.057 s 27.83/8.40 % (26582)Instructions burned: 104 (million) 27.83/8.40 % (26582)------------------------------ 27.83/8.40 % (26582)------------------------------ 27.96/8.44 % (26585)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_26322 for (2320ds/961Mi) 29.01/8.55 % (26583)Instruction limit reached! 29.01/8.55 % (26583)------------------------------ 29.01/8.55 % (26583)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 29.01/8.55 % (26583)Termination reason: Unknown 29.01/8.55 % (26583)Termination phase: Function definition elimination 29.01/8.55 29.01/8.55 % (26583)Memory used [KB]: 3070 29.01/8.55 % (26583)Time elapsed: 0.186 s 29.01/8.55 % (26583)Instructions burned: 415 (million) 29.01/8.55 % (26583)------------------------------ 29.01/8.55 % (26583)------------------------------ 29.01/8.55 % (26581)Instruction limit reached! 29.01/8.55 % (26581)------------------------------ 29.01/8.55 % (26581)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 29.01/8.55 % (26581)Termination reason: Unknown 29.01/8.55 % (26581)Termination phase: Function definition elimination 29.01/8.55 29.01/8.55 % (26581)Memory used [KB]: 2814 29.01/8.55 % (26581)Time elapsed: 0.212 s 29.01/8.55 % (26581)Instructions burned: 591 (million) 29.01/8.55 % (26581)------------------------------ 29.01/8.55 % (26581)------------------------------ 29.01/8.56 % (26587)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_26322 for (2318ds/1979Mi) 29.26/8.59 % (26586)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_26322 for (2318ds/1213Mi) 30.35/9.04 % (26584)Instruction limit reached! 30.35/9.04 % (26584)------------------------------ 30.35/9.04 % (26584)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 30.35/9.05 % (26578)Instruction limit reached! 30.35/9.05 % (26578)------------------------------ 30.35/9.05 % (26578)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 30.35/9.05 % (26578)Termination reason: Unknown 30.35/9.05 % (26578)Termination phase: Function definition elimination 30.35/9.05 30.35/9.05 % (26578)Memory used [KB]: 3070 30.35/9.05 % (26578)Time elapsed: 1.076 s 30.35/9.05 % (26578)Instructions burned: 3373 (million) 30.35/9.05 % (26578)------------------------------ 30.35/9.05 % (26578)------------------------------ 30.35/9.05 % (26584)Termination reason: Unknown 30.35/9.05 % (26584)Termination phase: Function definition elimination 30.35/9.05 30.35/9.05 % (26584)Memory used [KB]: 3070 30.35/9.05 % (26584)Time elapsed: 0.257 s 30.35/9.05 % (26584)Instructions burned: 715 (million) 30.35/9.05 % (26584)------------------------------ 30.35/9.05 % (26584)------------------------------ 30.35/9.06 % (26588)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_26322 for (2313ds/481Mi) 30.35/9.08 % (26589)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_26322 for (2313ds/783Mi) 31.36/9.20 % (26585)Instruction limit reached! 31.36/9.20 % (26585)------------------------------ 31.36/9.20 % (26585)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 31.74/9.22 % (26585)Termination reason: Unknown 31.74/9.22 % (26585)Termination phase: Function definition elimination 31.74/9.22 31.74/9.22 % (26585)Memory used [KB]: 2814 31.74/9.22 % (26585)Time elapsed: 0.416 s 31.74/9.22 % (26585)Instructions burned: 962 (million) 31.74/9.22 % (26585)------------------------------ 31.74/9.22 % (26585)------------------------------ 31.74/9.26 % (26590)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_26322 for (2312ds/432Mi) 31.74/9.30 % (26577)Refutation not found, non-redundant clauses discarded% (26577)------------------------------ 31.74/9.30 % (26577)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 31.74/9.30 % (26577)Termination reason: Refutation not found, non-redundant clauses discarded 31.74/9.30 31.74/9.30 % (26577)Memory used [KB]: 9210 31.74/9.30 % (26577)Time elapsed: 1.508 s 31.74/9.30 % (26577)Instructions burned: 1293 (million) 31.74/9.30 % (26577)------------------------------ 31.74/9.30 % (26577)------------------------------ 32.11/9.34 % (26591)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_26322 for (2311ds/1670Mi) 32.11/9.37 % (26587)Instruction limit reached! 32.11/9.37 % (26587)------------------------------ 32.11/9.37 % (26587)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 32.11/9.37 % (26587)Termination reason: Unknown 32.11/9.37 % (26587)Termination phase: Function definition elimination 32.11/9.37 32.11/9.37 % (26587)Memory used [KB]: 3070 32.11/9.37 % (26587)Time elapsed: 0.699 s 32.11/9.37 % (26587)Instructions burned: 1982 (million) 32.11/9.37 % (26587)------------------------------ 32.11/9.37 % (26587)------------------------------ 32.34/9.39 % (26592)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on E---3.1_26322 for (2310ds/90Mi) 32.34/9.40 % (26588)Instruction limit reached! 32.34/9.40 % (26588)------------------------------ 32.34/9.40 % (26588)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 32.34/9.40 % (26588)Termination reason: Unknown 32.34/9.40 % (26588)Termination phase: Function definition elimination 32.34/9.40 32.34/9.40 % (26588)Memory used [KB]: 3070 32.34/9.40 % (26588)Time elapsed: 0.202 s 32.34/9.40 % (26588)Instructions burned: 481 (million) 32.34/9.40 % (26588)------------------------------ 32.34/9.40 % (26588)------------------------------ 32.34/9.44 % (26593)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_26322 for (2310ds/346Mi) 32.34/9.46 % (26592)Instruction limit reached! 32.34/9.46 % (26592)------------------------------ 32.34/9.46 % (26592)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 32.34/9.46 % (26592)Termination reason: Unknown 32.34/9.46 % (26592)Termination phase: Property scanning 32.34/9.46 32.34/9.46 % (26592)Memory used [KB]: 2558 32.34/9.46 % (26592)Time elapsed: 0.048 s 32.34/9.46 % (26592)Instructions burned: 92 (million) 32.34/9.46 % (26592)------------------------------ 32.34/9.46 % (26592)------------------------------ 32.62/9.51 % (26594)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_26322 for (2309ds/401Mi) 32.63/9.57 % (26593)Instruction limit reached! 32.63/9.57 % (26593)------------------------------ 32.63/9.57 % (26593)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 32.63/9.57 % (26593)Termination reason: Unknown 32.63/9.57 % (26593)Termination phase: Function definition elimination 32.63/9.57 32.63/9.57 % (26593)Memory used [KB]: 3070 32.63/9.57 % (26593)Time elapsed: 0.129 s 32.63/9.57 % (26593)Instructions burned: 346 (million) 32.63/9.57 % (26593)------------------------------ 32.63/9.57 % (26593)------------------------------ 32.63/9.59 % (26595)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_26322 for (2308ds/6454Mi) 32.91/9.67 % (26595)Refutation not found, incomplete strategy 32.91/9.67 % (26595)------------------------------ 32.91/9.67 % (26595)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 32.91/9.67 % (26595)Termination reason: Refutation not found, incomplete strategy 32.91/9.67 32.91/9.67 32.91/9.67 % (26595)Memory used [KB]: 7291 32.91/9.67 % (26595)Time elapsed: 0.082 s 32.91/9.67 % (26595)Instructions burned: 170 (million) 32.91/9.67 % (26595)------------------------------ 32.91/9.67 % (26595)------------------------------ 32.91/9.69 % (26596)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_26322 for (2307ds/283Mi) 33.13/9.71 % (26590)Instruction limit reached! 33.13/9.71 % (26590)------------------------------ 33.13/9.71 % (26590)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 33.13/9.71 % (26590)Termination reason: Unknown 33.13/9.71 % (26590)Termination phase: Saturation 33.13/9.71 33.13/9.72 % (26590)Memory used [KB]: 8315 33.13/9.72 % (26590)Time elapsed: 0.482 s 33.13/9.72 % (26590)Instructions burned: 432 (million) 33.13/9.72 % (26590)------------------------------ 33.13/9.72 % (26590)------------------------------ 33.13/9.76 % (26597)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_26322 for (2307ds/865Mi) 33.13/9.80 % (26589)Instruction limit reached! 33.13/9.80 % (26589)------------------------------ 33.13/9.80 % (26589)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 33.13/9.80 % (26589)Termination reason: Unknown 33.13/9.80 % (26589)Termination phase: Saturation 33.13/9.80 33.13/9.80 % (26589)Memory used [KB]: 7931 33.13/9.80 % (26589)Time elapsed: 0.734 s 33.13/9.80 % (26589)Instructions burned: 783 (million) 33.13/9.80 % (26589)------------------------------ 33.13/9.80 % (26589)------------------------------ 33.13/9.80 % (26594)Instruction limit reached! 33.13/9.80 % (26594)------------------------------ 33.13/9.80 % (26594)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 33.13/9.80 % (26594)Termination reason: Unknown 33.13/9.80 % (26594)Termination phase: Function definition elimination 33.13/9.80 33.13/9.80 % (26594)Memory used [KB]: 3070 33.13/9.80 % (26594)Time elapsed: 0.178 s 33.13/9.80 % (26594)Instructions burned: 401 (million) 33.13/9.80 % (26594)------------------------------ 33.13/9.80 % (26594)------------------------------ 34.14/9.82 % (26586)Instruction limit reached! 34.14/9.82 % (26586)------------------------------ 34.14/9.82 % (26586)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 34.14/9.83 % (26586)Termination reason: Unknown 34.14/9.83 % (26586)Termination phase: Saturation 34.14/9.83 34.14/9.83 % (26586)Memory used [KB]: 9338 34.14/9.83 % (26586)Time elapsed: 1.268 s 34.14/9.83 % (26586)Instructions burned: 1214 (million) 34.14/9.83 % (26586)------------------------------ 34.14/9.83 % (26586)------------------------------ 34.19/9.83 % (26598)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_26322 for (2306ds/4528Mi) 34.19/9.84 % (26599)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_26322 for (2306ds/1001Mi) 34.19/9.86 % (26596)Instruction limit reached! 34.19/9.86 % (26596)------------------------------ 34.19/9.86 % (26596)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 34.19/9.86 % (26596)Termination reason: Unknown 34.19/9.86 % (26596)Termination phase: Function definition elimination 34.19/9.86 34.19/9.86 % (26596)Memory used [KB]: 2814 34.19/9.86 % (26596)Time elapsed: 0.117 s 34.19/9.86 % (26596)Instructions burned: 283 (million) 34.19/9.86 % (26596)------------------------------ 34.19/9.86 % (26596)------------------------------ 34.19/9.87 % (26600)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_26322 for (2305ds/102Mi) 34.19/9.91 % (26601)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_26322 for (2305ds/952Mi) 34.40/9.94 % (26598)Refutation not found, incomplete strategy 34.40/9.94 % (26598)------------------------------ 34.40/9.94 % (26598)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 34.40/9.94 % (26598)Termination reason: Refutation not found, incomplete strategy 34.40/9.94 34.40/9.94 34.40/9.94 % (26598)Memory used [KB]: 2686 34.40/9.94 % (26598)Time elapsed: 0.126 s 34.40/9.94 % (26598)Instructions burned: 114 (million) 34.40/9.94 % (26598)------------------------------ 34.40/9.94 % (26598)------------------------------ 34.40/9.96 % (26600)Instruction limit reached! 34.40/9.96 % (26600)------------------------------ 34.40/9.96 % (26600)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 34.40/9.96 % (26600)Termination reason: Unknown 34.40/9.96 % (26600)Termination phase: Property scanning 34.40/9.96 34.40/9.96 % (26600)Memory used [KB]: 2686 34.40/9.96 % (26600)Time elapsed: 0.059 s 34.40/9.96 % (26600)Instructions burned: 103 (million) 34.40/9.96 % (26600)------------------------------ 34.40/9.96 % (26600)------------------------------ 34.66/9.98 % (26602)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_26322 for (2304ds/578Mi) 34.66/10.00 % (26603)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_26322 for (2304ds/643Mi) 35.13/10.24 % (26597)Instruction limit reached! 35.13/10.24 % (26597)------------------------------ 35.13/10.24 % (26597)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 35.13/10.24 % (26597)Termination reason: Unknown 35.13/10.24 % (26597)Termination phase: Function definition elimination 35.13/10.24 35.13/10.24 % (26597)Memory used [KB]: 3070 35.13/10.24 % (26597)Time elapsed: 0.301 s 35.13/10.24 % (26597)Instructions burned: 867 (million) 35.13/10.24 % (26597)------------------------------ 35.13/10.24 % (26597)------------------------------ 35.23/10.28 % (26604)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_26322 for (2301ds/865Mi) 35.23/10.32 % (26591)Instruction limit reached! 35.23/10.32 % (26591)------------------------------ 35.23/10.32 % (26591)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 35.23/10.32 % (26591)Termination reason: Unknown 35.23/10.32 % (26591)Termination phase: Function definition elimination 35.23/10.32 35.23/10.32 % (26591)Memory used [KB]: 3070 35.23/10.32 % (26591)Time elapsed: 0.679 s 35.23/10.32 % (26591)Instructions burned: 1670 (million) 35.23/10.32 % (26591)------------------------------ 35.23/10.32 % (26591)------------------------------ 35.23/10.36 % (26605)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_26322 for (2301ds/1174Mi) 36.65/10.47 % (26603)Instruction limit reached! 36.65/10.47 % (26603)------------------------------ 36.65/10.47 % (26603)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 36.65/10.47 % (26599)Instruction limit reached! 36.65/10.47 % (26599)------------------------------ 36.65/10.47 % (26599)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 36.65/10.47 % (26603)Termination reason: Unknown 36.65/10.47 % (26603)Termination phase: Function definition elimination 36.65/10.47 36.65/10.47 % (26603)Memory used [KB]: 3070 36.65/10.47 % (26603)Time elapsed: 0.258 s 36.65/10.47 % (26603)Instructions burned: 645 (million) 36.65/10.47 % (26603)------------------------------ 36.65/10.47 % (26603)------------------------------ 36.65/10.47 % (26599)Termination reason: Unknown 36.65/10.47 % (26599)Termination phase: Function definition elimination 36.65/10.47 36.65/10.47 % (26599)Memory used [KB]: 3070 36.65/10.47 % (26599)Time elapsed: 0.374 s 36.65/10.48 % (26599)Instructions burned: 1002 (million) 36.65/10.48 % (26599)------------------------------ 36.65/10.48 % (26599)------------------------------ 36.65/10.49 % (26602)Instruction limit reached! 36.65/10.49 % (26602)------------------------------ 36.65/10.49 % (26602)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 36.65/10.49 % (26602)Termination reason: Unknown 36.65/10.49 % (26602)Termination phase: Saturation 36.65/10.49 36.65/10.49 % (26602)Memory used [KB]: 8571 36.65/10.49 % (26602)Time elapsed: 0.534 s 36.65/10.49 % (26602)Instructions burned: 579 (million) 36.65/10.49 % (26602)------------------------------ 36.65/10.49 % (26602)------------------------------ 36.65/10.49 % (26607)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on E---3.1_26322 for (2299ds/1201Mi) 36.65/10.52 % (26606)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_26322 for (2299ds/644Mi) 36.92/10.53 % (26608)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_26322 for (2299ds/1046Mi) 36.92/10.54 % (26601)Instruction limit reached! 36.92/10.54 % (26601)------------------------------ 36.92/10.54 % (26601)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 36.92/10.54 % (26601)Termination reason: Unknown 36.92/10.54 % (26601)Termination phase: Function definition elimination 36.92/10.54 36.92/10.54 % (26601)Memory used [KB]: 3070 36.92/10.54 % (26601)Time elapsed: 0.336 s 36.92/10.54 % (26601)Instructions burned: 952 (million) 36.92/10.54 % (26601)------------------------------ 36.92/10.54 % (26601)------------------------------ 37.04/10.58 % (26609)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_26322 for (2298ds/222Mi) 37.37/10.75 % (26609)Instruction limit reached! 37.37/10.75 % (26609)------------------------------ 37.37/10.75 % (26609)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 37.37/10.75 % (26609)Termination reason: Unknown 37.37/10.75 % (26609)Termination phase: Function definition elimination 37.37/10.75 37.37/10.75 % (26609)Memory used [KB]: 3070 37.37/10.75 % (26609)Time elapsed: 0.096 s 37.37/10.75 % (26609)Instructions burned: 223 (million) 37.37/10.75 % (26609)------------------------------ 37.37/10.75 % (26609)------------------------------ 37.37/10.78 % (26604)Instruction limit reached! 37.37/10.78 % (26604)------------------------------ 37.37/10.78 % (26604)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 37.37/10.79 % (26610)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_26322 for (2296ds/68Mi) 37.37/10.79 % (26604)Termination reason: Unknown 37.37/10.79 % (26604)Termination phase: Function definition elimination 37.37/10.79 37.37/10.79 % (26604)Memory used [KB]: 3070 37.37/10.79 % (26604)Time elapsed: 0.349 s 37.37/10.79 % (26604)Instructions burned: 866 (million) 37.37/10.79 % (26604)------------------------------ 37.37/10.79 % (26604)------------------------------ 37.62/10.83 % (26611)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_26322 for (2296ds/454Mi) 37.62/10.85 % (26610)Instruction limit reached! 37.62/10.85 % (26610)------------------------------ 37.62/10.85 % (26610)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 37.62/10.85 % (26610)Termination reason: Unknown 37.62/10.85 % (26610)Termination phase: Property scanning 37.62/10.85 37.62/10.85 % (26610)Memory used [KB]: 2558 37.62/10.85 % (26610)Time elapsed: 0.039 s 37.62/10.85 % (26610)Instructions burned: 69 (million) 37.62/10.85 % (26610)------------------------------ 37.62/10.85 % (26610)------------------------------ 37.73/10.89 % (26612)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_26322 for (2295ds/360Mi) 37.73/10.97 % (26606)Instruction limit reached! 37.73/10.97 % (26606)------------------------------ 37.73/10.97 % (26606)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 37.73/10.97 % (26606)Termination reason: Unknown 37.73/10.97 % (26606)Termination phase: Function definition elimination 37.73/10.97 37.73/10.97 % (26606)Memory used [KB]: 3070 37.73/10.97 % (26606)Time elapsed: 0.279 s 37.73/10.97 % (26606)Instructions burned: 646 (million) 37.73/10.97 % (26606)------------------------------ 37.73/10.97 % (26606)------------------------------ 38.79/11.01 % (26613)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_26322 for (2294ds/157Mi) 38.79/11.04 % (26605)Instruction limit reached! 38.79/11.04 % (26605)------------------------------ 38.79/11.04 % (26605)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 39.00/11.05 % (26605)Termination reason: Unknown 39.00/11.05 % (26605)Termination phase: Function definition elimination 39.00/11.05 39.00/11.05 % (26605)Memory used [KB]: 3070 39.00/11.05 % (26605)Time elapsed: 0.411 s 39.00/11.05 % (26605)Instructions burned: 1175 (million) 39.00/11.05 % (26605)------------------------------ 39.00/11.05 % (26605)------------------------------ 39.00/11.09 % (26614)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_26322 for (2293ds/5061Mi) 39.00/11.10 % (26611)Instruction limit reached! 39.00/11.10 % (26611)------------------------------ 39.00/11.10 % (26611)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 39.00/11.10 % (26611)Termination reason: Unknown 39.00/11.10 % (26611)Termination phase: Function definition elimination 39.00/11.10 39.00/11.10 % (26611)Memory used [KB]: 3070 39.00/11.10 % (26611)Time elapsed: 0.174 s 39.00/11.10 % (26611)Instructions burned: 456 (million) 39.00/11.10 % (26611)------------------------------ 39.00/11.10 % (26611)------------------------------ 39.19/11.12 % (26615)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on E---3.1_26322 for (2293ds/2401Mi) 39.29/11.16 % (26613)Instruction limit reached! 39.29/11.16 % (26613)------------------------------ 39.29/11.16 % (26613)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 39.29/11.16 % (26613)Termination reason: Unknown 39.29/11.16 % (26613)Termination phase: Function definition elimination 39.29/11.16 39.29/11.16 % (26613)Memory used [KB]: 2814 39.29/11.16 % (26613)Time elapsed: 0.103 s 39.29/11.16 % (26613)Instructions burned: 157 (million) 39.29/11.16 % (26613)------------------------------ 39.29/11.16 % (26613)------------------------------ 39.29/11.18 % (26612)Instruction limit reached! 39.29/11.18 % (26612)------------------------------ 39.29/11.18 % (26612)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 39.29/11.18 % (26612)Termination reason: Unknown 39.29/11.18 % (26612)Termination phase: Function definition elimination 39.29/11.18 39.29/11.18 % (26612)Memory used [KB]: 3070 39.29/11.18 % (26612)Time elapsed: 0.201 s 39.29/11.18 % (26612)Instructions burned: 362 (million) 39.29/11.18 % (26612)------------------------------ 39.29/11.18 % (26612)------------------------------ 39.29/11.19 % (26608)Instruction limit reached! 39.29/11.19 % (26608)------------------------------ 39.29/11.19 % (26608)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 39.29/11.19 % (26608)Termination reason: Unknown 39.29/11.19 % (26608)Termination phase: Function definition elimination 39.29/11.19 39.29/11.19 % (26608)Memory used [KB]: 3070 39.29/11.19 % (26608)Time elapsed: 0.359 s 39.29/11.19 % (26608)Instructions burned: 1047 (million) 39.29/11.19 % (26608)------------------------------ 39.29/11.19 % (26608)------------------------------ 39.29/11.19 % (26617)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_26322 for (2292ds/346Mi) 39.29/11.20 % (26616)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on E---3.1_26322 for (2292ds/5798Mi) 39.29/11.22 % (26607)Instruction limit reached! 39.29/11.22 % (26607)------------------------------ 39.29/11.22 % (26607)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 39.29/11.22 % (26607)Termination reason: Unknown 39.29/11.22 % (26607)Termination phase: Function definition elimination 39.29/11.22 39.29/11.22 % (26607)Memory used [KB]: 3070 39.29/11.22 % (26607)Time elapsed: 0.414 s 39.29/11.22 % (26607)Instructions burned: 1202 (million) 39.29/11.22 % (26607)------------------------------ 39.29/11.22 % (26607)------------------------------ 39.29/11.24 % (26618)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_26322 for (2292ds/1321Mi) 39.29/11.24 % (26619)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on E---3.1_26322 for (2291ds/1312Mi) 39.62/11.46 % (26617)Instruction limit reached! 39.62/11.46 % (26617)------------------------------ 39.62/11.46 % (26617)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 39.62/11.46 % (26617)Termination reason: Unknown 39.62/11.46 % (26617)Termination phase: Function definition elimination 39.62/11.46 39.62/11.46 % (26617)Memory used [KB]: 3070 39.62/11.46 % (26617)Time elapsed: 0.149 s 39.62/11.46 % (26617)Instructions burned: 348 (million) 39.62/11.46 % (26617)------------------------------ 39.62/11.46 % (26617)------------------------------ 39.62/11.47 % (26618)Refutation not found, incomplete strategy 39.62/11.47 % (26618)------------------------------ 39.62/11.47 % (26618)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 39.62/11.47 % (26618)Termination reason: Refutation not found, incomplete strategy 39.62/11.47 39.62/11.47 39.62/11.47 % (26618)Memory used [KB]: 3070 39.62/11.47 % (26618)Time elapsed: 0.285 s 39.62/11.47 % (26618)Instructions burned: 222 (million) 39.62/11.47 % (26618)------------------------------ 39.62/11.47 % (26618)------------------------------ 40.73/11.48 % (26621)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_26322 for (2289ds/1897Mi) 40.73/11.50 % (26620)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_26322 for (2289ds/672Mi) 41.06/11.60 % (26621)Refutation not found, incomplete strategy 41.06/11.60 % (26621)------------------------------ 41.06/11.60 % (26621)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 41.06/11.60 % (26621)Termination reason: Refutation not found, incomplete strategy 41.06/11.60 41.06/11.60 41.06/11.60 % (26621)Memory used [KB]: 7675 41.06/11.60 % (26621)Time elapsed: 0.118 s 41.06/11.60 % (26621)Instructions burned: 226 (million) 41.06/11.60 % (26621)------------------------------ 41.06/11.60 % (26621)------------------------------ 41.43/11.65 % (26622)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_26322 for (2288ds/1202Mi) 41.87/11.81 % (26619)Instruction limit reached! 41.87/11.81 % (26619)------------------------------ 41.87/11.81 % (26619)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 41.87/11.81 % (26619)Termination reason: Unknown 41.87/11.81 % (26619)Termination phase: Function definition elimination 41.87/11.81 41.87/11.81 % (26619)Memory used [KB]: 3070 41.87/11.81 % (26619)Time elapsed: 0.417 s 41.87/11.81 % (26619)Instructions burned: 1315 (million) 41.87/11.81 % (26619)------------------------------ 41.87/11.81 % (26619)------------------------------ 42.05/11.86 % (26623)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_26322 for (2286ds/1493Mi) 42.21/11.98 % (26620)Instruction limit reached! 42.21/11.98 % (26620)------------------------------ 42.21/11.98 % (26620)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 42.21/11.98 % (26620)Termination reason: Unknown 42.21/11.98 % (26620)Termination phase: Saturation 42.21/11.98 42.21/11.98 % (26620)Memory used [KB]: 8187 42.21/11.98 % (26620)Time elapsed: 0.506 s 42.21/11.98 % (26620)Instructions burned: 673 (million) 42.21/11.98 % (26620)------------------------------ 42.21/11.98 % (26620)------------------------------ 42.21/11.99 % (26624)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_26322 for (2284ds/7679Mi) 42.71/12.09 % (26623)Refutation not found, incomplete strategy 42.71/12.09 % (26623)------------------------------ 42.71/12.09 % (26623)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 42.71/12.09 % (26623)Termination reason: Refutation not found, incomplete strategy 42.71/12.09 42.71/12.09 42.71/12.09 % (26623)Memory used [KB]: 7803 42.71/12.09 % (26623)Time elapsed: 0.260 s 42.71/12.09 % (26623)Instructions burned: 235 (million) 42.71/12.09 % (26623)------------------------------ 42.71/12.09 % (26623)------------------------------ 43.40/12.13 % (26625)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_26322 for (2283ds/340Mi) 44.36/12.42 % (26625)Instruction limit reached! 44.36/12.42 % (26625)------------------------------ 44.36/12.42 % (26625)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 44.36/12.42 % (26625)Termination reason: Unknown 44.36/12.42 % (26625)Termination phase: Function definition elimination 44.36/12.42 44.36/12.42 % (26625)Memory used [KB]: 2814 44.36/12.42 % (26625)Time elapsed: 0.158 s 44.36/12.42 % (26625)Instructions burned: 340 (million) 44.36/12.42 % (26625)------------------------------ 44.36/12.42 % (26625)------------------------------ 44.36/12.46 % (26626)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_26322 for (2280ds/3672Mi) 44.96/12.52 % (26615)Instruction limit reached! 44.96/12.52 % (26615)------------------------------ 44.96/12.52 % (26615)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 44.96/12.52 % (26615)Termination reason: Unknown 44.96/12.52 % (26615)Termination phase: Function definition elimination 44.96/12.52 44.96/12.52 % (26615)Memory used [KB]: 3070 44.96/12.52 % (26615)Time elapsed: 0.783 s 44.96/12.52 % (26615)Instructions burned: 2403 (million) 44.96/12.52 % (26615)------------------------------ 44.96/12.52 % (26615)------------------------------ 44.96/12.54 % (26627)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_26322 for (2278ds/1535Mi) 46.91/12.94 % (26622)Instruction limit reached! 46.91/12.94 % (26622)------------------------------ 46.91/12.94 % (26622)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 46.91/12.94 % (26622)Termination reason: Unknown 46.91/12.94 % (26622)Termination phase: Saturation 46.91/12.95 46.91/12.95 % (26622)Memory used [KB]: 3965 46.91/12.95 % (26622)Time elapsed: 1.335 s 46.91/12.95 % (26622)Instructions burned: 1203 (million) 46.91/12.95 % (26622)------------------------------ 46.91/12.95 % (26622)------------------------------ 47.33/12.99 % (26628)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_26322 for (2274ds/4637Mi) 47.33/13.03 % (26627)Instruction limit reached! 47.33/13.03 % (26627)------------------------------ 47.33/13.03 % (26627)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 47.33/13.03 % (26627)Termination reason: Unknown 47.33/13.03 % (26627)Termination phase: Function definition elimination 47.33/13.03 47.33/13.03 % (26627)Memory used [KB]: 3070 47.33/13.03 % (26627)Time elapsed: 0.491 s 47.33/13.03 % (26627)Instructions burned: 1537 (million) 47.33/13.03 % (26627)------------------------------ 47.33/13.03 % (26627)------------------------------ 47.33/13.04 % (26629)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_26322 for (2273ds/3174Mi) 49.49/13.49 % (26551)Instruction limit reached! 49.49/13.49 % (26551)------------------------------ 49.49/13.49 % (26551)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 49.49/13.49 % (26551)Termination reason: Unknown 49.49/13.49 % (26551)Termination phase: Saturation 49.49/13.49 49.49/13.49 % (26551)Memory used [KB]: 15223 49.49/13.49 % (26551)Time elapsed: 8.413 s 49.49/13.49 % (26551)Instructions burned: 8250 (million) 49.49/13.49 % (26551)------------------------------ 49.49/13.49 % (26551)------------------------------ 49.93/13.54 % (26630)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_26322 for (2269ds/307Mi) 49.93/13.57 % (26614)Instruction limit reached! 49.93/13.57 % (26614)------------------------------ 49.93/13.57 % (26614)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 49.93/13.57 % (26614)Termination reason: Unknown 49.93/13.57 % (26614)Termination phase: Function definition elimination 49.93/13.57 49.93/13.57 % (26614)Memory used [KB]: 3070 49.93/13.57 % (26614)Time elapsed: 1.650 s 49.93/13.57 % (26614)Instructions burned: 5061 (million) 49.93/13.57 % (26614)------------------------------ 49.93/13.57 % (26614)------------------------------ 50.26/13.59 % (26631)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_26322 for (2268ds/3619Mi) 50.61/13.69 % (26631)Refutation not found, incomplete strategy 50.61/13.69 % (26631)------------------------------ 50.61/13.69 % (26631)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 50.61/13.69 % (26631)Termination reason: Refutation not found, incomplete strategy 50.61/13.69 50.61/13.69 50.61/13.69 % (26631)Memory used [KB]: 7547 50.61/13.69 % (26631)Time elapsed: 0.102 s 50.61/13.69 % (26631)Instructions burned: 214 (million) 50.61/13.69 % (26631)------------------------------ 50.61/13.69 % (26631)------------------------------ 50.61/13.70 % (26632)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_26322 for (2267ds/2325Mi) 50.86/13.77 % (26630)Instruction limit reached! 50.86/13.77 % (26630)------------------------------ 50.86/13.77 % (26630)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 50.86/13.77 % (26630)Termination reason: Unknown 50.86/13.77 % (26630)Termination phase: Function definition elimination 50.86/13.77 50.86/13.77 % (26630)Memory used [KB]: 3070 50.86/13.77 % (26630)Time elapsed: 0.132 s 50.86/13.77 % (26630)Instructions burned: 308 (million) 50.86/13.77 % (26630)------------------------------ 50.86/13.77 % (26630)------------------------------ 51.29/13.82 % (26633)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_26322 for (2266ds/2341Mi) 53.72/14.27 % (26616)Instruction limit reached! 53.72/14.27 % (26616)------------------------------ 53.72/14.27 % (26616)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 53.72/14.27 % (26616)Termination reason: Unknown 53.72/14.27 % (26616)Termination phase: Function definition elimination 53.72/14.27 53.72/14.27 % (26616)Memory used [KB]: 3070 53.72/14.27 % (26616)Time elapsed: 1.855 s 53.72/14.27 % (26616)Instructions burned: 5800 (million) 53.72/14.27 % (26616)------------------------------ 53.72/14.27 % (26616)------------------------------ 53.87/14.32 % (26634)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_26322 for (2261ds/7257Mi) 54.73/14.56 % (26629)Instruction limit reached! 54.73/14.56 % (26629)------------------------------ 54.73/14.56 % (26629)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 54.73/14.56 % (26629)Termination reason: Unknown 54.73/14.56 % (26629)Termination phase: Saturation 54.73/14.56 54.73/14.56 % (26629)Memory used [KB]: 9466 54.73/14.56 % (26629)Time elapsed: 1.520 s 54.73/14.56 % (26629)Instructions burned: 3174 (million) 54.73/14.56 % (26629)------------------------------ 54.73/14.56 % (26629)------------------------------ 55.26/14.60 % (26635)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_26322 for (2258ds/3710Mi) 59.37/15.62 % (26624)Instruction limit reached! 59.37/15.62 % (26624)------------------------------ 59.37/15.62 % (26624)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 59.37/15.62 % (26624)Termination reason: Unknown 59.37/15.62 % (26624)Termination phase: Saturation 59.37/15.62 59.37/15.62 % (26624)Memory used [KB]: 12025 59.37/15.62 % (26624)Time elapsed: 3.632 s 59.37/15.62 % (26624)Instructions burned: 7679 (million) 59.37/15.62 % (26624)------------------------------ 59.37/15.62 % (26624)------------------------------ 59.37/15.64 % (26637)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_26322 for (2247ds/326Mi) 59.76/15.75 % (26632)Instruction limit reached! 59.76/15.75 % (26632)------------------------------ 59.76/15.75 % (26632)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 59.76/15.75 % (26632)Termination reason: Unknown 59.76/15.75 % (26632)Termination phase: Saturation 59.76/15.75 59.76/15.75 % (26632)Memory used [KB]: 10490 59.76/15.75 % (26632)Time elapsed: 2.066 s 59.76/15.75 % (26632)Instructions burned: 2326 (million) 59.76/15.75 % (26632)------------------------------ 59.76/15.75 % (26632)------------------------------ 60.12/15.80 % (26637)Instruction limit reached! 60.12/15.80 % (26637)------------------------------ 60.12/15.80 % (26637)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 60.12/15.80 % (26637)Termination reason: Unknown 60.12/15.80 % (26637)Termination phase: Saturation 60.12/15.80 60.12/15.80 % (26637)Memory used [KB]: 8187 60.12/15.80 % (26637)Time elapsed: 0.163 s 60.12/15.80 % (26637)Instructions burned: 326 (million) 60.12/15.80 % (26637)------------------------------ 60.12/15.80 % (26637)------------------------------ 60.16/15.81 % (26638)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_26322 for (2246ds/1100Mi) 60.16/15.82 % (26639)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_26322 for (2246ds/406Mi) 60.64/16.02 % (26639)Instruction limit reached! 60.64/16.02 % (26639)------------------------------ 60.64/16.02 % (26639)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 60.64/16.02 % (26639)Termination reason: Unknown 60.64/16.02 % (26639)Termination phase: Saturation 60.64/16.02 60.64/16.02 % (26639)Memory used [KB]: 8187 60.64/16.02 % (26639)Time elapsed: 0.201 s 60.64/16.02 % (26639)Instructions burned: 407 (million) 60.64/16.02 % (26639)------------------------------ 60.64/16.02 % (26639)------------------------------ 60.64/16.03 % (26640)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_26322 for (2244ds/1871Mi) 62.60/16.46 % (26633)Instruction limit reached! 62.60/16.46 % (26633)------------------------------ 62.60/16.46 % (26633)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 62.60/16.46 % (26633)Termination reason: Unknown 62.60/16.46 % (26633)Termination phase: Saturation 62.60/16.46 62.60/16.46 % (26633)Memory used [KB]: 12537 62.60/16.46 % (26633)Time elapsed: 2.671 s 62.60/16.46 % (26633)Instructions burned: 2341 (million) 62.60/16.46 % (26633)------------------------------ 62.60/16.46 % (26633)------------------------------ 62.93/16.50 % (26657)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_26322 for (2239ds/1194Mi) 63.24/16.66 % (26626)Instruction limit reached! 63.24/16.66 % (26626)------------------------------ 63.24/16.66 % (26626)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 63.24/16.66 % (26626)Termination reason: Unknown 63.24/16.66 % (26626)Termination phase: Saturation 63.24/16.66 63.24/16.66 % (26626)Memory used [KB]: 14456 63.24/16.66 % (26626)Time elapsed: 4.223 s 63.24/16.66 % (26626)Instructions burned: 3672 (million) 63.24/16.66 % (26626)------------------------------ 63.24/16.66 % (26626)------------------------------ 63.66/16.71 % (26658)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_26322 for (2237ds/474Mi) 63.66/16.77 % (26638)Instruction limit reached! 63.66/16.77 % (26638)------------------------------ 63.66/16.77 % (26638)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 63.66/16.77 % (26638)Termination reason: Unknown 63.66/16.77 % (26638)Termination phase: Function definition elimination 63.66/16.77 63.66/16.77 % (26638)Memory used [KB]: 3070 63.66/16.77 % (26638)Time elapsed: 0.518 s 63.66/16.77 % (26638)Instructions burned: 1101 (million) 63.66/16.77 % (26638)------------------------------ 63.66/16.77 % (26638)------------------------------ 63.90/16.82 % (26659)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_26322 for (2236ds/3115Mi) 64.14/16.90 % (26635)Instruction limit reached! 64.14/16.90 % (26635)------------------------------ 64.14/16.90 % (26635)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 64.14/16.90 % (26635)Termination reason: Unknown 64.14/16.90 % (26635)Termination phase: Function definition elimination 64.14/16.90 64.14/16.90 % (26635)Memory used [KB]: 3070 64.14/16.90 % (26635)Time elapsed: 1.242 s 64.14/16.90 % (26635)Instructions burned: 3711 (million) 64.14/16.90 % (26635)------------------------------ 64.14/16.90 % (26635)------------------------------ 64.14/16.95 % (26660)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_26322 for (2235ds/831Mi) 64.14/17.00 % (26640)Instruction limit reached! 64.14/17.00 % (26640)------------------------------ 64.14/17.00 % (26640)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 64.14/17.00 % (26640)Termination reason: Unknown 64.14/17.00 % (26640)Termination phase: Saturation 64.14/17.00 64.14/17.00 % (26640)Memory used [KB]: 10874 64.14/17.00 % (26640)Time elapsed: 0.966 s 64.14/17.00 % (26640)Instructions burned: 1872 (million) 64.14/17.00 % (26640)------------------------------ 64.14/17.00 % (26640)------------------------------ 64.99/17.02 % (26661)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_26322 for (2234ds/1188Mi) 65.04/17.10 % (26628)Instruction limit reached! 65.04/17.10 % (26628)------------------------------ 65.04/17.10 % (26628)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 65.04/17.10 % (26628)Termination reason: Unknown 65.04/17.10 % (26628)Termination phase: Saturation 65.04/17.10 65.04/17.10 % (26628)Memory used [KB]: 8827 65.04/17.10 % (26628)Time elapsed: 4.129 s 65.04/17.10 % (26628)Instructions burned: 4638 (million) 65.04/17.10 % (26628)------------------------------ 65.04/17.10 % (26628)------------------------------ 65.31/17.12 % (26658)Instruction limit reached! 65.31/17.12 % (26658)------------------------------ 65.31/17.12 % (26658)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 65.31/17.12 % (26658)Termination reason: Unknown 65.31/17.13 % (26658)Termination phase: Function definition elimination 65.31/17.13 65.31/17.13 % (26658)Memory used [KB]: 3070 65.31/17.13 % (26658)Time elapsed: 0.226 s 65.31/17.13 % (26658)Instructions burned: 474 (million) 65.31/17.13 % (26658)------------------------------ 65.31/17.13 % (26658)------------------------------ 65.31/17.14 % (26662)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_26322 for (2233ds/2868Mi) 65.31/17.17 % (26663)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_26322 for (2232ds/1516Mi) 65.76/17.38 % (26657)Instruction limit reached! 65.76/17.38 % (26657)------------------------------ 65.76/17.38 % (26657)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 65.76/17.38 % (26657)Termination reason: Unknown 65.76/17.38 % (26657)Termination phase: Function definition elimination 65.76/17.38 65.76/17.38 % (26657)Memory used [KB]: 3070 65.76/17.38 % (26657)Time elapsed: 0.496 s 65.76/17.38 % (26657)Instructions burned: 1194 (million) 65.76/17.38 % (26657)------------------------------ 65.76/17.38 % (26657)------------------------------ 65.76/17.39 % (26661)Instruction limit reached! 65.76/17.39 % (26661)------------------------------ 65.76/17.39 % (26661)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 65.76/17.39 % (26661)Termination reason: Unknown 65.76/17.39 % (26661)Termination phase: Function definition elimination 65.76/17.39 65.76/17.39 % (26661)Memory used [KB]: 3070 65.76/17.39 % (26661)Time elapsed: 0.379 s 65.76/17.39 % (26661)Instructions burned: 1189 (million) 65.76/17.39 % (26661)------------------------------ 65.76/17.39 % (26661)------------------------------ 66.31/17.41 % (26665)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_26322 for (2230ds/2812Mi) 66.31/17.42 % (26664)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_26322 for (2230ds/2321Mi) 66.43/17.49 % (26660)Instruction limit reached! 66.43/17.49 % (26660)------------------------------ 66.43/17.49 % (26660)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 66.43/17.49 % (26660)Termination reason: Unknown 66.43/17.49 % (26660)Termination phase: Function definition elimination 66.43/17.49 66.43/17.49 % (26660)Memory used [KB]: 3070 66.43/17.49 % (26660)Time elapsed: 0.297 s 66.43/17.49 % (26660)Instructions burned: 834 (million) 66.43/17.49 % (26660)------------------------------ 66.43/17.49 % (26660)------------------------------ 66.43/17.53 % (26666)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on E---3.1_26322 for (2229ds/4604Mi) 69.87/18.32 % (26665)Instruction limit reached! 69.87/18.32 % (26665)------------------------------ 69.87/18.32 % (26665)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 69.87/18.32 % (26665)Termination reason: Unknown 69.87/18.32 % (26665)Termination phase: Function definition elimination 69.87/18.32 69.87/18.32 % (26665)Memory used [KB]: 3070 69.87/18.32 % (26665)Time elapsed: 0.878 s 69.87/18.32 % (26665)Instructions burned: 2814 (million) 69.87/18.32 % (26665)------------------------------ 69.87/18.32 % (26665)------------------------------ 70.26/18.33 % (26667)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_26322 for (2221ds/2678Mi) 72.25/18.85 % (26663)Instruction limit reached! 72.25/18.85 % (26663)------------------------------ 72.25/18.85 % (26663)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 72.25/18.85 % (26663)Termination reason: Unknown 72.25/18.85 % (26663)Termination phase: Saturation 72.25/18.85 72.25/18.85 % (26663)Memory used [KB]: 10106 72.25/18.85 % (26663)Time elapsed: 1.696 s 72.25/18.85 % (26663)Instructions burned: 1517 (million) 72.25/18.85 % (26663)------------------------------ 72.25/18.85 % (26663)------------------------------ 72.25/18.89 % (26662)Instruction limit reached! 72.25/18.89 % (26662)------------------------------ 72.25/18.89 % (26662)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 72.25/18.89 % (26662)Termination reason: Unknown 72.25/18.89 % (26662)Termination phase: Function definition elimination 72.25/18.89 72.25/18.89 % (26662)Memory used [KB]: 3070 72.25/18.89 % (26662)Time elapsed: 0.954 s 72.25/18.89 % (26662)Instructions burned: 2869 (million) 72.25/18.89 % (26662)------------------------------ 72.25/18.89 % (26662)------------------------------ 72.54/18.92 % (26698)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_26322 for (2215ds/643Mi) 72.54/18.94 % (26699)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_26322 for (2215ds/458Mi) 73.02/19.09 % (26664)Instruction limit reached! 73.02/19.09 % (26664)------------------------------ 73.02/19.09 % (26664)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 73.02/19.09 % (26664)Termination reason: Unknown 73.02/19.09 % (26664)Termination phase: Function definition elimination 73.02/19.09 73.02/19.09 % (26664)Memory used [KB]: 3070 73.02/19.09 % (26664)Time elapsed: 1.0000 s 73.02/19.09 % (26664)Instructions burned: 2324 (million) 73.02/19.09 % (26664)------------------------------ 73.02/19.09 % (26664)------------------------------ 73.12/19.10 % (26700)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_26322 for (2213ds/2546Mi) 73.36/19.24 % (26667)Instruction limit reached! 73.36/19.24 % (26667)------------------------------ 73.36/19.24 % (26667)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 73.36/19.24 % (26667)Termination reason: Unknown 73.36/19.24 % (26667)Termination phase: Function definition elimination 73.36/19.24 73.36/19.24 % (26667)Memory used [KB]: 3070 73.36/19.24 % (26667)Time elapsed: 0.890 s 73.36/19.24 % (26667)Instructions burned: 2681 (million) 73.36/19.24 % (26667)------------------------------ 73.36/19.24 % (26667)------------------------------ 73.36/19.25 % (26699)Instruction limit reached! 73.36/19.25 % (26699)------------------------------ 73.36/19.25 % (26699)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 73.36/19.25 % (26699)Termination reason: Unknown 73.36/19.25 % (26699)Termination phase: Function definition elimination 73.36/19.25 73.36/19.25 % (26699)Memory used [KB]: 3070 73.36/19.25 % (26699)Time elapsed: 0.172 s 73.36/19.25 % (26699)Instructions burned: 459 (million) 73.36/19.25 % (26699)------------------------------ 73.36/19.25 % (26699)------------------------------ 73.98/19.28 % (26701)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_26322 for (2211ds/1432Mi) 73.98/19.29 % (26702)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_26322 for (2211ds/386Mi) 74.69/19.55 % (26698)Instruction limit reached! 74.69/19.55 % (26698)------------------------------ 74.69/19.55 % (26698)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 74.69/19.55 % (26698)Termination reason: Unknown 74.69/19.55 % (26698)Termination phase: Function definition elimination 74.69/19.55 74.69/19.55 % (26698)Memory used [KB]: 3070 74.69/19.55 % (26698)Time elapsed: 0.254 s 74.69/19.55 % (26698)Instructions burned: 643 (million) 74.69/19.55 % (26698)------------------------------ 74.69/19.55 % (26698)------------------------------ 74.69/19.56 % (26702)Instruction limit reached! 74.69/19.56 % (26702)------------------------------ 74.69/19.56 % (26702)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 74.69/19.56 % (26702)Termination reason: Unknown 74.69/19.56 % (26702)Termination phase: Function definition elimination 74.69/19.56 74.69/19.56 % (26702)Memory used [KB]: 3070 74.69/19.56 % (26702)Time elapsed: 0.151 s 74.69/19.56 % (26702)Instructions burned: 386 (million) 74.69/19.56 % (26702)------------------------------ 74.69/19.56 % (26702)------------------------------ 74.69/19.57 % (26703)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_26322 for (2208ds/360Mi) 74.95/19.60 % (26704)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_26322 for (2208ds/5446Mi) 74.95/19.63 % (26659)Instruction limit reached! 74.95/19.63 % (26659)------------------------------ 74.95/19.63 % (26659)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 74.95/19.63 % (26659)Termination reason: Unknown 74.95/19.63 % (26659)Termination phase: Function definition elimination 74.95/19.63 74.95/19.63 % (26659)Memory used [KB]: 3070 74.95/19.63 % (26659)Time elapsed: 1.402 s 74.95/19.63 % (26659)Instructions burned: 3116 (million) 74.95/19.63 % (26659)------------------------------ 74.95/19.63 % (26659)------------------------------ 75.32/19.72 % (26705)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_26322 for (2207ds/2573Mi) 76.26/19.92 % (26703)Instruction limit reached! 76.26/19.92 % (26703)------------------------------ 76.26/19.92 % (26703)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 76.26/19.92 % (26703)Termination reason: Unknown 76.26/19.92 % (26703)Termination phase: Function definition elimination 76.26/19.92 76.26/19.92 % (26703)Memory used [KB]: 3070 76.26/19.92 % (26703)Time elapsed: 0.171 s 76.26/19.92 % (26703)Instructions burned: 361 (million) 76.26/19.92 % (26703)------------------------------ 76.26/19.92 % (26703)------------------------------ 76.26/19.95 % (26706)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_26322 for (2204ds/2655Mi) 77.65/20.35 % (26701)Instruction limit reached! 77.65/20.35 % (26701)------------------------------ 77.65/20.35 % (26701)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 77.65/20.35 % (26701)Termination reason: Unknown 77.65/20.35 % (26701)Termination phase: Function definition elimination 77.65/20.35 77.65/20.35 % (26701)Memory used [KB]: 3070 77.65/20.35 % (26701)Time elapsed: 0.581 s 77.65/20.35 % (26701)Instructions burned: 1432 (million) 77.65/20.35 % (26701)------------------------------ 77.65/20.35 % (26701)------------------------------ 77.65/20.40 % (26707)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_26322 for (2200ds/2781Mi) 79.72/20.82 % (26666)Instruction limit reached! 79.72/20.82 % (26666)------------------------------ 79.72/20.82 % (26666)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 79.72/20.82 % (26666)Termination reason: Unknown 79.72/20.82 % (26666)Termination phase: Saturation 79.72/20.82 79.72/20.82 % (26666)Memory used [KB]: 14328 79.72/20.82 % (26666)Time elapsed: 3.324 s 79.72/20.82 % (26666)Instructions burned: 4605 (million) 79.72/20.82 % (26666)------------------------------ 79.72/20.82 % (26666)------------------------------ 79.72/20.83 % (26708)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_26322 for (2195ds/307Mi) 80.12/20.90 % (26700)Instruction limit reached! 80.12/20.90 % (26700)------------------------------ 80.12/20.90 % (26700)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 80.12/20.90 % (26700)Termination reason: Unknown 80.12/20.90 % (26700)Termination phase: Function definition elimination 80.12/20.90 80.12/20.90 % (26700)Memory used [KB]: 3070 80.12/20.90 % (26700)Time elapsed: 1.033 s 80.12/20.90 % (26700)Instructions burned: 2549 (million) 80.12/20.90 % (26700)------------------------------ 80.12/20.90 % (26700)------------------------------ 80.20/20.94 % (26709)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_26322 for (2195ds/1548Mi) 80.20/20.95 % (26708)Instruction limit reached! 80.20/20.95 % (26708)------------------------------ 80.20/20.95 % (26708)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 80.20/20.95 % (26708)Termination reason: Unknown 80.20/20.95 % (26708)Termination phase: Function definition elimination 80.20/20.95 80.20/20.95 % (26708)Memory used [KB]: 3070 80.20/20.95 % (26708)Time elapsed: 0.119 s 80.20/20.95 % (26708)Instructions burned: 308 (million) 80.20/20.95 % (26708)------------------------------ 80.20/20.95 % (26708)------------------------------ 80.20/20.97 % (26710)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_26322 for (2194ds/5214Mi) 82.66/21.52 % (26705)Instruction limit reached! 82.66/21.52 % (26705)------------------------------ 82.66/21.52 % (26705)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 82.66/21.52 % (26705)Termination reason: Unknown 82.66/21.52 % (26705)Termination phase: Function definition elimination 82.66/21.52 82.66/21.52 % (26705)Memory used [KB]: 3070 82.66/21.52 % (26705)Time elapsed: 0.945 s 82.66/21.52 % (26705)Instructions burned: 2575 (million) 82.66/21.52 % (26705)------------------------------ 82.66/21.52 % (26705)------------------------------ 82.74/21.56 % (26712)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on E---3.1_26322 for (2188ds/3201Mi) 82.74/21.60 % (26706)Instruction limit reached! 82.74/21.60 % (26706)------------------------------ 82.74/21.60 % (26706)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 82.74/21.60 % (26706)Termination reason: Unknown 82.74/21.60 % (26706)Termination phase: Function definition elimination 82.74/21.60 82.74/21.60 % (26706)Memory used [KB]: 3070 82.74/21.60 % (26706)Time elapsed: 0.890 s 82.74/21.60 % (26706)Instructions burned: 2657 (million) 82.74/21.60 % (26706)------------------------------ 82.74/21.60 % (26706)------------------------------ 83.05/21.66 % (26713)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_26322 for (2188ds/454Mi) 83.24/21.73 % (26634)Instruction limit reached! 83.24/21.73 % (26634)------------------------------ 83.24/21.73 % (26634)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 83.24/21.73 % (26634)Termination reason: Unknown 83.24/21.73 % (26634)Termination phase: Saturation 83.24/21.73 83.24/21.73 % (26634)Memory used [KB]: 16375 83.24/21.73 % (26634)Time elapsed: 7.443 s 83.24/21.73 % (26634)Instructions burned: 7257 (million) 83.24/21.73 % (26634)------------------------------ 83.24/21.73 % (26634)------------------------------ 83.24/21.75 % (26714)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_26322 for (2186ds/3049Mi) 84.75/22.05 % (26713)Instruction limit reached! 84.75/22.05 % (26713)------------------------------ 84.75/22.05 % (26713)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 84.75/22.05 % (26713)Termination reason: Unknown 84.75/22.05 % (26713)Termination phase: Function definition elimination 84.75/22.05 84.75/22.05 % (26713)Memory used [KB]: 3070 84.75/22.05 % (26713)Time elapsed: 0.181 s 84.75/22.05 % (26713)Instructions burned: 457 (million) 84.75/22.05 % (26713)------------------------------ 84.75/22.05 % (26713)------------------------------ 85.07/22.10 % (26715)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_26322 for (2183ds/7311Mi) 86.14/22.36 % (26707)Instruction limit reached! 86.14/22.36 % (26707)------------------------------ 86.14/22.36 % (26707)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 86.14/22.36 % (26707)Termination reason: Unknown 86.14/22.36 % (26707)Termination phase: Function definition elimination 86.14/22.36 86.14/22.36 % (26707)Memory used [KB]: 3070 86.14/22.36 % (26707)Time elapsed: 1.064 s 86.14/22.36 % (26707)Instructions burned: 2783 (million) 86.14/22.36 % (26707)------------------------------ 86.14/22.36 % (26707)------------------------------ 86.14/22.38 % (26716)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_26322 for (2180ds/6804Mi) 87.02/22.49 % (26716)Refutation not found, incomplete strategy 87.02/22.49 % (26716)------------------------------ 87.02/22.49 % (26716)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 87.02/22.49 % (26716)Termination reason: Refutation not found, incomplete strategy 87.02/22.49 87.02/22.49 87.02/22.49 % (26716)Memory used [KB]: 7547 87.02/22.49 % (26716)Time elapsed: 0.111 s 87.02/22.49 % (26716)Instructions burned: 213 (million) 87.02/22.49 % (26716)------------------------------ 87.02/22.49 % (26716)------------------------------ 87.44/22.51 % (26717)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_26322 for (2179ds/1683Mi) 87.44/22.51 % (26709)Instruction limit reached! 87.44/22.51 % (26709)------------------------------ 87.44/22.51 % (26709)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 87.44/22.51 % (26709)Termination reason: Unknown 87.44/22.51 % (26709)Termination phase: Saturation 87.44/22.51 87.44/22.51 % (26709)Memory used [KB]: 11641 87.44/22.51 % (26709)Time elapsed: 1.589 s 87.44/22.51 % (26709)Instructions burned: 1548 (million) 87.44/22.51 % (26709)------------------------------ 87.44/22.51 % (26709)------------------------------ 87.66/22.56 % (26718)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_26322 for (2179ds/4688Mi) 87.66/22.59 % (26710)Instruction limit reached! 87.66/22.59 % (26710)------------------------------ 87.66/22.59 % (26710)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 87.66/22.59 % (26710)Termination reason: Unknown 87.66/22.59 % (26710)Termination phase: Function definition elimination 87.66/22.59 87.66/22.59 % (26710)Memory used [KB]: 3070 87.66/22.59 % (26710)Time elapsed: 1.623 s 87.66/22.59 % (26710)Instructions burned: 5215 (million) 87.66/22.59 % (26710)------------------------------ 87.66/22.59 % (26710)------------------------------ 87.66/22.63 % (26719)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on E---3.1_26322 for (2178ds/2207Mi) 87.95/22.67 % (26712)Instruction limit reached! 87.95/22.67 % (26712)------------------------------ 87.95/22.67 % (26712)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 87.95/22.67 % (26712)Termination reason: Unknown 87.95/22.67 % (26712)Termination phase: Function definition elimination 87.95/22.68 87.95/22.68 % (26712)Memory used [KB]: 3070 87.95/22.68 % (26712)Time elapsed: 0.986 s 87.95/22.68 % (26712)Instructions burned: 3202 (million) 87.95/22.68 % (26712)------------------------------ 87.95/22.68 % (26712)------------------------------ 88.05/22.71 % (26720)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_26322 for (2177ds/8216Mi) 88.23/22.81 % (26714)Instruction limit reached! 88.23/22.81 % (26714)------------------------------ 88.23/22.81 % (26714)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 88.23/22.81 % (26714)Termination reason: Unknown 88.23/22.81 % (26714)Termination phase: Function definition elimination 88.23/22.81 88.23/22.81 % (26714)Memory used [KB]: 3070 88.23/22.81 % (26714)Time elapsed: 0.963 s 88.23/22.81 % (26714)Instructions burned: 3049 (million) 88.23/22.81 % (26714)------------------------------ 88.23/22.81 % (26714)------------------------------ 88.23/22.85 % (26721)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_26322 for (2176ds/430Mi) 89.63/23.12 % (26721)Instruction limit reached! 89.63/23.12 % (26721)------------------------------ 89.63/23.12 % (26721)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 89.96/23.13 % (26721)Termination reason: Unknown 89.96/23.13 % (26721)Termination phase: Function definition elimination 89.96/23.13 89.96/23.13 % (26721)Memory used [KB]: 3070 89.96/23.13 % (26721)Time elapsed: 0.155 s 89.96/23.13 % (26721)Instructions burned: 430 (million) 89.96/23.13 % (26721)------------------------------ 89.96/23.13 % (26721)------------------------------ 89.96/23.17 % (26722)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_26322 for (2172ds/2012Mi) 91.07/23.42 % (26719)Instruction limit reached! 91.07/23.42 % (26719)------------------------------ 91.07/23.42 % (26719)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 91.07/23.42 % (26719)Termination reason: Unknown 91.07/23.42 % (26719)Termination phase: Function definition elimination 91.07/23.42 91.07/23.42 % (26719)Memory used [KB]: 3070 91.07/23.42 % (26719)Time elapsed: 0.715 s 91.07/23.42 % (26719)Instructions burned: 2208 (million) 91.07/23.42 % (26719)------------------------------ 91.07/23.42 % (26719)------------------------------ 91.07/23.44 % (26723)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_26322 for (2169ds/631Mi) 91.93/23.62 % (26704)Instruction limit reached! 91.93/23.62 % (26704)------------------------------ 91.93/23.62 % (26704)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 91.93/23.62 % (26704)Termination reason: Unknown 91.93/23.62 % (26704)Termination phase: Function definition elimination 91.93/23.62 91.93/23.62 % (26704)Memory used [KB]: 3070 91.93/23.62 % (26704)Time elapsed: 1.998 s 91.93/23.62 % (26704)Instructions burned: 5446 (million) 91.93/23.62 % (26704)------------------------------ 91.93/23.62 % (26704)------------------------------ 91.93/23.66 % (26723)Instruction limit reached! 91.93/23.66 % (26723)------------------------------ 91.93/23.66 % (26723)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 91.93/23.66 % (26723)Termination reason: Unknown 91.93/23.66 % (26723)Termination phase: Function definition elimination 91.93/23.66 91.93/23.66 % (26723)Memory used [KB]: 3070 91.93/23.66 % (26723)Time elapsed: 0.204 s 91.93/23.66 % (26723)Instructions burned: 632 (million) 91.93/23.66 % (26723)------------------------------ 91.93/23.66 % (26723)------------------------------ 91.93/23.66 % (26724)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_26322 for (2168ds/8785Mi) 92.20/23.72 % (26725)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_26322 for (2167ds/739Mi) 95.33/24.40 % (26717)Instruction limit reached! 95.33/24.40 % (26717)------------------------------ 95.33/24.40 % (26717)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 95.33/24.40 % (26717)Termination reason: Unknown 95.33/24.40 % (26717)Termination phase: Saturation 95.33/24.40 95.33/24.40 % (26717)Memory used [KB]: 10362 95.33/24.40 % (26717)Time elapsed: 1.888 s 95.33/24.40 % (26717)Instructions burned: 1683 (million) 95.33/24.40 % (26717)------------------------------ 95.33/24.40 % (26717)------------------------------ 95.33/24.44 % (26726)dis+1002_1:1024_fe=off:hud=5:prag=on:i=5473:si=on:rtra=on_0 on E---3.1_26322 for (2160ds/5473Mi) 95.95/24.60 % (26725)Instruction limit reached! 95.95/24.60 % (26725)------------------------------ 95.95/24.60 % (26725)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 95.95/24.60 % (26725)Termination reason: Unknown 95.95/24.60 % (26725)Termination phase: Saturation 95.95/24.60 95.95/24.60 % (26725)Memory used [KB]: 8699 95.95/24.60 % (26725)Time elapsed: 0.936 s 95.95/24.60 % (26725)Instructions burned: 740 (million) 95.95/24.60 % (26725)------------------------------ 95.95/24.60 % (26725)------------------------------ 96.40/24.64 % (26727)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_26322 for (2158ds/43570Mi) 96.40/24.66 % (26722)Instruction limit reached! 96.40/24.66 % (26722)------------------------------ 96.40/24.66 % (26722)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 96.40/24.66 % (26722)Termination reason: Unknown 96.40/24.66 % (26722)Termination phase: Function definition elimination 96.40/24.66 96.40/24.66 % (26722)Memory used [KB]: 3070 96.40/24.66 % (26722)Time elapsed: 0.682 s 96.40/24.66 % (26722)Instructions burned: 2014 (million) 96.40/24.66 % (26722)------------------------------ 96.40/24.66 % (26722)------------------------------ 96.73/24.71 % (26728)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_26322 for (2157ds/8382Mi) 96.73/24.74 % (26727)Refutation not found, incomplete strategy 96.73/24.74 % (26727)------------------------------ 96.73/24.74 % (26727)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 96.73/24.74 % (26727)Termination reason: Refutation not found, incomplete strategy 96.73/24.74 96.73/24.74 96.73/24.74 % (26727)Memory used [KB]: 7164 96.73/24.74 % (26727)Time elapsed: 0.134 s 96.73/24.74 % (26727)Instructions burned: 115 (million) 96.73/24.74 % (26727)------------------------------ 96.73/24.74 % (26727)------------------------------ 97.10/24.78 % (26729)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_26322 for (2156ds/407Mi) 98.77/25.08 % (26729)Instruction limit reached! 98.77/25.08 % (26729)------------------------------ 98.77/25.08 % (26729)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 98.77/25.08 % (26729)Termination reason: Unknown 98.77/25.08 % (26729)Termination phase: Function definition elimination 98.77/25.08 98.77/25.08 % (26729)Memory used [KB]: 2814 98.77/25.08 % (26729)Time elapsed: 0.204 s 98.77/25.08 % (26729)Instructions burned: 407 (million) 98.77/25.08 % (26729)------------------------------ 98.77/25.08 % (26729)------------------------------ 98.77/25.13 % (26730)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_26322 for (2153ds/2971Mi) 99.27/25.19 % (26718)Instruction limit reached! 99.27/25.19 % (26718)------------------------------ 99.27/25.19 % (26718)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 99.27/25.19 % (26718)Termination reason: Unknown 99.27/25.19 % (26718)Termination phase: Function definition elimination 99.27/25.19 99.27/25.19 % (26718)Memory used [KB]: 3070 99.27/25.19 % (26718)Time elapsed: 1.737 s 99.27/25.19 % (26718)Instructions burned: 4690 (million) 99.27/25.19 % (26718)------------------------------ 99.27/25.19 % (26718)------------------------------ 99.52/25.24 % (26731)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_26322 for (2152ds/9822Mi) 100.81/25.49 % (26731)Refutation not found, incomplete strategy 100.81/25.49 % (26731)------------------------------ 100.81/25.49 % (26731)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 100.81/25.49 % (26731)Termination reason: Refutation not found, incomplete strategy 100.81/25.49 100.81/25.49 100.81/25.49 % (26731)Memory used [KB]: 7675 100.81/25.49 % (26731)Time elapsed: 0.298 s 100.81/25.49 % (26731)Instructions burned: 239 (million) 100.81/25.49 % (26731)------------------------------ 100.81/25.49 % (26731)------------------------------ 100.95/25.54 % (26732)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_26322 for (2149ds/8425Mi) 107.59/26.84 % (26715)Instruction limit reached! 107.59/26.84 % (26715)------------------------------ 107.59/26.84 % (26715)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 107.59/26.84 % (26715)Termination reason: Unknown 107.59/26.84 % (26715)Termination phase: Saturation 107.59/26.84 107.59/26.84 % (26715)Memory used [KB]: 20724 107.59/26.84 % (26715)Time elapsed: 4.770 s 107.59/26.84 % (26715)Instructions burned: 7312 (million) 107.59/26.84 % (26715)------------------------------ 107.59/26.84 % (26715)------------------------------ 107.93/26.89 % (26733)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_26322 for (2135ds/3107Mi) 107.93/26.96 % (26730)Instruction limit reached! 107.93/26.96 % (26730)------------------------------ 107.93/26.96 % (26730)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 107.93/26.96 % (26730)Termination reason: Unknown 107.93/26.96 % (26730)Termination phase: Function definition elimination 107.93/26.96 107.93/26.96 % (26730)Memory used [KB]: 3070 107.93/26.96 % (26730)Time elapsed: 1.127 s 107.93/26.96 % (26730)Instructions burned: 2972 (million) 107.93/26.96 % (26730)------------------------------ 107.93/26.96 % (26730)------------------------------ 108.47/27.03 % (26720)Instruction limit reached! 108.47/27.03 % (26720)------------------------------ 108.47/27.03 % (26720)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 108.47/27.03 % (26720)Termination reason: Unknown 108.47/27.03 % (26720)Termination phase: Saturation 108.47/27.03 108.47/27.03 % (26720)Memory used [KB]: 15863 108.47/27.03 % (26720)Time elapsed: 4.346 s 108.47/27.03 % (26720)Instructions burned: 8216 (million) 108.47/27.03 % (26720)------------------------------ 108.47/27.03 % (26720)------------------------------ 108.55/27.04 % (26734)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_26322 for (2134ds/7967Mi) 108.55/27.09 % (26735)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_26322 for (2133ds/3629Mi) 110.02/27.44 % (26728)Instruction limit reached! 110.02/27.44 % (26728)------------------------------ 110.02/27.44 % (26728)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 110.02/27.44 % (26728)Termination reason: Unknown 110.02/27.44 % (26728)Termination phase: Function definition elimination 110.02/27.44 110.02/27.44 % (26728)Memory used [KB]: 3070 110.02/27.44 % (26728)Time elapsed: 2.571 s 110.02/27.44 % (26728)Instructions burned: 8383 (million) 110.02/27.44 % (26728)------------------------------ 110.02/27.44 % (26728)------------------------------ 110.32/27.51 % (26736)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_26322 for (2129ds/939Mi) 110.69/27.67 % (26726)Instruction limit reached! 110.69/27.67 % (26726)------------------------------ 110.69/27.67 % (26726)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 110.69/27.67 % (26726)Termination reason: Unknown 110.69/27.67 % (26726)Termination phase: Function definition elimination 110.69/27.67 110.69/27.67 % (26726)Memory used [KB]: 3070 110.69/27.67 % (26726)Time elapsed: 1.739 s 110.69/27.67 % (26726)Instructions burned: 5473 (million) 110.69/27.67 % (26726)------------------------------ 110.69/27.67 % (26726)------------------------------ 110.69/27.69 % (26737)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_26322 for (2127ds/1188Mi) 111.42/27.88 % (26724)Instruction limit reached! 111.42/27.88 % (26724)------------------------------ 111.42/27.88 % (26724)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 111.42/27.88 % (26724)Termination reason: Unknown 111.42/27.88 % (26724)Termination phase: Function definition elimination 111.42/27.88 111.42/27.88 % (26724)Memory used [KB]: 3070 111.42/27.88 % (26724)Time elapsed: 2.721 s 111.42/27.88 % (26724)Instructions burned: 8786 (million) 111.42/27.88 % (26724)------------------------------ 111.42/27.88 % (26724)------------------------------ 111.42/27.90 % (26738)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_26322 for (2125ds/3205Mi) 112.08/28.07 % (26737)Instruction limit reached! 112.08/28.07 % (26737)------------------------------ 112.08/28.07 % (26737)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 112.08/28.07 % (26737)Termination reason: Unknown 112.08/28.07 % (26737)Termination phase: Function definition elimination 112.08/28.07 112.08/28.07 % (26737)Memory used [KB]: 3070 112.08/28.07 % (26737)Time elapsed: 0.376 s 112.08/28.07 % (26737)Instructions burned: 1190 (million) 112.08/28.07 % (26737)------------------------------ 112.08/28.07 % (26737)------------------------------ 112.37/28.13 % (26739)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_26322 for (2123ds/865Mi) 113.85/28.44 % (26739)Instruction limit reached! 113.85/28.44 % (26739)------------------------------ 113.85/28.44 % (26739)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 113.85/28.44 % (26739)Termination reason: Unknown 113.85/28.44 % (26739)Termination phase: Function definition elimination 113.85/28.44 113.85/28.44 % (26739)Memory used [KB]: 3070 113.85/28.44 % (26739)Time elapsed: 0.318 s 113.85/28.44 % (26739)Instructions burned: 866 (million) 113.85/28.44 % (26739)------------------------------ 113.85/28.44 % (26739)------------------------------ 113.85/28.44 % (26736)Instruction limit reached! 113.85/28.44 % (26736)------------------------------ 113.85/28.44 % (26736)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 113.85/28.44 % (26736)Termination reason: Unknown 113.85/28.44 % (26736)Termination phase: Function definition elimination 113.85/28.44 113.85/28.44 % (26736)Memory used [KB]: 3070 113.85/28.44 % (26736)Time elapsed: 0.346 s 113.85/28.44 % (26736)Instructions burned: 941 (million) 113.85/28.44 % (26736)------------------------------ 113.85/28.44 % (26736)------------------------------ 113.85/28.48 % (26741)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_26322 for (2119ds/4165Mi) 113.85/28.48 % (26740)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_26322 for (2119ds/7469Mi) 115.15/28.85 % (26738)Instruction limit reached! 115.15/28.85 % (26738)------------------------------ 115.15/28.85 % (26738)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 115.15/28.85 % (26738)Termination reason: Unknown 115.15/28.85 % (26738)Termination phase: Function definition elimination 115.15/28.85 115.15/28.85 % (26738)Memory used [KB]: 3070 115.15/28.85 % (26738)Time elapsed: 0.953 s 115.15/28.85 % (26738)Instructions burned: 3205 (million) 115.15/28.85 % (26738)------------------------------ 115.15/28.85 % (26738)------------------------------ 115.37/28.88 % (26733)Instruction limit reached! 115.37/28.88 % (26733)------------------------------ 115.37/28.88 % (26733)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 115.37/28.88 % (26733)Termination reason: Unknown 115.37/28.88 % (26733)Termination phase: Function definition elimination 115.37/28.88 115.37/28.88 % (26733)Memory used [KB]: 3070 115.37/28.88 % (26733)Time elapsed: 1.194 s 115.37/28.88 % (26733)Instructions burned: 3107 (million) 115.37/28.88 % (26733)------------------------------ 115.37/28.88 % (26733)------------------------------ 115.37/28.88 % (26742)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_26322 for (2115ds/13468Mi) 115.37/28.92 % (26743)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_26322 for (2115ds/2635Mi) 120.17/29.77 % (26743)Instruction limit reached! 120.17/29.77 % (26743)------------------------------ 120.17/29.77 % (26743)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 120.17/29.77 % (26743)Termination reason: Unknown 120.17/29.77 % (26743)Termination phase: Function definition elimination 120.17/29.77 120.17/29.77 % (26743)Memory used [KB]: 3070 120.17/29.77 % (26743)Time elapsed: 0.805 s 120.17/29.77 % (26743)Instructions burned: 2637 (million) 120.17/29.77 % (26743)------------------------------ 120.17/29.77 % (26743)------------------------------ 120.17/29.81 % (26744)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_26322 for (2106ds/631Mi) 120.17/29.85 % (26735)Instruction limit reached! 120.17/29.85 % (26735)------------------------------ 120.17/29.85 % (26735)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 120.17/29.85 % (26735)Termination reason: Unknown 120.17/29.85 % (26735)Termination phase: Function definition elimination 120.17/29.85 120.17/29.85 % (26735)Memory used [KB]: 3198 120.17/29.85 % (26735)Time elapsed: 1.492 s 120.17/29.85 % (26735)Instructions burned: 3630 (million) 120.17/29.85 % (26735)------------------------------ 120.17/29.85 % (26735)------------------------------ 120.70/29.90 % (26745)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_26322 for (2105ds/15557Mi) 122.42/30.24 % (26744)Instruction limit reached! 122.42/30.24 % (26744)------------------------------ 122.42/30.24 % (26744)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 122.42/30.24 % (26744)Termination reason: Unknown 122.42/30.24 % (26744)Termination phase: Function definition elimination 122.42/30.24 122.42/30.24 % (26744)Memory used [KB]: 3070 122.42/30.24 % (26744)Time elapsed: 0.223 s 122.42/30.24 % (26744)Instructions burned: 631 (million) 122.42/30.24 % (26744)------------------------------ 122.42/30.24 % (26744)------------------------------ 122.42/30.28 % (26746)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_26322 for (2101ds/2142Mi) 124.71/30.75 % (26732)Instruction limit reached! 124.71/30.75 % (26732)------------------------------ 124.71/30.75 % (26732)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 124.71/30.75 % (26732)Termination reason: Unknown 124.71/30.75 % (26732)Termination phase: Function definition elimination 124.71/30.75 124.71/30.75 % (26732)Memory used [KB]: 3070 124.71/30.75 % (26732)Time elapsed: 2.873 s 124.71/30.75 % (26732)Instructions burned: 8425 (million) 124.71/30.75 % (26732)------------------------------ 124.71/30.75 % (26732)------------------------------ 125.18/30.80 % (26747)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_26322 for (2096ds/5624Mi) 125.25/30.85 % (26741)Instruction limit reached! 125.25/30.85 % (26741)------------------------------ 125.25/30.85 % (26741)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 125.25/30.85 % (26741)Termination reason: Unknown 125.25/30.85 % (26741)Termination phase: Saturation 125.25/30.85 125.25/30.85 % (26741)Memory used [KB]: 16119 125.25/30.85 % (26741)Time elapsed: 2.401 s 125.25/30.85 % (26741)Instructions burned: 4165 (million) 125.25/30.85 % (26741)------------------------------ 125.25/30.85 % (26741)------------------------------ 125.25/30.86 % (26748)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_26322 for (2095ds/1665Mi) 127.28/31.22 % (26734)Instruction limit reached! 127.28/31.22 % (26734)------------------------------ 127.28/31.22 % (26734)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 127.28/31.22 % (26734)Termination reason: Unknown 127.28/31.22 % (26734)Termination phase: Function definition elimination 127.28/31.22 127.28/31.22 % (26734)Memory used [KB]: 3070 127.28/31.22 % (26734)Time elapsed: 2.475 s 127.28/31.22 % (26734)Instructions burned: 7970 (million) 127.28/31.22 % (26734)------------------------------ 127.28/31.22 % (26734)------------------------------ 127.28/31.26 % (26749)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_26322 for (2091ds/64912Mi) 127.95/31.47 % (26748)Instruction limit reached! 127.95/31.47 % (26748)------------------------------ 127.95/31.47 % (26748)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 127.95/31.47 % (26748)Termination reason: Unknown 127.95/31.47 % (26748)Termination phase: Function definition elimination 127.95/31.47 127.95/31.47 % (26748)Memory used [KB]: 3070 127.95/31.47 % (26748)Time elapsed: 0.603 s 127.95/31.47 % (26748)Instructions burned: 1667 (million) 127.95/31.47 % (26748)------------------------------ 127.95/31.47 % (26748)------------------------------ 127.95/31.48 % (26750)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_26322 for (2089ds/7801Mi) 131.31/32.29 % (26740)Instruction limit reached! 131.31/32.29 % (26740)------------------------------ 131.31/32.29 % (26740)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 131.31/32.29 % (26740)Termination reason: Unknown 131.31/32.29 % (26740)Termination phase: Function definition elimination 131.31/32.29 131.31/32.29 % (26740)Memory used [KB]: 3070 131.31/32.29 % (26740)Time elapsed: 2.692 s 131.31/32.29 % (26740)Instructions burned: 7470 (million) 131.31/32.29 % (26740)------------------------------ 131.31/32.29 % (26740)------------------------------ 131.61/32.34 % (26751)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_26322 for (2081ds/15194Mi) 131.84/32.43 % (26746)Instruction limit reached! 131.84/32.43 % (26746)------------------------------ 131.84/32.43 % (26746)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 131.84/32.43 % (26746)Termination reason: Unknown 131.84/32.43 % (26746)Termination phase: Saturation 131.84/32.43 131.84/32.43 % (26746)Memory used [KB]: 12281 131.84/32.43 % (26746)Time elapsed: 2.194 s 131.84/32.43 % (26746)Instructions burned: 2143 (million) 131.84/32.43 % (26746)------------------------------ 131.84/32.43 % (26746)------------------------------ 131.84/32.47 % (26752)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_26322 for (2079ds/6753Mi) 133.06/32.69 % (26752)Refutation not found, incomplete strategy 133.06/32.69 % (26752)------------------------------ 133.06/32.69 % (26752)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 133.06/32.69 % (26752)Termination reason: Refutation not found, incomplete strategy 133.06/32.69 133.06/32.69 133.06/32.69 % (26752)Memory used [KB]: 7675 133.06/32.69 % (26752)Time elapsed: 0.246 s 133.06/32.69 % (26752)Instructions burned: 225 (million) 133.06/32.69 % (26752)------------------------------ 133.06/32.69 % (26752)------------------------------ 133.33/32.75 % (26753)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_26322 for (2077ds/1003Mi) 137.13/33.69 % (26753)Instruction limit reached! 137.13/33.69 % (26753)------------------------------ 137.13/33.69 % (26753)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 137.13/33.69 % (26753)Termination reason: Unknown 137.13/33.69 % (26753)Termination phase: Function definition elimination 137.13/33.70 137.13/33.70 % (26753)Memory used [KB]: 3070 137.13/33.70 % (26753)Time elapsed: 0.359 s 137.13/33.70 % (26753)Instructions burned: 1006 (million) 137.13/33.70 % (26753)------------------------------ 137.13/33.70 % (26753)------------------------------ 137.50/33.74 % (26754)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_26322 for (2067ds/13018Mi) 144.49/35.04 % (26747)Instruction limit reached! 144.49/35.04 % (26747)------------------------------ 144.49/35.04 % (26747)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 144.49/35.04 % (26747)Termination reason: Unknown 144.49/35.04 % (26747)Termination phase: Saturation 144.49/35.04 144.49/35.04 % (26747)Memory used [KB]: 9978 144.49/35.04 % (26747)Time elapsed: 4.301 s 144.49/35.04 % (26747)Instructions burned: 5625 (million) 144.49/35.04 % (26747)------------------------------ 144.49/35.04 % (26747)------------------------------ 144.49/35.06 % (26755)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_26322 for (2053ds/1267Mi) 148.55/35.68 % (26755)Instruction limit reached! 148.55/35.68 % (26755)------------------------------ 148.55/35.68 % (26755)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 148.55/35.68 % (26755)Termination reason: Unknown 148.55/35.68 % (26755)Termination phase: Saturation 148.55/35.68 148.55/35.68 % (26755)Memory used [KB]: 9850 148.55/35.68 % (26755)Time elapsed: 0.626 s 148.55/35.68 % (26755)Instructions burned: 1268 (million) 148.55/35.68 % (26755)------------------------------ 148.55/35.68 % (26755)------------------------------ 148.55/35.73 % (26745)Instruction limit reached! 148.55/35.73 % (26745)------------------------------ 148.55/35.73 % (26745)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 148.55/35.73 % (26745)Termination reason: Unknown 148.55/35.73 % (26745)Termination phase: Function definition elimination 148.55/35.73 148.55/35.73 % (26745)Memory used [KB]: 3198 148.55/35.73 % (26745)Time elapsed: 4.708 s 148.55/35.73 % (26745)Instructions burned: 15559 (million) 148.55/35.73 % (26745)------------------------------ 148.55/35.73 % (26745)------------------------------ 148.55/35.73 % (26756)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_26322 for (2047ds/2570Mi) 148.55/35.74 % (26757)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=13163:si=on:rtra=on_0 on E---3.1_26322 for (2046ds/13163Mi) 149.22/35.85 % (26750)Instruction limit reached! 149.22/35.85 % (26750)------------------------------ 149.22/35.85 % (26750)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 149.22/35.85 % (26750)Termination reason: Unknown 149.22/35.85 % (26750)Termination phase: Saturation 149.22/35.85 149.22/35.85 % (26750)Memory used [KB]: 26353 149.22/35.85 % (26750)Time elapsed: 4.369 s 149.22/35.85 % (26750)Instructions burned: 7802 (million) 149.22/35.85 % (26750)------------------------------ 149.22/35.85 % (26750)------------------------------ 149.43/35.92 % (26758)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_26322 for (2045ds/5087Mi) 155.19/37.09 % (26758)Refutation not found, incomplete strategy 155.19/37.09 % (26758)------------------------------ 155.19/37.09 % (26758)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 155.19/37.09 % (26758)Termination reason: Refutation not found, incomplete strategy 155.19/37.09 155.19/37.09 155.19/37.09 % (26758)Memory used [KB]: 9210 155.19/37.09 % (26758)Time elapsed: 1.229 s 155.19/37.09 % (26758)Instructions burned: 1146 (million) 155.19/37.09 % (26758)------------------------------ 155.19/37.09 % (26758)------------------------------ 155.45/37.14 % (26759)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_26322 for (2033ds/10380Mi) 156.13/37.29 % (26759)Refutation not found, incomplete strategy 156.13/37.29 % (26759)------------------------------ 156.13/37.29 % (26759)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 156.13/37.29 % (26759)Termination reason: Refutation not found, incomplete strategy 156.13/37.29 156.13/37.29 156.13/37.29 % (26759)Memory used [KB]: 7547 156.13/37.29 % (26759)Time elapsed: 0.180 s 156.13/37.29 % (26759)Instructions burned: 159 (million) 156.13/37.29 % (26759)------------------------------ 156.13/37.29 % (26759)------------------------------ 156.45/37.34 % (26760)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_26322 for (2031ds/4218Mi) 156.79/37.44 % (26756)Instruction limit reached! 156.79/37.44 % (26756)------------------------------ 156.79/37.44 % (26756)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 156.79/37.44 % (26756)Termination reason: Unknown 156.79/37.44 % (26756)Termination phase: Function definition elimination 156.79/37.44 156.79/37.44 % (26756)Memory used [KB]: 3070 156.79/37.44 % (26756)Time elapsed: 0.907 s 156.79/37.44 % (26756)Instructions burned: 2571 (million) 156.79/37.44 % (26756)------------------------------ 156.79/37.44 % (26756)------------------------------ 156.79/37.46 % (26761)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_26322 for (2029ds/3971Mi) 160.51/38.02 % (26742)Instruction limit reached! 160.51/38.02 % (26742)------------------------------ 160.51/38.02 % (26742)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 160.51/38.02 % (26742)Termination reason: Unknown 160.51/38.02 % (26742)Termination phase: Saturation 160.51/38.02 160.51/38.02 % (26742)Memory used [KB]: 25841 160.51/38.02 % (26742)Time elapsed: 9.164 s 160.51/38.02 % (26742)Instructions burned: 13469 (million) 160.51/38.02 % (26742)------------------------------ 160.51/38.02 % (26742)------------------------------ 160.51/38.04 % (26762)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_26322 for (2024ds/14014Mi) 161.24/38.13 % (26754)Instruction limit reached! 161.24/38.13 % (26754)------------------------------ 161.24/38.13 % (26754)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 161.24/38.13 % (26754)Termination reason: Unknown 161.24/38.13 % (26754)Termination phase: Function definition elimination 161.24/38.13 161.24/38.13 % (26754)Memory used [KB]: 3070 161.24/38.13 % (26754)Time elapsed: 3.914 s 161.24/38.13 % (26754)Instructions burned: 13019 (million) 161.24/38.13 % (26754)------------------------------ 161.24/38.13 % (26754)------------------------------ 161.24/38.18 % (26763)lrs+10_1:1_ins=1:sgt=8:ss=axioms:i=8517:si=on:rtra=on_0 on E---3.1_26322 for (2022ds/8517Mi) 166.09/38.99 % (26761)Instruction limit reached! 166.09/38.99 % (26761)------------------------------ 166.09/38.99 % (26761)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 166.09/38.99 % (26761)Termination reason: Unknown 166.09/38.99 % (26761)Termination phase: Function definition elimination 166.09/38.99 166.09/38.99 % (26761)Memory used [KB]: 3070 166.09/38.99 % (26761)Time elapsed: 1.338 s 166.09/38.99 % (26761)Instructions burned: 3974 (million) 166.09/38.99 % (26761)------------------------------ 166.09/38.99 % (26761)------------------------------ 166.15/39.02 % (26764)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=10148:si=on:rtra=on_0 on E---3.1_26322 for (2014ds/10148Mi) 168.68/39.48 % (26760)Instruction limit reached! 168.68/39.48 % (26760)------------------------------ 168.68/39.48 % (26760)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 168.68/39.48 % (26760)Termination reason: Unknown 168.68/39.48 % (26760)Termination phase: Saturation 168.68/39.48 168.68/39.48 % (26760)Memory used [KB]: 14967 168.68/39.48 % (26760)Time elapsed: 2.187 s 168.68/39.48 % (26760)Instructions burned: 4218 (million) 168.68/39.48 % (26760)------------------------------ 168.68/39.48 % (26760)------------------------------ 169.18/39.53 % (26765)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_26322 for (2009ds/9078Mi) 172.89/40.29 % (26757)Instruction limit reached! 172.89/40.29 % (26757)------------------------------ 172.89/40.29 % (26757)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 172.89/40.29 % (26757)Termination reason: Unknown 172.89/40.29 % (26757)Termination phase: Function definition elimination 172.89/40.29 172.89/40.29 % (26757)Memory used [KB]: 3070 172.89/40.29 % (26757)Time elapsed: 4.547 s 172.89/40.29 % (26757)Instructions burned: 13163 (million) 172.89/40.29 % (26757)------------------------------ 172.89/40.29 % (26757)------------------------------ 173.11/40.34 % (26766)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_26322 for (2001ds/16164Mi) 176.08/41.06 % (26763)Instruction limit reached! 176.08/41.06 % (26763)------------------------------ 176.08/41.06 % (26763)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 176.08/41.06 % (26763)Termination reason: Unknown 176.08/41.06 % (26763)Termination phase: Function definition elimination 176.08/41.06 176.08/41.06 % (26763)Memory used [KB]: 3070 176.08/41.06 % (26763)Time elapsed: 2.716 s 176.08/41.06 % (26763)Instructions burned: 8517 (million) 176.08/41.06 % (26763)------------------------------ 176.08/41.06 % (26763)------------------------------ 176.08/41.10 % (26767)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_26322 for (1993ds/6102Mi) 181.53/42.45 % (26751)First to succeed. 182.17/42.61 % (26751)Refutation found. Thanks to Tanya! 182.17/42.61 % SZS status Theorem for E---3.1_26322 182.17/42.61 % SZS output start Proof for E---3.1_26322 182.17/42.61 thf(func_def_0, type, is_of: $i > ($i > $o) > $o). 182.17/42.61 thf(func_def_2, type, all_of: ($i > $o) > ($i > $o) > $o). 182.17/42.61 thf(func_def_3, type, eps: ($i > $o) > $i). 182.17/42.61 thf(func_def_4, type, in: $i > $i > $o). 182.17/42.61 thf(func_def_5, type, d_Subq: $i > $i > $o). 182.17/42.61 thf(func_def_7, type, union: $i > $i). 182.17/42.61 thf(func_def_8, type, power: $i > $i). 182.17/42.61 thf(func_def_9, type, repl: $i > ($i > $i) > $i). 182.17/42.61 thf(func_def_10, type, d_Union_closed: $i > $o). 182.17/42.61 thf(func_def_11, type, d_Power_closed: $i > $o). 182.17/42.61 thf(func_def_12, type, d_Repl_closed: $i > $o). 182.17/42.61 thf(func_def_13, type, d_ZF_closed: $i > $o). 182.17/42.61 thf(func_def_14, type, univof: $i > $i). 182.17/42.61 thf(func_def_15, type, if: $o > $i > $i > $i). 182.17/42.61 thf(func_def_16, type, nIn: $i > $i > $o). 182.17/42.61 thf(func_def_17, type, d_UPair: $i > $i > $i). 182.17/42.61 thf(func_def_18, type, d_Sing: $i > $i). 182.17/42.61 thf(func_def_19, type, binunion: $i > $i > $i). 182.17/42.61 thf(func_def_20, type, famunion: $i > ($i > $i) > $i). 182.17/42.61 thf(func_def_21, type, d_Sep: $i > ($i > $o) > $i). 182.17/42.61 thf(func_def_22, type, d_ReplSep: $i > ($i > $o) > ($i > $i) > $i). 182.17/42.61 thf(func_def_23, type, setminus: $i > $i > $i). 182.17/42.61 thf(func_def_24, type, d_In_rec_G: ($i > ($i > $i) > $i) > $i > $i > $o). 182.17/42.61 thf(func_def_25, type, d_In_rec: ($i > ($i > $i) > $i) > $i > $i). 182.17/42.61 thf(func_def_26, type, ordsucc: $i > $i). 182.17/42.61 thf(func_def_27, type, nat_p: $i > $o). 182.17/42.61 thf(func_def_29, type, d_Inj1: $i > $i). 182.17/42.61 thf(func_def_30, type, d_Inj0: $i > $i). 182.17/42.61 thf(func_def_31, type, d_Unj: $i > $i). 182.17/42.61 thf(func_def_32, type, pair: $i > $i > $i). 182.17/42.61 thf(func_def_33, type, proj0: $i > $i). 182.17/42.61 thf(func_def_34, type, proj1: $i > $i). 182.17/42.61 thf(func_def_35, type, d_Sigma: $i > ($i > $i) > $i). 182.17/42.61 thf(func_def_36, type, setprod: $i > $i > $i). 182.17/42.61 thf(func_def_37, type, ap: $i > $i > $i). 182.17/42.61 thf(func_def_38, type, pair_p: $i > $o). 182.17/42.61 thf(func_def_39, type, d_Pi: $i > ($i > $i) > $i). 182.17/42.61 thf(func_def_40, type, imp: $o > $o > $o). 182.17/42.61 thf(func_def_41, type, d_not: $o > $o). 182.17/42.61 thf(func_def_42, type, wel: $o > $o). 182.17/42.61 thf(func_def_44, type, l_ec: $o > $o > $o). 182.17/42.61 thf(func_def_45, type, d_and: $o > $o > $o). 182.17/42.61 thf(func_def_46, type, l_or: $o > $o > $o). 182.17/42.61 thf(func_def_47, type, orec: $o > $o > $o). 182.17/42.61 thf(func_def_48, type, l_iff: $o > $o > $o). 182.17/42.61 thf(func_def_49, type, all: $i > ($i > $o) > $o). 182.17/42.61 thf(func_def_50, type, non: $i > ($i > $o) > $i > $o). 182.17/42.61 thf(func_def_51, type, l_some: $i > ($i > $o) > $o). 182.17/42.61 thf(func_def_52, type, or3: $o > $o > $o > $o). 182.17/42.61 thf(func_def_53, type, and3: $o > $o > $o > $o). 182.17/42.61 thf(func_def_54, type, ec3: $o > $o > $o > $o). 182.17/42.61 thf(func_def_55, type, orec3: $o > $o > $o > $o). 182.17/42.61 thf(func_def_56, type, e_is: $i > $i > $i > $o). 182.17/42.61 thf(func_def_57, type, amone: $i > ($i > $o) > $o). 182.17/42.61 thf(func_def_58, type, one: $i > ($i > $o) > $o). 182.17/42.61 thf(func_def_59, type, ind: $i > ($i > $o) > $i). 182.17/42.61 thf(func_def_60, type, injective: $i > $i > $i > $o). 182.17/42.61 thf(func_def_61, type, image: $i > $i > $i > $i > $o). 182.17/42.61 thf(func_def_62, type, tofs: $i > $i > $i > $i > $i). 182.17/42.61 thf(func_def_63, type, soft: $i > $i > $i > $i > $i). 182.17/42.61 thf(func_def_64, type, inverse: $i > $i > $i > $i). 182.17/42.61 thf(func_def_65, type, surjective: $i > $i > $i > $o). 182.17/42.61 thf(func_def_66, type, bijective: $i > $i > $i > $o). 182.17/42.61 thf(func_def_67, type, invf: $i > $i > $i > $i). 182.17/42.61 thf(func_def_68, type, inj_h: $i > $i > $i > $i > $i > $i). 182.17/42.61 thf(func_def_69, type, e_in: $i > ($i > $o) > $i > $i). 182.17/42.61 thf(func_def_70, type, out: $i > ($i > $o) > $i > $i). 182.17/42.61 thf(func_def_71, type, d_pair: $i > $i > $i > $i > $i). 182.17/42.61 thf(func_def_72, type, first: $i > $i > $i > $i). 182.17/42.61 thf(func_def_73, type, second: $i > $i > $i > $i). 182.17/42.61 thf(func_def_74, type, prop1: $o > $i > $i > $i > $i > $o). 182.17/42.61 thf(func_def_75, type, ite: $o > $i > $i > $i > $i). 182.17/42.61 thf(func_def_76, type, wissel_wa: $i > $i > $i > $i > $i). 182.17/42.61 thf(func_def_77, type, wissel_wb: $i > $i > $i > $i > $i). 182.17/42.61 thf(func_def_78, type, wissel: $i > $i > $i > $i). 182.17/42.61 thf(func_def_79, type, changef: $i > $i > $i > $i > $i > $i). 182.17/42.61 thf(func_def_80, type, r_ec: $o > $o > $o). 182.17/42.61 thf(func_def_81, type, esti: $i > $i > $i > $o). 182.17/42.61 thf(func_def_82, type, empty: $i > $i > $o). 182.17/42.61 thf(func_def_83, type, nonempty: $i > $i > $o). 182.17/42.61 thf(func_def_84, type, incl: $i > $i > $i > $o). 182.17/42.61 thf(func_def_85, type, st_disj: $i > $i > $i > $o). 182.17/42.61 thf(func_def_86, type, nissetprop: $i > $i > $i > $i > $o). 182.17/42.61 thf(func_def_87, type, unmore: $i > $i > $i > $i). 182.17/42.61 thf(func_def_88, type, ecelt: $i > ($i > $i > $o) > $i > $i). 182.17/42.61 thf(func_def_89, type, ecp: $i > ($i > $i > $o) > $i > $i > $o). 182.17/42.61 thf(func_def_90, type, anec: $i > ($i > $i > $o) > $i > $o). 182.17/42.61 thf(func_def_91, type, ect: $i > ($i > $i > $o) > $i). 182.17/42.61 thf(func_def_92, type, ectset: $i > ($i > $i > $o) > $i > $i). 182.17/42.61 thf(func_def_93, type, ectelt: $i > ($i > $i > $o) > $i > $i). 182.17/42.61 thf(func_def_94, type, ecect: $i > ($i > $i > $o) > $i > $i). 182.17/42.61 thf(func_def_95, type, fixfu: $i > ($i > $i > $o) > $i > $i > $o). 182.17/42.61 thf(func_def_96, type, d_10_prop1: $i > ($i > $i > $o) > $i > $i > $i > $i > $i > $o). 182.17/42.61 thf(func_def_97, type, prop2: $i > ($i > $i > $o) > $i > $i > $i > $i > $o). 182.17/42.61 thf(func_def_98, type, indeq: $i > ($i > $i > $o) > $i > $i > $i > $i). 182.17/42.61 thf(func_def_99, type, fixfu2: $i > ($i > $i > $o) > $i > $i > $o). 182.17/42.61 thf(func_def_100, type, d_11_i: $i > ($i > $i > $o) > $i > $i > $i > $i). 182.17/42.61 thf(func_def_101, type, indeq2: $i > ($i > $i > $o) > $i > $i > $i > $i > $i). 182.17/42.61 thf(func_def_103, type, n_is: $i > $i > $o). 182.17/42.61 thf(func_def_104, type, nis: $i > $i > $o). 182.17/42.61 thf(func_def_105, type, n_in: $i > $i > $o). 182.17/42.61 thf(func_def_106, type, n_some: ($i > $o) > $o). 182.17/42.61 thf(func_def_107, type, n_all: ($i > $o) > $o). 182.17/42.61 thf(func_def_108, type, n_one: ($i > $o) > $o). 182.17/42.61 thf(func_def_110, type, cond1: $i > $o). 182.17/42.61 thf(func_def_111, type, cond2: $i > $o). 182.17/42.61 thf(func_def_112, type, i1_s: ($i > $o) > $i). 182.17/42.61 thf(func_def_113, type, d_22_prop1: $i > $o). 182.17/42.61 thf(func_def_114, type, d_23_prop1: $i > $o). 182.17/42.61 thf(func_def_115, type, d_24_prop1: $i > $o). 182.17/42.61 thf(func_def_116, type, d_24_prop2: $i > $i > $o). 182.17/42.61 thf(func_def_117, type, prop3: $i > $i > $i > $o). 182.17/42.61 thf(func_def_118, type, prop4: $i > $o). 182.17/42.61 thf(func_def_119, type, d_24_g: $i > $i). 182.17/42.61 thf(func_def_120, type, plus: $i > $i). 182.17/42.61 thf(func_def_121, type, n_pl: $i > $i > $i). 182.17/42.61 thf(func_def_122, type, d_25_prop1: $i > $i > $i > $o). 182.17/42.61 thf(func_def_123, type, d_26_prop1: $i > $i > $o). 182.17/42.61 thf(func_def_124, type, d_27_prop1: $i > $i > $o). 182.17/42.61 thf(func_def_125, type, d_28_prop1: $i > $i > $i > $o). 182.17/42.61 thf(func_def_126, type, diffprop: $i > $i > $i > $o). 182.17/42.61 thf(func_def_127, type, d_29_ii: $i > $i > $o). 182.17/42.61 thf(func_def_128, type, iii: $i > $i > $o). 182.17/42.61 thf(func_def_129, type, d_29_prop1: $i > $i > $o). 182.17/42.61 thf(func_def_130, type, moreis: $i > $i > $o). 182.17/42.61 thf(func_def_131, type, lessis: $i > $i > $o). 182.17/42.61 thf(func_def_132, type, lbprop: ($i > $o) > $i > $i > $o). 182.17/42.61 thf(func_def_133, type, n_lb: ($i > $o) > $i > $o). 182.17/42.61 thf(func_def_134, type, min: ($i > $o) > $i > $o). 182.17/42.61 thf(func_def_135, type, d_428_prop1: $i > $i > $o). 182.17/42.61 thf(func_def_136, type, d_428_prop2: $i > $i > $o). 182.17/42.61 thf(func_def_137, type, d_428_prop4: $i > $o). 182.17/42.61 thf(func_def_139, type, d_428_g: $i > $i). 182.17/42.61 thf(func_def_140, type, times: $i > $i). 182.17/42.61 thf(func_def_141, type, n_ts: $i > $i > $i). 182.17/42.61 thf(func_def_142, type, d_429_prop1: $i > $i > $o). 182.17/42.61 thf(func_def_143, type, d_430_prop1: $i > $i > $i > $o). 182.17/42.61 thf(func_def_144, type, d_431_prop1: $i > $i > $i > $o). 182.17/42.61 thf(func_def_145, type, n_mn: $i > $i > $i). 182.17/42.61 thf(func_def_146, type, d_1to: $i > $i). 182.17/42.61 thf(func_def_147, type, outn: $i > $i > $i). 182.17/42.61 thf(func_def_148, type, inn: $i > $i > $i). 182.17/42.61 thf(func_def_150, type, singlet_u0: $i > $i). 182.17/42.61 thf(func_def_154, type, pair_u0: $i > $i). 182.17/42.61 thf(func_def_155, type, pair1type: $i > $i). 182.17/42.61 thf(func_def_156, type, pair1: $i > $i > $i > $i). 182.17/42.61 thf(func_def_157, type, first1: $i > $i > $i). 182.17/42.61 thf(func_def_158, type, second1: $i > $i > $i). 182.17/42.61 thf(func_def_159, type, pair_q0: $i > $i > $i). 182.17/42.61 thf(func_def_160, type, d_1out: $i > $i). 182.17/42.61 thf(func_def_161, type, xout: $i > $i). 182.17/42.61 thf(func_def_162, type, left1to: $i > $i > $i > $i). 182.17/42.61 thf(func_def_163, type, right1to: $i > $i > $i > $i). 182.17/42.61 thf(func_def_164, type, left: $i > $i > $i > $i > $i). 182.17/42.61 thf(func_def_165, type, right: $i > $i > $i > $i > $i). 182.17/42.61 thf(func_def_166, type, left_f1: $i > $i > $i > $i > $i). 182.17/42.61 thf(func_def_167, type, left_f2: $i > $i > $i > $i > $i). 182.17/42.61 thf(func_def_169, type, n_fr: $i > $i > $i). 182.17/42.61 thf(func_def_170, type, num: $i > $i). 182.17/42.61 thf(func_def_171, type, den: $i > $i). 182.17/42.61 thf(func_def_172, type, n_eq: $i > $i > $o). 182.17/42.61 thf(func_def_173, type, moref: $i > $i > $o). 182.17/42.61 thf(func_def_174, type, lessf: $i > $i > $o). 182.17/42.61 thf(func_def_175, type, moreq: $i > $i > $o). 182.17/42.61 thf(func_def_176, type, lesseq: $i > $i > $o). 182.17/42.61 thf(func_def_177, type, n_pf: $i > $i > $i). 182.17/42.61 thf(func_def_178, type, d_367_vo: $i > $i > $i). 182.17/42.61 thf(func_def_179, type, d_367_w: $i > $i > $i). 182.17/42.61 thf(func_def_180, type, n_tf: $i > $i > $i). 182.17/42.61 thf(func_def_181, type, d_477_v: $i > $i > $i). 182.17/42.61 thf(func_def_182, type, inf: $i > $i > $o). 182.17/42.61 thf(func_def_184, type, rt_is: $i > $i > $o). 182.17/42.61 thf(func_def_185, type, rt_nis: $i > $i > $o). 182.17/42.61 thf(func_def_186, type, rt_some: ($i > $o) > $o). 182.17/42.61 thf(func_def_187, type, rt_all: ($i > $o) > $o). 182.17/42.61 thf(func_def_188, type, rt_one: ($i > $o) > $o). 182.17/42.61 thf(func_def_189, type, rt_in: $i > $i > $o). 182.17/42.61 thf(func_def_190, type, ratof: $i > $i). 182.17/42.61 thf(func_def_191, type, class: $i > $i). 182.17/42.61 thf(func_def_192, type, fixf: $i > $i > $o). 182.17/42.61 thf(func_def_193, type, indrat: $i > $i > $i > $i > $i). 182.17/42.61 thf(func_def_194, type, rt_more: $i > $i > $o). 182.17/42.61 thf(func_def_195, type, propm: $i > $i > $i > $i > $o). 182.17/42.61 thf(func_def_196, type, rt_less: $i > $i > $o). 182.17/42.61 thf(func_def_197, type, propl: $i > $i > $i > $i > $o). 182.17/42.61 thf(func_def_198, type, rt_moreis: $i > $i > $o). 182.17/42.61 thf(func_def_199, type, rt_lessis: $i > $i > $o). 182.17/42.61 thf(func_def_218, type, sK0: ($i > $o) > $i). 182.17/42.61 thf(func_def_219, type, sK1: $i > $i > $i > $i). 182.17/42.61 thf(func_def_220, type, sK2: ($i > $o) > $i). 182.17/42.61 thf(func_def_221, type, sK3: $i > $i). 182.17/42.61 thf(func_def_222, type, sK4: ($i > $i) > ($i > $i) > $i > $i). 182.17/42.61 thf(func_def_224, type, sK6: $i > $i > $o). 182.17/42.61 thf(func_def_225, type, sK7: $i > $i > $i > $i). 182.17/42.61 thf(func_def_226, type, sK8: ($i > $o) > $i). 182.17/42.61 thf(func_def_227, type, sK9: $i > $i > $o). 182.17/42.61 thf(func_def_228, type, sK10: $i > $i > $o). 182.17/42.61 thf(func_def_231, type, sK13: $i > $i > $o). 182.17/42.61 thf(func_def_232, type, sK14: ($i > $o) > $i). 182.17/42.61 thf(func_def_233, type, sK15: ($i > $o) > $i). 182.17/42.61 thf(func_def_234, type, sK16: ($i > $o) > $i). 182.17/42.61 thf(func_def_235, type, sK17: $i > $i > $o). 182.17/42.61 thf(func_def_236, type, ph18: !>[X0: $tType]:(X0)). 182.17/42.61 thf(func_def_237, type, sK19: $i > ($i > $o) > $i). 182.17/42.61 thf(func_def_238, type, sK20: $i > ($i > $o) > $i). 182.17/42.61 thf(func_def_239, type, sK21: $i > ($i > $o) > $i). 182.17/42.61 thf(func_def_240, type, sK22: $i > ($i > $o) > $i). 182.17/42.61 thf(func_def_241, type, sK23: $i > ($i > $o) > $i). 182.17/42.61 thf(func_def_242, type, sK24: ($i > $i) > $i > $i). 182.17/42.61 thf(func_def_243, type, sK25: $i > ($i > $o) > $i). 182.17/42.61 thf(func_def_244, type, sK26: ($i > $i) > $i > $i). 182.17/42.61 thf(func_def_245, type, sK27: ($i > $i) > $i > $i). 182.17/42.61 thf(func_def_246, type, sK28: $i > ($i > $o) > $i). 182.17/42.61 thf(func_def_247, type, sK29: ($i > $i) > $i > $i). 182.17/42.61 thf(func_def_250, type, sK32: $i > ($i > $o) > $i). 182.17/42.61 thf(func_def_252, type, sK34: $i > ($i > $o) > $i). 182.17/42.61 thf(func_def_254, type, sK36: $i > ($i > $o) > $i). 182.17/42.61 thf(f7657,plain,( 182.17/42.61 $false), 182.17/42.61 inference(trivial_inequality_removal,[],[f7656])). 182.17/42.61 thf(f7656,plain,( 182.17/42.61 ($false = $true)), 182.17/42.61 inference(backward_demodulation,[],[f3694,f7655])). 182.17/42.61 thf(f7655,plain,( 182.17/42.61 ($false = (in @ sK12 @ rat))), 182.17/42.61 inference(trivial_inequality_removal,[],[f7654])). 182.17/42.61 thf(f7654,plain,( 182.17/42.61 ($false = $true) | ($false = (in @ sK12 @ rat))), 182.17/42.61 inference(forward_demodulation,[],[f7653,f3690])). 182.17/42.61 thf(f3690,plain,( 182.17/42.61 ((in @ sK11 @ rat) = $true)), 182.17/42.61 inference(binary_proxy_clausification,[],[f3688])). 182.17/42.61 thf(f3688,plain,( 182.17/42.61 ($false = ((in @ sK11 @ rat) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ rat) => ((~ (l_some @ frac @ (^[Y1 : $i]: (l_some @ frac @ (^[Y2 : $i]: (~ ((in @ Y1 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y3 : $i]: ((^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3))))))) @ sK11)) => ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y3 : $i]: ((^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3))))))) @ Y0)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ (^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y1) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y1)) @ Y3))))))))))))) => ((~ (l_some @ frac @ (^[Y1 : $i]: (l_some @ frac @ (^[Y2 : $i]: (~ ((in @ Y1 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y3 : $i]: ((^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3))))))) @ sK11)) => ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y3 : $i]: ((^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3))))))) @ Y0)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ (^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y1)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y1) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2)) @ Y3))))))))))))) => (sK11 = Y0))))))))), 182.17/42.61 inference(beta_eta_normalization,[],[f3687])). 182.17/42.61 thf(f3687,plain,( 182.17/42.61 ($false = ((^[Y0 : $i]: ((in @ Y0 @ rat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ rat) => ((~ (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (~ ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: 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(second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ 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Y6)))))))) @ emptyset) @ Y2)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) @ Y4))))))))))))) => (Y0 = Y1))))))))))), 182.17/42.61 inference(boolean_simplification,[],[f3685])). 182.17/42.61 thf(f3685,plain,( 182.17/42.61 ($true != (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ rat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ rat) => ((~ (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (~ ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => ((l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) @ Y4)))) => $false))))))))) => ((~ (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (~ ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) @ Y4))))))))))))) => (Y0 = Y1))))))))))), 182.17/42.61 inference(boolean_simplification,[],[f3684])). 182.17/42.61 thf(f3684,plain,( 182.17/42.61 ($true != (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ rat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ rat) => ((~ (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (~ ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => (~ (~ ((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => ((l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) @ Y4)))) => $false))))))))))) => ((~ (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (~ ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) @ Y4))))))))))))) => (Y0 = Y1))))))))))), 182.17/42.61 inference(boolean_simplification,[],[f3683])). 182.17/42.61 thf(f3683,plain,( 182.17/42.61 ($true != (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ rat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ rat) => ((~ (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (~ ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => (~ (((in @ 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Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => ((l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) @ Y4)))) => $false)) => $false))))))))) => ((~ (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (~ ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) @ Y4))))))))))))) => (Y0 = Y1))))))))))), 182.17/42.61 inference(boolean_simplification,[],[f3682])). 182.17/42.61 thf(f3682,plain,( 182.17/42.61 ($true != (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ rat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ rat) => ((~ (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (~ ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => ((l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) @ Y4)))) => $false)) => $false) => $false)))))))) => ((~ (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (~ ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) @ Y4))))))))))))) => (Y0 = Y1))))))))))), 182.17/42.61 inference(boolean_simplification,[],[f3681])). 182.17/42.61 thf(f3681,plain,( 182.17/42.61 ($true != (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ rat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ rat) => ((~ (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => ((l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) @ Y4)))) => $false)) => $false) => $false)) => $false)))))) => ((~ (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (~ ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) @ Y4))))))))))))) => (Y0 = Y1))))))))))), 182.17/42.61 inference(boolean_simplification,[],[f3680])). 182.17/42.61 thf(f3680,plain,( 182.17/42.61 ($true != (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ rat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ rat) => (((l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => ((l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) @ Y4)))) => $false)) => $false) => $false)) => $false))))) => $false) => ((~ (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (~ ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) @ Y4))))))))))))) => (Y0 = Y1))))))))))), 182.17/42.61 inference(boolean_simplification,[],[f3679])). 182.17/42.61 thf(f3679,plain,( 182.17/42.61 ($true != (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ rat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ rat) => (((l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => ((l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) @ Y4)))) => $false)) => $false) => $false)) => $false))))) => $false) => ((~ (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (~ ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => ((l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) @ Y4)))) => $false))))))))) => (Y0 = Y1))))))))))), 182.17/42.61 inference(boolean_simplification,[],[f3678])). 182.17/42.61 thf(f3678,plain,( 182.17/42.61 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ rat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ rat) => (((l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => ((l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) @ Y4)))) => $false)) => $false) => $false)) => $false))))) => $false) => ((~ (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (~ ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => (~ (~ ((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => ((l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) @ Y4)))) => $false))))))))))) => (Y0 = Y1))))))))) != $true)), 182.17/42.61 inference(boolean_simplification,[],[f3677])). 182.17/42.61 thf(f3677,plain,( 182.17/42.61 ($true != (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ rat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ rat) => (((l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => ((l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) @ Y4)))) => $false)) => $false) => $false)) => $false))))) => $false) => ((~ (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (~ ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => (~ (((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => ((l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) @ Y4)))) => $false)) => $false))))))))) => (Y0 = Y1))))))))))), 182.17/42.61 inference(boolean_simplification,[],[f3676])). 182.17/42.61 thf(f3676,plain,( 182.17/42.61 ($true != (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ rat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ rat) => (((l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => ((l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) @ Y4)))) => $false)) => $false) => $false)) => $false))))) => $false) => ((~ (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (~ ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => ((l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) @ Y4)))) => $false)) => $false) => $false)))))))) => (Y0 = Y1))))))))))), 182.17/42.61 inference(boolean_simplification,[],[f3675])). 182.17/42.61 thf(f3675,plain,( 182.17/42.61 ($true != (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ rat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ rat) => (((l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => ((l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) @ Y4)))) => $false)) => $false) => $false)) => $false))))) => $false) => ((~ (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => ((l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) @ Y4)))) => $false)) => $false) => $false)) => $false)))))) => (Y0 = Y1))))))))))), 182.17/42.61 inference(boolean_simplification,[],[f3674])). 182.17/42.61 thf(f3674,plain,( 182.17/42.61 ($true != (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ rat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ rat) => (((l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => ((l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) @ Y4)))) => $false)) => $false) => $false)) => $false))))) => $false) => (((l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => ((l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) @ Y4)))) => $false)) => $false) => $false)) => $false))))) => $false) => (Y0 = Y1))))))))))), 182.17/42.61 inference(beta_eta_normalization,[],[f1771])). 182.17/42.61 thf(f1771,plain,( 182.17/42.61 (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i > $o]: (Y4 @ Y3)))) @ Y2 @ Y0) => (Y1 @ Y2))))))) @ (^[Y0 : $i]: (in @ Y0 @ rat)) @ (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: (!! @ $i @ (^[Y3 : $i]: (((^[Y4 : $i]: ((^[Y5 : $i > $o]: (Y5 @ Y4)))) @ Y3 @ Y1) => (Y2 @ Y3))))))) @ (^[Y1 : $i]: (in @ Y1 @ rat)) @ (^[Y1 : $i]: (((^[Y2 : $o]: ((^[Y3 : $o]: ((^[Y4 : $o]: (Y3 => Y4)))) @ Y2 @ $false)) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (l_some @ frac @ (^[Y4 : $i]: (l_some @ frac @ (^[Y5 : $i]: ((^[Y6 : $o]: ((^[Y7 : $o]: ((^[Y8 : $o]: ((^[Y9 : $o]: ((^[Y10 : $o]: ((^[Y11 : $o]: ((^[Y12 : $o]: ((^[Y13 : $o]: (Y12 => Y13)))) @ Y11 @ $false)) @ ((^[Y11 : $o]: ((^[Y12 : $o]: ((^[Y13 : $o]: ((^[Y14 : $o]: (Y13 => Y14)))) @ Y11 @ ((^[Y13 : $o]: ((^[Y14 : $o]: ((^[Y15 : $o]: (Y14 => Y15)))) @ Y13 @ $false)) @ Y12))))) @ Y9 @ Y10))))) @ Y6 @ ((^[Y9 : $o]: ((^[Y10 : $o]: ((^[Y11 : $o]: ((^[Y12 : $o]: ((^[Y13 : $o]: (Y12 => Y13)))) @ Y11 @ $false)) @ ((^[Y11 : $o]: ((^[Y12 : $o]: ((^[Y13 : $o]: ((^[Y14 : $o]: (Y13 => Y14)))) @ Y11 @ ((^[Y13 : $o]: ((^[Y14 : $o]: ((^[Y15 : $o]: (Y14 => Y15)))) @ Y13 @ $false)) @ Y12))))) @ Y9 @ Y10))))) @ Y7 @ Y8))))))) @ ((^[Y6 : $i]: (in)) @ frac @ Y4 @ ((^[Y6 : $i]: ((^[Y7 : $i > $i > $o]: (e_in @ (power @ Y6) @ (anec @ Y6 @ Y7))))) @ frac @ (^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (Y9 = Y10)))))) @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ (n_ts @ (first1 @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ Y6) @ (second1 @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ Y7)) @ (n_ts @ (first1 @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ Y7) @ (second1 @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ Y6)))))) @ Y2)) @ ((^[Y6 : $i]: (in)) @ frac @ Y5 @ ((^[Y6 : $i]: ((^[Y7 : $i > $i > $o]: (e_in @ (power @ Y6) @ (anec @ Y6 @ Y7))))) @ frac @ (^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (Y9 = Y10)))))) @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ 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(^[Y8 : $i]: (~ (emptyset = Y8)))) @ (n_ts @ (first1 @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ Y6) @ (second1 @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ Y7)) @ (n_ts @ (first1 @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ Y7) @ (second1 @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ Y6)))))) @ Y3)) @ ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: (l_some @ ((^[Y10 : $i]: ((^[Y11 : $i > $o]: (if @ (?? @ $i @ (^[Y12 : $i]: ((Y11 @ Y12) & (in @ Y12 @ Y10)))) @ (repl @ Y10 @ (^[Y12 : $i]: (if @ (Y11 @ Y12) @ Y12 @ (eps @ (^[Y13 : $i]: ((in @ Y13 @ Y10) & (Y11 @ Y13))))))) @ emptyset)))) @ omega @ (^[Y10 : $i]: (~ (emptyset = Y10)))) @ ((^[Y10 : $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: ((^[Y13 : $i]: ((^[Y14 : $i]: ((^[Y15 : $i]: (Y14 = Y15)))))) @ ((^[Y13 : $i]: ((^[Y14 : $i > $o]: (if @ (?? @ $i @ (^[Y15 : $i]: ((Y14 @ Y15) & (in @ Y15 @ Y13)))) @ (repl @ Y13 @ (^[Y15 : $i]: (if @ (Y14 @ Y15) @ Y15 @ (eps @ (^[Y16 : $i]: ((in @ Y16 @ Y13) & (Y14 @ Y16))))))) @ emptyset)))) @ omega @ (^[Y13 : $i]: (~ (emptyset = Y13)))) @ Y10 @ (n_pl @ Y11 @ Y12))))))) @ Y9 @ Y8))))) @ (n_ts @ (first1 @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ Y6) @ (second1 @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ Y7)) @ (n_ts @ (first1 @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ Y7) @ (second1 @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ Y6)))))) @ Y4 @ Y5))))))))) @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (Y3 = Y4)))))) @ rat @ Y0 @ Y1))))))), 182.17/42.61 inference(definition_unfolding,[],[f1658,f1668,f1702,f1694])). 182.17/42.61 thf(f1694,plain,( 182.17/42.61 (rt_is = ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y1 = Y2)))))) @ rat))), 182.17/42.61 inference(definition_unfolding,[],[f1560,f1381])). 182.17/42.61 thf(f1381,plain,( 182.17/42.61 (e_is = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y1 = Y2)))))))), 182.17/42.61 inference(cnf_transformation,[],[f1256])). 182.17/42.61 thf(f1256,plain,( 182.17/42.61 (e_is = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y1 = Y2)))))))), 182.17/42.61 inference(fool_elimination,[],[f1255])). 182.17/42.61 thf(f1255,plain,( 182.17/42.61 (e_is = (^[X0 : $i, X1 : $i, X2 : $i] : ((X1 = X2))))), 182.17/42.61 inference(rectify,[],[f49])). 182.17/42.61 thf(f49,axiom,( 182.17/42.61 (e_is = (^[X0 : $i, X7 : $i, X8 : $i] : ((X7 = X8))))), 182.17/42.61 file('/export/starexec/sandbox2/tmp/tmp.Wx2OXKe4bp/E---3.1_26322.p',def_e_is)). 182.17/42.61 thf(f1560,plain,( 182.17/42.61 (rt_is = (e_is @ rat))), 182.17/42.61 inference(cnf_transformation,[],[f470])). 182.17/42.61 thf(f470,axiom,( 182.17/42.61 (rt_is = (e_is @ rat))), 182.17/42.61 file('/export/starexec/sandbox2/tmp/tmp.Wx2OXKe4bp/E---3.1_26322.p',def_rt_is)). 182.17/42.61 thf(f1702,plain,( 182.17/42.61 (rt_less = (^[Y0 : $i]: ((^[Y1 : $i]: (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: ((^[Y4 : $o]: ((^[Y5 : $o]: ((^[Y6 : $o]: ((^[Y7 : $o]: ((^[Y8 : $o]: ((^[Y9 : $o]: ((^[Y10 : $o]: ((^[Y11 : $o]: (Y10 => Y11)))) @ Y9 @ $false)) @ ((^[Y9 : $o]: ((^[Y10 : $o]: ((^[Y11 : $o]: ((^[Y12 : $o]: (Y11 => Y12)))) @ Y9 @ ((^[Y11 : $o]: ((^[Y12 : $o]: ((^[Y13 : $o]: (Y12 => Y13)))) @ Y11 @ $false)) @ Y10))))) @ Y7 @ Y8))))) @ Y4 @ ((^[Y7 : $o]: ((^[Y8 : $o]: ((^[Y9 : $o]: ((^[Y10 : $o]: ((^[Y11 : $o]: (Y10 => Y11)))) @ Y9 @ $false)) @ ((^[Y9 : $o]: ((^[Y10 : $o]: ((^[Y11 : $o]: ((^[Y12 : $o]: (Y11 => Y12)))) @ Y9 @ ((^[Y11 : $o]: ((^[Y12 : $o]: ((^[Y13 : $o]: (Y12 => Y13)))) @ Y11 @ $false)) @ Y10))))) @ Y7 @ Y8))))) @ Y5 @ Y6))))))) @ ((^[Y4 : $i]: (in)) @ frac @ Y2 @ ((^[Y4 : $i]: ((^[Y5 : $i > $i > $o]: (e_in @ (power @ Y4) @ (anec @ Y4 @ Y5))))) @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (Y7 = Y8)))))) @ ((^[Y6 : $i]: ((^[Y7 : $i > $o]: (if @ (?? @ $i @ (^[Y8 : $i]: ((Y7 @ Y8) & (in @ Y8 @ Y6)))) @ (repl @ Y6 @ (^[Y8 : $i]: (if @ (Y7 @ Y8) @ Y8 @ (eps @ (^[Y9 : $i]: ((in @ Y9 @ Y6) & (Y7 @ Y9))))))) @ emptyset)))) @ omega @ (^[Y6 : $i]: (~ (emptyset = Y6)))) @ (n_ts @ (first1 @ ((^[Y6 : $i]: ((^[Y7 : $i > $o]: (if @ (?? @ $i @ (^[Y8 : $i]: ((Y7 @ Y8) & (in @ Y8 @ Y6)))) @ (repl @ Y6 @ (^[Y8 : $i]: (if @ (Y7 @ Y8) @ Y8 @ (eps @ (^[Y9 : $i]: ((in @ Y9 @ Y6) & (Y7 @ Y9))))))) @ emptyset)))) @ omega @ (^[Y6 : $i]: (~ (emptyset = Y6)))) @ Y4) @ (second1 @ ((^[Y6 : $i]: ((^[Y7 : $i > $o]: (if @ (?? @ $i @ (^[Y8 : $i]: ((Y7 @ Y8) & (in @ Y8 @ Y6)))) @ (repl @ Y6 @ (^[Y8 : $i]: (if @ (Y7 @ Y8) @ Y8 @ (eps @ (^[Y9 : $i]: ((in @ Y9 @ Y6) & (Y7 @ Y9))))))) @ emptyset)))) @ omega @ (^[Y6 : $i]: (~ (emptyset = Y6)))) @ Y5)) @ (n_ts @ (first1 @ ((^[Y6 : $i]: ((^[Y7 : $i > $o]: (if @ (?? @ $i @ (^[Y8 : $i]: ((Y7 @ Y8) & (in @ Y8 @ Y6)))) @ (repl @ Y6 @ (^[Y8 : $i]: (if @ (Y7 @ Y8) @ Y8 @ (eps @ (^[Y9 : $i]: ((in @ Y9 @ Y6) & (Y7 @ Y9))))))) @ emptyset)))) @ omega @ (^[Y6 : $i]: (~ (emptyset = Y6)))) @ Y5) @ (second1 @ ((^[Y6 : $i]: ((^[Y7 : $i > $o]: (if @ (?? @ $i @ (^[Y8 : $i]: ((Y7 @ Y8) & (in @ Y8 @ Y6)))) @ (repl @ Y6 @ (^[Y8 : $i]: (if @ (Y7 @ Y8) @ Y8 @ (eps @ (^[Y9 : $i]: ((in @ Y9 @ Y6) & (Y7 @ Y9))))))) @ emptyset)))) @ omega @ (^[Y6 : $i]: (~ (emptyset = Y6)))) @ Y4)))))) @ Y0)) @ ((^[Y4 : $i]: (in)) @ frac @ Y3 @ ((^[Y4 : $i]: ((^[Y5 : $i > $i > $o]: (e_in @ (power @ Y4) @ (anec @ Y4 @ Y5))))) @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (Y7 = Y8)))))) @ ((^[Y6 : $i]: ((^[Y7 : $i > $o]: (if @ (?? @ $i @ (^[Y8 : $i]: ((Y7 @ Y8) & (in @ Y8 @ Y6)))) @ (repl @ Y6 @ (^[Y8 : $i]: (if @ (Y7 @ Y8) @ Y8 @ (eps @ (^[Y9 : $i]: ((in @ Y9 @ Y6) & (Y7 @ Y9))))))) @ emptyset)))) @ omega @ (^[Y6 : $i]: (~ (emptyset = Y6)))) @ (n_ts @ (first1 @ ((^[Y6 : $i]: ((^[Y7 : $i > $o]: (if @ (?? @ $i @ (^[Y8 : $i]: ((Y7 @ Y8) & (in @ Y8 @ Y6)))) @ (repl @ Y6 @ (^[Y8 : $i]: (if @ (Y7 @ Y8) @ Y8 @ (eps @ (^[Y9 : $i]: ((in @ Y9 @ Y6) & (Y7 @ Y9))))))) @ emptyset)))) @ omega @ (^[Y6 : $i]: (~ (emptyset = Y6)))) @ Y4) @ (second1 @ ((^[Y6 : $i]: ((^[Y7 : $i > $o]: (if @ (?? @ $i @ (^[Y8 : $i]: ((Y7 @ Y8) & (in @ Y8 @ Y6)))) @ (repl @ Y6 @ (^[Y8 : $i]: (if @ (Y7 @ Y8) @ Y8 @ (eps @ (^[Y9 : $i]: ((in @ Y9 @ Y6) & (Y7 @ Y9))))))) @ emptyset)))) @ omega @ (^[Y6 : $i]: (~ (emptyset = Y6)))) @ Y5)) @ (n_ts @ (first1 @ ((^[Y6 : $i]: ((^[Y7 : $i > $o]: (if @ (?? @ $i @ (^[Y8 : $i]: ((Y7 @ Y8) & (in @ Y8 @ Y6)))) @ (repl @ Y6 @ (^[Y8 : $i]: (if @ (Y7 @ Y8) @ Y8 @ (eps @ (^[Y9 : $i]: ((in @ Y9 @ Y6) & (Y7 @ Y9))))))) @ emptyset)))) @ omega @ (^[Y6 : $i]: (~ (emptyset = Y6)))) @ Y5) @ (second1 @ ((^[Y6 : $i]: ((^[Y7 : $i > $o]: (if @ (?? @ $i @ (^[Y8 : $i]: ((Y7 @ Y8) & (in @ Y8 @ Y6)))) @ (repl @ Y6 @ (^[Y8 : $i]: (if @ (Y7 @ Y8) @ Y8 @ (eps @ (^[Y9 : $i]: ((in @ Y9 @ Y6) & (Y7 @ Y9))))))) @ emptyset)))) @ omega @ (^[Y6 : $i]: (~ (emptyset = Y6)))) @ Y4)))))) @ Y1)) @ ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (l_some @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ ((^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: ((^[Y13 : $i]: (Y12 = Y13)))))) @ ((^[Y11 : $i]: ((^[Y12 : $i > $o]: (if @ (?? @ $i @ (^[Y13 : $i]: ((Y12 @ Y13) & (in @ Y13 @ Y11)))) @ (repl @ Y11 @ (^[Y13 : $i]: (if @ (Y12 @ Y13) @ Y13 @ (eps @ (^[Y14 : $i]: ((in @ Y14 @ Y11) & (Y12 @ Y14))))))) @ emptyset)))) @ omega @ (^[Y11 : $i]: (~ (emptyset = Y11)))) @ Y8 @ (n_pl @ Y9 @ Y10))))))) @ Y7 @ Y6))))) @ (n_ts @ (first1 @ ((^[Y6 : $i]: ((^[Y7 : $i > $o]: (if @ (?? @ $i @ (^[Y8 : $i]: ((Y7 @ Y8) & (in @ Y8 @ Y6)))) @ (repl @ Y6 @ (^[Y8 : $i]: (if @ (Y7 @ Y8) @ Y8 @ (eps @ (^[Y9 : $i]: ((in @ Y9 @ Y6) & (Y7 @ Y9))))))) @ emptyset)))) @ omega @ (^[Y6 : $i]: (~ (emptyset = Y6)))) @ Y4) @ (second1 @ ((^[Y6 : $i]: ((^[Y7 : $i > $o]: (if @ (?? @ $i @ (^[Y8 : $i]: ((Y7 @ Y8) & (in @ Y8 @ Y6)))) @ (repl @ Y6 @ (^[Y8 : $i]: (if @ (Y7 @ Y8) @ Y8 @ (eps @ (^[Y9 : $i]: ((in @ Y9 @ Y6) & (Y7 @ Y9))))))) @ emptyset)))) @ omega @ (^[Y6 : $i]: (~ (emptyset = Y6)))) @ Y5)) @ (n_ts @ (first1 @ ((^[Y6 : $i]: ((^[Y7 : $i > $o]: (if @ (?? @ $i @ (^[Y8 : $i]: ((Y7 @ Y8) & (in @ Y8 @ Y6)))) @ (repl @ Y6 @ (^[Y8 : $i]: (if @ (Y7 @ Y8) @ Y8 @ (eps @ (^[Y9 : $i]: ((in @ Y9 @ Y6) & (Y7 @ Y9))))))) @ emptyset)))) @ omega @ (^[Y6 : $i]: (~ (emptyset = Y6)))) @ Y5) @ (second1 @ ((^[Y6 : $i]: ((^[Y7 : $i > $o]: (if @ (?? @ $i @ (^[Y8 : $i]: ((Y7 @ Y8) & (in @ Y8 @ Y6)))) @ (repl @ Y6 @ (^[Y8 : $i]: (if @ (Y7 @ Y8) @ Y8 @ (eps @ (^[Y9 : $i]: ((in @ Y9 @ Y6) & (Y7 @ Y9))))))) @ emptyset)))) @ omega @ (^[Y6 : $i]: (~ (emptyset = Y6)))) @ Y4)))))) @ Y2 @ Y3))))))))))), 182.17/42.61 inference(definition_unfolding,[],[f1475,f1691,f1699,f1696,f1699,f1696,f1685])). 182.17/42.61 thf(f1685,plain,( 182.17/42.61 (lessf = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (l_some @ ((^[Y4 : $i]: ((^[Y5 : $i > $o]: (if @ (?? @ $i @ (^[Y6 : $i]: ((Y5 @ Y6) & (in @ Y6 @ Y4)))) @ (repl @ Y4 @ (^[Y6 : $i]: (if @ (Y5 @ Y6) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ Y4) & (Y5 @ Y7))))))) @ emptyset)))) @ omega @ (^[Y4 : $i]: (~ (emptyset = Y4)))) @ ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: (Y8 = Y9)))))) @ ((^[Y7 : $i]: ((^[Y8 : $i > $o]: (if @ (?? @ $i @ (^[Y9 : $i]: ((Y8 @ Y9) & (in @ Y9 @ Y7)))) @ (repl @ Y7 @ (^[Y9 : $i]: (if @ (Y8 @ Y9) @ Y9 @ (eps @ (^[Y10 : $i]: ((in @ Y10 @ Y7) & (Y8 @ Y10))))))) @ emptyset)))) @ omega @ (^[Y7 : $i]: (~ (emptyset = Y7)))) @ Y4 @ (n_pl @ Y5 @ Y6))))))) @ Y3 @ Y2))))) @ (n_ts @ (first1 @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: (if @ (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (in @ Y4 @ Y2)))) @ (repl @ Y2 @ (^[Y4 : $i]: (if @ (Y3 @ Y4) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (Y3 @ Y5))))))) @ emptyset)))) @ omega @ (^[Y2 : $i]: (~ (emptyset = Y2)))) @ Y0) @ (second1 @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: (if @ (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (in @ Y4 @ Y2)))) @ (repl @ Y2 @ (^[Y4 : $i]: (if @ (Y3 @ Y4) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (Y3 @ Y5))))))) @ emptyset)))) @ omega @ (^[Y2 : $i]: (~ (emptyset = Y2)))) @ Y1)) @ (n_ts @ (first1 @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: (if @ (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (in @ Y4 @ Y2)))) @ (repl @ Y2 @ (^[Y4 : $i]: (if @ (Y3 @ Y4) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (Y3 @ Y5))))))) @ emptyset)))) @ omega @ (^[Y2 : $i]: (~ (emptyset = Y2)))) @ Y1) @ (second1 @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: (if @ (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (in @ Y4 @ Y2)))) @ (repl @ Y2 @ (^[Y4 : $i]: (if @ (Y3 @ Y4) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (Y3 @ Y5))))))) @ emptyset)))) @ omega @ (^[Y2 : $i]: (~ (emptyset = Y2)))) @ Y0)))))))), 182.17/42.61 inference(definition_unfolding,[],[f1488,f1665,f1672,f1673,f1672,f1673])). 182.17/42.61 thf(f1673,plain,( 182.17/42.61 (den = (second1 @ ((^[Y0 : $i]: ((^[Y1 : $i > $o]: (if @ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) @ (repl @ Y0 @ (^[Y2 : $i]: (if @ (Y1 @ Y2) @ Y2 @ (eps @ (^[Y3 : $i]: ((in @ Y3 @ Y0) & (Y1 @ Y3))))))) @ emptyset)))) @ omega @ (^[Y0 : $i]: (~ (emptyset = Y0))))))), 182.17/42.61 inference(definition_unfolding,[],[f1608,f1661])). 182.17/42.61 thf(f1661,plain,( 182.17/42.61 (nat = ((^[Y0 : $i]: ((^[Y1 : $i > $o]: (if @ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) @ (repl @ Y0 @ (^[Y2 : $i]: (if @ (Y1 @ Y2) @ Y2 @ (eps @ (^[Y3 : $i]: ((in @ Y3 @ Y0) & (Y1 @ Y3))))))) @ emptyset)))) @ omega @ (^[Y0 : $i]: (~ (emptyset = Y0)))))), 182.17/42.61 inference(definition_unfolding,[],[f1507,f1495])). 182.17/42.61 thf(f1495,plain,( 182.17/42.61 (d_Sep = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (if @ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) @ (repl @ Y0 @ (^[Y2 : $i]: (if @ (Y1 @ Y2) @ Y2 @ (eps @ (^[Y3 : $i]: ((in @ Y3 @ Y0) & (Y1 @ Y3))))))) @ emptyset)))))), 182.17/42.61 inference(cnf_transformation,[],[f666])). 182.17/42.61 thf(f666,plain,( 182.17/42.61 (d_Sep = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (if @ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) @ (repl @ Y0 @ (^[Y2 : $i]: (if @ (Y1 @ Y2) @ Y2 @ (eps @ (^[Y3 : $i]: ((in @ Y3 @ Y0) & (Y1 @ Y3))))))) @ emptyset)))))), 182.17/42.61 inference(fool_elimination,[],[f665])). 182.17/42.61 thf(f665,plain,( 182.17/42.61 (d_Sep = (^[X0 : $i, X1 : $i > $o] : (if @ ? [X2] : ((in @ X2 @ X0) & (X1 @ X2)) @ (repl @ X0 @ (^[X3 : $i] : (if @ (X1 @ X3) @ X3 @ (eps @ (^[X4 : $i] : ((X1 @ X4) & (in @ X4 @ X0))))))) @ emptyset)))), 182.17/42.61 inference(rectify,[],[f14])). 182.17/42.61 thf(f14,axiom,( 182.17/42.61 (d_Sep = (^[X0 : $i, X1 : $i > $o] : (if @ ? [X2] : ((in @ X2 @ X0) & (X1 @ X2)) @ (repl @ X0 @ (^[X2 : $i] : (if @ (X1 @ X2) @ X2 @ (eps @ (^[X3 : $i] : ((X1 @ X3) & (in @ X3 @ X0))))))) @ emptyset)))), 182.17/42.61 file('/export/starexec/sandbox2/tmp/tmp.Wx2OXKe4bp/E---3.1_26322.p',def_d_Sep)). 182.17/42.61 thf(f1507,plain,( 182.17/42.61 (nat = (d_Sep @ omega @ (^[Y0 : $i]: (~ (emptyset = Y0)))))), 182.17/42.61 inference(cnf_transformation,[],[f1259])). 182.17/42.61 thf(f1259,plain,( 182.17/42.61 (nat = (d_Sep @ omega @ (^[Y0 : $i]: (~ (emptyset = Y0)))))), 182.17/42.61 inference(fool_elimination,[],[f95])). 182.17/42.61 thf(f95,axiom,( 182.17/42.61 (nat = (d_Sep @ omega @ (^[X0 : $i] : ((emptyset != X0)))))), 182.17/42.61 file('/export/starexec/sandbox2/tmp/tmp.Wx2OXKe4bp/E---3.1_26322.p',def_nat)). 182.17/42.61 thf(f1608,plain,( 182.17/42.61 (den = (second1 @ nat))), 182.17/42.61 inference(cnf_transformation,[],[f230])). 182.17/42.61 thf(f230,axiom,( 182.17/42.61 (den = (second1 @ nat))), 182.17/42.61 file('/export/starexec/sandbox2/tmp/tmp.Wx2OXKe4bp/E---3.1_26322.p',def_den)). 182.17/42.61 thf(f1672,plain,( 182.17/42.61 (num = (first1 @ ((^[Y0 : $i]: ((^[Y1 : $i > $o]: (if @ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) @ (repl @ Y0 @ (^[Y2 : $i]: (if @ (Y1 @ Y2) @ Y2 @ (eps @ (^[Y3 : $i]: ((in @ Y3 @ Y0) & (Y1 @ Y3))))))) @ emptyset)))) @ omega @ (^[Y0 : $i]: (~ (emptyset = Y0))))))), 182.17/42.61 inference(definition_unfolding,[],[f1334,f1661])). 182.17/42.61 thf(f1334,plain,( 182.17/42.61 (num = (first1 @ nat))), 182.17/42.61 inference(cnf_transformation,[],[f229])). 182.17/42.61 thf(f229,axiom,( 182.17/42.61 (num = (first1 @ nat))), 182.17/42.61 file('/export/starexec/sandbox2/tmp/tmp.Wx2OXKe4bp/E---3.1_26322.p',def_num)). 182.17/42.61 thf(f1665,plain,( 182.17/42.61 (iii = (^[Y0 : $i]: ((^[Y1 : $i]: (l_some @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: (if @ (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (in @ Y4 @ Y2)))) @ (repl @ Y2 @ (^[Y4 : $i]: (if @ (Y3 @ Y4) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (Y3 @ Y5))))))) @ emptyset)))) @ omega @ (^[Y2 : $i]: (~ (emptyset = Y2)))) @ ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (Y6 = Y7)))))) @ ((^[Y5 : $i]: ((^[Y6 : $i > $o]: (if @ (?? @ $i @ (^[Y7 : $i]: ((Y6 @ Y7) & (in @ Y7 @ Y5)))) @ (repl @ Y5 @ (^[Y7 : $i]: (if @ (Y6 @ Y7) @ Y7 @ (eps @ (^[Y8 : $i]: ((in @ Y8 @ Y5) & (Y6 @ Y8))))))) @ emptyset)))) @ omega @ (^[Y5 : $i]: (~ (emptyset = Y5)))) @ Y2 @ (n_pl @ Y3 @ Y4))))))) @ Y1 @ Y0))))))), 182.17/42.61 inference(definition_unfolding,[],[f1496,f1662,f1664])). 182.17/42.61 thf(f1664,plain,( 182.17/42.61 (diffprop = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (Y4 = Y5)))))) @ ((^[Y3 : $i]: ((^[Y4 : $i > $o]: (if @ (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (in @ Y5 @ Y3)))) @ (repl @ Y3 @ (^[Y5 : $i]: (if @ (Y4 @ Y5) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ Y3) & (Y4 @ Y6))))))) @ emptyset)))) @ omega @ (^[Y3 : $i]: (~ (emptyset = Y3)))) @ Y0 @ (n_pl @ Y1 @ Y2))))))))), 182.17/42.61 inference(definition_unfolding,[],[f1506,f1663])). 182.17/42.61 thf(f1663,plain,( 182.17/42.61 (n_is = ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y1 = Y2)))))) @ ((^[Y0 : $i]: ((^[Y1 : $i > $o]: (if @ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) @ (repl @ Y0 @ (^[Y2 : $i]: (if @ (Y1 @ Y2) @ Y2 @ (eps @ (^[Y3 : $i]: ((in @ Y3 @ Y0) & (Y1 @ Y3))))))) @ emptyset)))) @ omega @ (^[Y0 : $i]: (~ (emptyset = Y0))))))), 182.17/42.61 inference(definition_unfolding,[],[f1510,f1381,f1661])). 182.17/42.61 thf(f1510,plain,( 182.17/42.61 (n_is = (e_is @ nat))), 182.17/42.61 inference(cnf_transformation,[],[f96])). 182.17/42.61 thf(f96,axiom,( 182.17/42.61 (n_is = (e_is @ nat))), 182.17/42.61 file('/export/starexec/sandbox2/tmp/tmp.Wx2OXKe4bp/E---3.1_26322.p',def_n_is)). 182.17/42.61 thf(f1506,plain,( 182.17/42.61 (diffprop = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (n_is @ Y0 @ (n_pl @ Y1 @ Y2))))))))), 182.17/42.61 inference(cnf_transformation,[],[f1134])). 182.17/42.61 thf(f1134,plain,( 182.17/42.61 (diffprop = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (n_is @ Y0 @ (n_pl @ Y1 @ Y2))))))))), 182.17/42.61 inference(fool_elimination,[],[f185])). 182.17/42.61 thf(f185,axiom,( 182.17/42.61 ((^[X0 : $i, X1 : $i, X2 : $i] : (n_is @ X0 @ (n_pl @ X1 @ X2))) = diffprop)), 182.17/42.61 file('/export/starexec/sandbox2/tmp/tmp.Wx2OXKe4bp/E---3.1_26322.p',def_diffprop)). 182.17/42.61 thf(f1662,plain,( 182.17/42.61 (n_some = (l_some @ ((^[Y0 : $i]: ((^[Y1 : $i > $o]: (if @ (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (in @ Y2 @ Y0)))) @ (repl @ Y0 @ (^[Y2 : $i]: (if @ (Y1 @ Y2) @ Y2 @ (eps @ (^[Y3 : $i]: ((in @ Y3 @ Y0) & (Y1 @ Y3))))))) @ emptyset)))) @ omega @ (^[Y0 : $i]: (~ (emptyset = Y0))))))), 182.17/42.61 inference(definition_unfolding,[],[f1483,f1661])). 182.17/42.61 thf(f1483,plain,( 182.17/42.61 (n_some = (l_some @ nat))), 182.17/42.61 inference(cnf_transformation,[],[f99])). 182.17/42.61 thf(f99,axiom,( 182.17/42.61 (n_some = (l_some @ nat))), 182.17/42.61 file('/export/starexec/sandbox2/tmp/tmp.Wx2OXKe4bp/E---3.1_26322.p',def_n_some)). 182.17/42.61 thf(f1496,plain,( 182.17/42.61 (iii = (^[Y0 : $i]: ((^[Y1 : $i]: (n_some @ (diffprop @ Y1 @ Y0))))))), 182.17/42.61 inference(cnf_transformation,[],[f1095])). 182.17/42.61 thf(f1095,plain,( 182.17/42.61 (iii = (^[Y0 : $i]: ((^[Y1 : $i]: (n_some @ (diffprop @ Y1 @ Y0))))))), 182.17/42.61 inference(fool_elimination,[],[f187])). 182.17/42.61 thf(f187,axiom,( 182.17/42.61 ((^[X0 : $i, X1 : $i] : (n_some @ (diffprop @ X1 @ X0))) = iii)), 182.17/42.61 file('/export/starexec/sandbox2/tmp/tmp.Wx2OXKe4bp/E---3.1_26322.p',def_iii)). 182.17/42.61 thf(f1488,plain,( 182.17/42.61 (lessf = (^[Y0 : $i]: ((^[Y1 : $i]: (iii @ (n_ts @ (num @ Y0) @ (den @ Y1)) @ (n_ts @ (num @ Y1) @ (den @ Y0)))))))), 182.17/42.61 inference(cnf_transformation,[],[f664])). 182.17/42.61 thf(f664,plain,( 182.17/42.61 (lessf = (^[Y0 : $i]: ((^[Y1 : $i]: (iii @ (n_ts @ (num @ Y0) @ (den @ Y1)) @ (n_ts @ (num @ Y1) @ (den @ Y0)))))))), 182.17/42.61 inference(fool_elimination,[],[f233])). 182.17/42.61 thf(f233,axiom,( 182.17/42.61 (lessf = (^[X0 : $i, X1 : $i] : (iii @ (n_ts @ (num @ X0) @ (den @ X1)) @ (n_ts @ (num @ X1) @ (den @ X0)))))), 182.17/42.61 file('/export/starexec/sandbox2/tmp/tmp.Wx2OXKe4bp/E---3.1_26322.p',def_lessf)). 182.17/42.61 thf(f1696,plain,( 182.17/42.61 (class = ((^[Y0 : $i]: ((^[Y1 : $i > $i > $o]: (e_in @ (power @ Y0) @ (anec @ Y0 @ Y1))))) @ frac @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (Y3 = Y4)))))) @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: (if @ (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (in @ Y4 @ Y2)))) @ (repl @ Y2 @ (^[Y4 : $i]: (if @ (Y3 @ Y4) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (Y3 @ Y5))))))) @ emptyset)))) @ omega @ (^[Y2 : $i]: (~ (emptyset = Y2)))) @ (n_ts @ (first1 @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: (if @ (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (in @ Y4 @ Y2)))) @ (repl @ Y2 @ (^[Y4 : $i]: (if @ (Y3 @ Y4) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (Y3 @ Y5))))))) @ emptyset)))) @ omega @ (^[Y2 : $i]: (~ (emptyset = Y2)))) @ Y0) @ (second1 @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: (if @ (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (in @ Y4 @ Y2)))) @ (repl @ Y2 @ (^[Y4 : $i]: (if @ (Y3 @ Y4) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (Y3 @ Y5))))))) @ emptyset)))) @ omega @ (^[Y2 : $i]: (~ (emptyset = Y2)))) @ Y1)) @ (n_ts @ (first1 @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: (if @ (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (in @ Y4 @ Y2)))) @ (repl @ Y2 @ (^[Y4 : $i]: (if @ (Y3 @ Y4) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (Y3 @ Y5))))))) @ emptyset)))) @ omega @ (^[Y2 : $i]: (~ (emptyset = Y2)))) @ Y1) @ (second1 @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: (if @ (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (in @ Y4 @ Y2)))) @ (repl @ Y2 @ (^[Y4 : $i]: (if @ (Y3 @ Y4) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (Y3 @ Y5))))))) @ emptyset)))) @ omega @ (^[Y2 : $i]: (~ (emptyset = Y2)))) @ Y0))))))))), 182.17/42.61 inference(definition_unfolding,[],[f1447,f1407,f1674])). 182.17/42.61 thf(f1674,plain,( 182.17/42.61 (n_eq = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (Y3 = Y4)))))) @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: (if @ (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (in @ Y4 @ Y2)))) @ (repl @ Y2 @ (^[Y4 : $i]: (if @ (Y3 @ Y4) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (Y3 @ Y5))))))) @ emptyset)))) @ omega @ (^[Y2 : $i]: (~ (emptyset = Y2)))) @ (n_ts @ (first1 @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: (if @ (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (in @ Y4 @ Y2)))) @ (repl @ Y2 @ (^[Y4 : $i]: (if @ (Y3 @ Y4) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (Y3 @ Y5))))))) @ emptyset)))) @ omega @ (^[Y2 : $i]: (~ (emptyset = Y2)))) @ Y0) @ (second1 @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: (if @ (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (in @ Y4 @ Y2)))) @ (repl @ Y2 @ (^[Y4 : $i]: (if @ (Y3 @ Y4) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (Y3 @ Y5))))))) @ emptyset)))) @ omega @ (^[Y2 : $i]: (~ (emptyset = Y2)))) @ Y1)) @ (n_ts @ (first1 @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: (if @ (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (in @ Y4 @ Y2)))) @ (repl @ Y2 @ (^[Y4 : $i]: (if @ (Y3 @ Y4) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (Y3 @ Y5))))))) @ emptyset)))) @ omega @ (^[Y2 : $i]: (~ (emptyset = Y2)))) @ Y1) @ (second1 @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: (if @ (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (in @ Y4 @ Y2)))) @ (repl @ Y2 @ (^[Y4 : $i]: (if @ (Y3 @ Y4) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (Y3 @ Y5))))))) @ emptyset)))) @ omega @ (^[Y2 : $i]: (~ (emptyset = Y2)))) @ Y0)))))))), 182.17/42.61 inference(definition_unfolding,[],[f1505,f1663,f1672,f1673,f1672,f1673])). 182.17/42.61 thf(f1505,plain,( 182.17/42.61 (n_eq = (^[Y0 : $i]: ((^[Y1 : $i]: (n_is @ (n_ts @ (num @ Y0) @ (den @ Y1)) @ (n_ts @ (num @ Y1) @ (den @ Y0)))))))), 182.17/42.61 inference(cnf_transformation,[],[f1035])). 182.17/42.61 thf(f1035,plain,( 182.17/42.61 (n_eq = (^[Y0 : $i]: ((^[Y1 : $i]: (n_is @ (n_ts @ (num @ Y0) @ (den @ Y1)) @ (n_ts @ (num @ Y1) @ (den @ Y0)))))))), 182.17/42.61 inference(fool_elimination,[],[f231])). 182.17/42.61 thf(f231,axiom,( 182.17/42.61 ((^[X0 : $i, X1 : $i] : (n_is @ (n_ts @ (num @ X0) @ (den @ X1)) @ (n_ts @ (num @ X1) @ (den @ X0)))) = n_eq)), 182.17/42.61 file('/export/starexec/sandbox2/tmp/tmp.Wx2OXKe4bp/E---3.1_26322.p',def_n_eq)). 182.17/42.61 thf(f1407,plain,( 182.17/42.61 (ecect = (^[Y0 : $i]: ((^[Y1 : $i > $i > $o]: (e_in @ (power @ Y0) @ (anec @ Y0 @ Y1))))))), 182.17/42.61 inference(cnf_transformation,[],[f868])). 182.17/42.61 thf(f868,plain,( 182.17/42.61 (ecect = (^[Y0 : $i]: ((^[Y1 : $i > $i > $o]: (e_in @ (power @ Y0) @ (anec @ Y0 @ Y1))))))), 182.17/42.61 inference(fool_elimination,[],[f87])). 182.17/42.61 thf(f87,axiom,( 182.17/42.61 ((^[X0 : $i, X1 : $i > $i > $o] : (e_in @ (power @ X0) @ (anec @ X0 @ X1))) = ecect)), 182.17/42.61 file('/export/starexec/sandbox2/tmp/tmp.Wx2OXKe4bp/E---3.1_26322.p',def_ecect)). 182.17/42.61 thf(f1447,plain,( 182.17/42.61 (class = (ecect @ frac @ n_eq))), 182.17/42.61 inference(cnf_transformation,[],[f477])). 182.17/42.61 thf(f477,axiom,( 182.17/42.61 (class = (ecect @ frac @ n_eq))), 182.17/42.61 file('/export/starexec/sandbox2/tmp/tmp.Wx2OXKe4bp/E---3.1_26322.p',def_class)). 182.17/42.61 thf(f1699,plain,( 182.17/42.61 (inf = ((^[Y0 : $i]: (in)) @ frac))), 182.17/42.61 inference(definition_unfolding,[],[f1378,f1319])). 182.17/42.61 thf(f1319,plain,( 182.17/42.61 (esti = (^[Y0 : $i]: (in)))), 182.17/42.61 inference(cnf_transformation,[],[f1024])). 182.17/42.61 thf(f1024,plain,( 182.17/42.61 (esti = (^[Y0 : $i]: (in)))), 182.17/42.61 inference(fool_elimination,[],[f74])). 182.17/42.61 thf(f74,axiom,( 182.17/42.61 (esti = (^[X0 : $i] : (in)))), 182.17/42.61 file('/export/starexec/sandbox2/tmp/tmp.Wx2OXKe4bp/E---3.1_26322.p',def_esti)). 182.17/42.61 thf(f1378,plain,( 182.17/42.61 (inf = (esti @ frac))), 182.17/42.61 inference(cnf_transformation,[],[f468])). 182.17/42.61 thf(f468,axiom,( 182.17/42.61 (inf = (esti @ frac))), 182.17/42.61 file('/export/starexec/sandbox2/tmp/tmp.Wx2OXKe4bp/E---3.1_26322.p',def_inf)). 182.17/42.61 thf(f1691,plain,( 182.17/42.61 (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))))))))), 182.17/42.61 inference(definition_unfolding,[],[f1345,f1684,f1684])). 182.17/42.61 thf(f1684,plain,( 182.17/42.61 (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))))))), 182.17/42.61 inference(definition_unfolding,[],[f1401,f1667,f1680])). 182.17/42.61 thf(f1680,plain,( 182.17/42.61 (l_ec = (^[Y0 : $o]: ((^[Y1 : $o]: ((^[Y2 : $o]: ((^[Y3 : $o]: (Y2 => Y3)))) @ Y0 @ ((^[Y2 : $o]: ((^[Y3 : $o]: ((^[Y4 : $o]: (Y3 => Y4)))) @ Y2 @ $false)) @ Y1))))))), 182.17/42.61 inference(definition_unfolding,[],[f1625,f1648,f1667])). 182.17/42.61 thf(f1648,plain,( 182.17/42.61 (imp = (^[Y0 : $o]: ((^[Y1 : $o]: (Y0 => Y1)))))), 182.17/42.61 inference(cnf_transformation,[],[f516])). 182.17/42.61 thf(f516,plain,( 182.17/42.61 (imp = (^[Y0 : $o]: ((^[Y1 : $o]: (Y0 => Y1)))))), 182.17/42.61 inference(fool_elimination,[],[f515])). 182.17/42.61 thf(f515,plain,( 182.17/42.61 ((^[X0 : $o, X1 : $o] : (X0 => X1)) = imp)), 182.17/42.61 inference(rectify,[],[f33])). 182.17/42.61 thf(f33,axiom,( 182.17/42.61 ((^[X0 : $o, X1 : $o] : (X0 => X1)) = imp)), 182.17/42.61 file('/export/starexec/sandbox2/tmp/tmp.Wx2OXKe4bp/E---3.1_26322.p',def_imp)). 182.17/42.61 thf(f1625,plain,( 182.17/42.61 (l_ec = (^[Y0 : $o]: ((^[Y1 : $o]: (imp @ Y0 @ (d_not @ Y1))))))), 182.17/42.61 inference(cnf_transformation,[],[f727])). 182.17/42.61 thf(f727,plain,( 182.17/42.61 (l_ec = (^[Y0 : $o]: ((^[Y1 : $o]: (imp @ Y0 @ (d_not @ Y1))))))), 182.17/42.61 inference(fool_elimination,[],[f37])). 182.17/42.61 thf(f37,axiom,( 182.17/42.61 (l_ec = (^[X0 : $o, X1 : $o] : (imp @ X0 @ (d_not @ X1))))), 182.17/42.61 file('/export/starexec/sandbox2/tmp/tmp.Wx2OXKe4bp/E---3.1_26322.p',def_l_ec)). 182.17/42.61 thf(f1401,plain,( 182.17/42.61 (d_and = (^[Y0 : $o]: ((^[Y1 : $o]: (d_not @ (l_ec @ Y0 @ Y1))))))), 182.17/42.61 inference(cnf_transformation,[],[f1250])). 182.17/42.61 thf(f1250,plain,( 182.17/42.61 (d_and = (^[Y0 : $o]: ((^[Y1 : $o]: (d_not @ (l_ec @ Y0 @ Y1))))))), 182.17/42.61 inference(fool_elimination,[],[f38])). 182.17/42.61 thf(f38,axiom,( 182.17/42.61 (d_and = (^[X0 : $o, X1 : $o] : (d_not @ (l_ec @ X0 @ X1))))), 182.17/42.61 file('/export/starexec/sandbox2/tmp/tmp.Wx2OXKe4bp/E---3.1_26322.p',def_d_and)). 182.17/42.61 thf(f1345,plain,( 182.17/42.61 (and3 = (^[Y0 : $o]: ((^[Y1 : $o]: ((^[Y2 : $o]: (d_and @ Y0 @ (d_and @ Y1 @ Y2))))))))), 182.17/42.61 inference(cnf_transformation,[],[f1188])). 182.17/42.61 thf(f1188,plain,( 182.17/42.61 (and3 = (^[Y0 : $o]: ((^[Y1 : $o]: ((^[Y2 : $o]: (d_and @ Y0 @ (d_and @ Y1 @ Y2))))))))), 182.17/42.61 inference(fool_elimination,[],[f46])). 182.17/42.61 thf(f46,axiom,( 182.17/42.61 (and3 = (^[X0 : $o, X1 : $o, X2 : $o] : (d_and @ X0 @ (d_and @ X1 @ X2))))), 182.17/42.61 file('/export/starexec/sandbox2/tmp/tmp.Wx2OXKe4bp/E---3.1_26322.p',def_and3)). 182.17/42.61 thf(f1475,plain,( 182.17/42.61 (rt_less = (^[Y0 : $i]: ((^[Y1 : $i]: (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (and3 @ (inf @ Y2 @ (class @ Y0)) @ (inf @ Y3 @ (class @ Y1)) @ (lessf @ Y2 @ Y3))))))))))), 182.17/42.61 inference(cnf_transformation,[],[f534])). 182.17/42.61 thf(f534,plain,( 182.17/42.61 (rt_less = (^[Y0 : $i]: ((^[Y1 : $i]: (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (and3 @ (inf @ Y2 @ (class @ Y0)) @ (inf @ Y3 @ (class @ Y1)) @ (lessf @ Y2 @ Y3))))))))))), 182.17/42.61 inference(fool_elimination,[],[f482])). 182.17/42.61 thf(f482,axiom,( 182.17/42.61 (rt_less = (^[X0 : $i, X1 : $i] : (l_some @ frac @ (^[X2 : $i] : (l_some @ frac @ (^[X3 : $i] : (and3 @ (inf @ X2 @ (class @ X0)) @ (inf @ X3 @ (class @ X1)) @ (lessf @ X2 @ X3))))))))), 182.17/42.61 file('/export/starexec/sandbox2/tmp/tmp.Wx2OXKe4bp/E---3.1_26322.p',def_rt_less)). 182.17/42.61 thf(f1668,plain,( 182.17/42.61 (l_or = (^[Y0 : $o]: ((^[Y1 : $o]: ((^[Y2 : $o]: (Y1 => Y2)))) @ ((^[Y1 : $o]: ((^[Y2 : $o]: ((^[Y3 : $o]: (Y2 => Y3)))) @ Y1 @ $false)) @ Y0))))), 182.17/42.61 inference(definition_unfolding,[],[f1477,f1648,f1667])). 182.17/42.61 thf(f1477,plain,( 182.17/42.61 (l_or = (^[Y0 : $o]: (imp @ (d_not @ Y0))))), 182.17/42.61 inference(cnf_transformation,[],[f796])). 182.17/42.61 thf(f796,plain,( 182.17/42.61 (l_or = (^[Y0 : $o]: (imp @ (d_not @ Y0))))), 182.17/42.61 inference(fool_elimination,[],[f39])). 182.17/42.61 thf(f39,axiom,( 182.17/42.61 (l_or = (^[X0 : $o] : (imp @ (d_not @ X0))))), 182.17/42.61 file('/export/starexec/sandbox2/tmp/tmp.Wx2OXKe4bp/E---3.1_26322.p',def_l_or)). 182.17/42.61 thf(f1658,plain,( 182.17/42.61 (rt_lessis = (^[Y0 : $i]: ((^[Y1 : $i]: (l_or @ (rt_less @ Y0 @ Y1) @ (rt_is @ Y0 @ Y1))))))), 182.17/42.61 inference(cnf_transformation,[],[f750])). 182.17/42.61 thf(f750,plain,( 182.17/42.61 (rt_lessis = (^[Y0 : $i]: ((^[Y1 : $i]: (l_or @ (rt_less @ Y0 @ Y1) @ (rt_is @ Y0 @ Y1))))))), 182.17/42.61 inference(fool_elimination,[],[f485])). 182.17/42.61 thf(f485,axiom,( 182.17/42.61 ((^[X0 : $i, X1 : $i] : (l_or @ (rt_less @ X0 @ X1) @ (rt_is @ X0 @ X1))) = rt_lessis)), 182.17/42.61 file('/export/starexec/sandbox2/tmp/tmp.Wx2OXKe4bp/E---3.1_26322.p',def_rt_lessis)). 182.17/42.61 thf(f1700,plain,( 182.17/42.61 (rt_more = (^[Y0 : $i]: ((^[Y1 : $i]: (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: ((^[Y4 : $o]: ((^[Y5 : $o]: ((^[Y6 : $o]: ((^[Y7 : $o]: ((^[Y8 : $o]: ((^[Y9 : $o]: ((^[Y10 : $o]: ((^[Y11 : $o]: (Y10 => Y11)))) @ Y9 @ $false)) @ ((^[Y9 : $o]: ((^[Y10 : $o]: ((^[Y11 : $o]: ((^[Y12 : $o]: (Y11 => Y12)))) @ Y9 @ ((^[Y11 : $o]: ((^[Y12 : $o]: ((^[Y13 : $o]: (Y12 => Y13)))) @ Y11 @ $false)) @ Y10))))) @ Y7 @ Y8))))) @ Y4 @ ((^[Y7 : $o]: ((^[Y8 : $o]: ((^[Y9 : $o]: ((^[Y10 : $o]: ((^[Y11 : $o]: (Y10 => Y11)))) @ Y9 @ $false)) @ ((^[Y9 : $o]: ((^[Y10 : $o]: ((^[Y11 : $o]: ((^[Y12 : $o]: (Y11 => Y12)))) @ Y9 @ ((^[Y11 : $o]: ((^[Y12 : $o]: ((^[Y13 : $o]: (Y12 => Y13)))) @ Y11 @ $false)) @ Y10))))) @ Y7 @ Y8))))) @ Y5 @ Y6))))))) @ ((^[Y4 : $i]: (in)) @ frac @ Y2 @ ((^[Y4 : $i]: ((^[Y5 : $i > $i > $o]: (e_in @ (power @ Y4) @ (anec @ Y4 @ Y5))))) @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (Y7 = Y8)))))) @ ((^[Y6 : $i]: ((^[Y7 : $i > $o]: (if @ (?? @ $i @ (^[Y8 : $i]: ((Y7 @ Y8) & (in @ Y8 @ Y6)))) @ (repl @ Y6 @ (^[Y8 : $i]: (if @ (Y7 @ Y8) @ Y8 @ (eps @ (^[Y9 : $i]: ((in @ Y9 @ Y6) & (Y7 @ Y9))))))) @ emptyset)))) @ omega @ (^[Y6 : $i]: (~ (emptyset = Y6)))) @ (n_ts @ (first1 @ ((^[Y6 : $i]: ((^[Y7 : $i > $o]: (if @ (?? @ $i @ (^[Y8 : $i]: ((Y7 @ Y8) & (in @ Y8 @ Y6)))) @ (repl @ Y6 @ (^[Y8 : $i]: (if @ (Y7 @ Y8) @ Y8 @ (eps @ (^[Y9 : $i]: ((in @ Y9 @ Y6) & (Y7 @ Y9))))))) @ emptyset)))) @ omega @ (^[Y6 : $i]: (~ (emptyset = Y6)))) @ Y4) @ (second1 @ ((^[Y6 : $i]: ((^[Y7 : $i > $o]: (if @ (?? @ $i @ (^[Y8 : $i]: ((Y7 @ Y8) & (in @ Y8 @ Y6)))) @ (repl @ Y6 @ (^[Y8 : $i]: (if @ (Y7 @ Y8) @ Y8 @ (eps @ (^[Y9 : $i]: ((in @ Y9 @ Y6) & (Y7 @ Y9))))))) @ emptyset)))) @ omega @ (^[Y6 : $i]: (~ (emptyset = Y6)))) @ Y5)) @ (n_ts @ (first1 @ ((^[Y6 : $i]: ((^[Y7 : $i > $o]: (if @ (?? @ $i @ (^[Y8 : $i]: ((Y7 @ Y8) & (in @ Y8 @ Y6)))) @ (repl @ Y6 @ (^[Y8 : $i]: (if @ (Y7 @ Y8) @ Y8 @ (eps @ (^[Y9 : $i]: ((in @ Y9 @ Y6) & (Y7 @ Y9))))))) @ emptyset)))) @ omega @ (^[Y6 : $i]: (~ (emptyset = Y6)))) @ Y5) @ (second1 @ ((^[Y6 : $i]: ((^[Y7 : $i > $o]: (if @ (?? @ $i @ (^[Y8 : $i]: ((Y7 @ Y8) & (in @ Y8 @ Y6)))) @ (repl @ Y6 @ (^[Y8 : $i]: (if @ (Y7 @ Y8) @ Y8 @ (eps @ (^[Y9 : $i]: ((in @ Y9 @ Y6) & (Y7 @ Y9))))))) @ emptyset)))) @ omega @ (^[Y6 : $i]: (~ (emptyset = Y6)))) @ Y4)))))) @ Y0)) @ ((^[Y4 : $i]: (in)) @ frac @ Y3 @ ((^[Y4 : $i]: ((^[Y5 : $i > $i > $o]: (e_in @ (power @ Y4) @ (anec @ Y4 @ Y5))))) @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (Y7 = Y8)))))) @ ((^[Y6 : $i]: ((^[Y7 : $i > $o]: (if @ (?? @ $i @ (^[Y8 : $i]: ((Y7 @ Y8) & (in @ Y8 @ Y6)))) @ (repl @ Y6 @ (^[Y8 : $i]: (if @ (Y7 @ Y8) @ Y8 @ (eps @ (^[Y9 : $i]: ((in @ Y9 @ Y6) & (Y7 @ Y9))))))) @ emptyset)))) @ omega @ (^[Y6 : $i]: (~ (emptyset = Y6)))) @ (n_ts @ (first1 @ ((^[Y6 : $i]: ((^[Y7 : $i > $o]: (if @ (?? @ $i @ (^[Y8 : $i]: ((Y7 @ Y8) & (in @ Y8 @ Y6)))) @ (repl @ Y6 @ (^[Y8 : $i]: (if @ (Y7 @ Y8) @ Y8 @ (eps @ (^[Y9 : $i]: ((in @ Y9 @ Y6) & (Y7 @ Y9))))))) @ emptyset)))) @ omega @ (^[Y6 : $i]: (~ (emptyset = Y6)))) @ Y4) @ (second1 @ ((^[Y6 : $i]: ((^[Y7 : $i > $o]: (if @ (?? @ $i @ (^[Y8 : $i]: ((Y7 @ Y8) & (in @ Y8 @ Y6)))) @ (repl @ Y6 @ (^[Y8 : $i]: (if @ (Y7 @ Y8) @ Y8 @ (eps @ (^[Y9 : $i]: ((in @ Y9 @ Y6) & (Y7 @ Y9))))))) @ emptyset)))) @ omega @ (^[Y6 : $i]: (~ (emptyset = Y6)))) @ Y5)) @ (n_ts @ (first1 @ ((^[Y6 : $i]: ((^[Y7 : $i > $o]: (if @ (?? @ $i @ (^[Y8 : $i]: ((Y7 @ Y8) & (in @ Y8 @ Y6)))) @ (repl @ Y6 @ (^[Y8 : $i]: (if @ (Y7 @ Y8) @ Y8 @ (eps @ (^[Y9 : $i]: ((in @ Y9 @ Y6) & (Y7 @ Y9))))))) @ emptyset)))) @ omega @ (^[Y6 : $i]: (~ (emptyset = Y6)))) @ Y5) @ (second1 @ ((^[Y6 : $i]: ((^[Y7 : $i > $o]: (if @ (?? @ $i @ (^[Y8 : $i]: ((Y7 @ Y8) & (in @ Y8 @ Y6)))) @ (repl @ Y6 @ (^[Y8 : $i]: (if @ (Y7 @ Y8) @ Y8 @ (eps @ (^[Y9 : $i]: ((in @ Y9 @ Y6) & (Y7 @ Y9))))))) @ emptyset)))) @ omega @ (^[Y6 : $i]: (~ (emptyset = Y6)))) @ Y4)))))) @ Y1)) @ ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (l_some @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ ((^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: ((^[Y13 : $i]: (Y12 = Y13)))))) @ ((^[Y11 : $i]: ((^[Y12 : $i > $o]: (if @ (?? @ $i @ (^[Y13 : $i]: ((Y12 @ Y13) & (in @ Y13 @ Y11)))) @ (repl @ Y11 @ (^[Y13 : $i]: (if @ (Y12 @ Y13) @ Y13 @ (eps @ (^[Y14 : $i]: ((in @ Y14 @ Y11) & (Y12 @ Y14))))))) @ emptyset)))) @ omega @ (^[Y11 : $i]: (~ (emptyset = Y11)))) @ Y8 @ (n_pl @ Y9 @ Y10))))))) @ Y6 @ Y7))))) @ (n_ts @ (first1 @ ((^[Y6 : $i]: ((^[Y7 : $i > $o]: (if @ (?? @ $i @ (^[Y8 : $i]: ((Y7 @ Y8) & (in @ Y8 @ Y6)))) @ (repl @ Y6 @ (^[Y8 : $i]: (if @ (Y7 @ Y8) @ Y8 @ (eps @ (^[Y9 : $i]: ((in @ Y9 @ Y6) & (Y7 @ Y9))))))) @ emptyset)))) @ omega @ (^[Y6 : $i]: (~ (emptyset = Y6)))) @ Y4) @ (second1 @ ((^[Y6 : $i]: ((^[Y7 : $i > $o]: (if @ (?? @ $i @ (^[Y8 : $i]: ((Y7 @ Y8) & (in @ Y8 @ Y6)))) @ (repl @ Y6 @ (^[Y8 : $i]: (if @ (Y7 @ Y8) @ Y8 @ (eps @ (^[Y9 : $i]: ((in @ Y9 @ Y6) & (Y7 @ Y9))))))) @ emptyset)))) @ omega @ (^[Y6 : $i]: (~ (emptyset = Y6)))) @ Y5)) @ (n_ts @ (first1 @ ((^[Y6 : $i]: ((^[Y7 : $i > $o]: (if @ (?? @ $i @ (^[Y8 : $i]: ((Y7 @ Y8) & (in @ Y8 @ Y6)))) @ (repl @ Y6 @ (^[Y8 : $i]: (if @ (Y7 @ Y8) @ Y8 @ (eps @ (^[Y9 : $i]: ((in @ Y9 @ Y6) & (Y7 @ Y9))))))) @ emptyset)))) @ omega @ (^[Y6 : $i]: (~ (emptyset = Y6)))) @ Y5) @ (second1 @ ((^[Y6 : $i]: ((^[Y7 : $i > $o]: (if @ (?? @ $i @ (^[Y8 : $i]: ((Y7 @ Y8) & (in @ Y8 @ Y6)))) @ (repl @ Y6 @ (^[Y8 : $i]: (if @ (Y7 @ Y8) @ Y8 @ (eps @ (^[Y9 : $i]: ((in @ Y9 @ Y6) & (Y7 @ Y9))))))) @ emptyset)))) @ omega @ (^[Y6 : $i]: (~ (emptyset = Y6)))) @ Y4)))))) @ Y2 @ Y3))))))))))), 182.17/42.61 inference(definition_unfolding,[],[f1579,f1691,f1699,f1696,f1699,f1696,f1679])). 182.17/42.61 thf(f1679,plain,( 182.17/42.61 (moref = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (l_some @ ((^[Y4 : $i]: ((^[Y5 : $i > $o]: (if @ (?? @ $i @ (^[Y6 : $i]: ((Y5 @ Y6) & (in @ Y6 @ Y4)))) @ (repl @ Y4 @ (^[Y6 : $i]: (if @ (Y5 @ Y6) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ Y4) & (Y5 @ Y7))))))) @ emptyset)))) @ omega @ (^[Y4 : $i]: (~ (emptyset = Y4)))) @ ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: (Y8 = Y9)))))) @ ((^[Y7 : $i]: ((^[Y8 : $i > $o]: (if @ (?? @ $i @ (^[Y9 : $i]: ((Y8 @ Y9) & (in @ Y9 @ Y7)))) @ (repl @ Y7 @ (^[Y9 : $i]: (if @ (Y8 @ Y9) @ Y9 @ (eps @ (^[Y10 : $i]: ((in @ Y10 @ Y7) & (Y8 @ Y10))))))) @ emptyset)))) @ omega @ (^[Y7 : $i]: (~ (emptyset = Y7)))) @ Y4 @ (n_pl @ Y5 @ Y6))))))) @ Y2 @ Y3))))) @ (n_ts @ (first1 @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: (if @ (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (in @ Y4 @ Y2)))) @ (repl @ Y2 @ (^[Y4 : $i]: (if @ (Y3 @ Y4) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (Y3 @ Y5))))))) @ emptyset)))) @ omega @ (^[Y2 : $i]: (~ (emptyset = Y2)))) @ Y0) @ (second1 @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: (if @ (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (in @ Y4 @ Y2)))) @ (repl @ Y2 @ (^[Y4 : $i]: (if @ (Y3 @ Y4) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (Y3 @ Y5))))))) @ emptyset)))) @ omega @ (^[Y2 : $i]: (~ (emptyset = Y2)))) @ Y1)) @ (n_ts @ (first1 @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: (if @ (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (in @ Y4 @ Y2)))) @ (repl @ Y2 @ (^[Y4 : $i]: (if @ (Y3 @ Y4) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (Y3 @ Y5))))))) @ emptyset)))) @ omega @ (^[Y2 : $i]: (~ (emptyset = Y2)))) @ Y1) @ (second1 @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: (if @ (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (in @ Y4 @ Y2)))) @ (repl @ Y2 @ (^[Y4 : $i]: (if @ (Y3 @ Y4) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (Y3 @ Y5))))))) @ emptyset)))) @ omega @ (^[Y2 : $i]: (~ (emptyset = Y2)))) @ Y0)))))))), 182.17/42.61 inference(definition_unfolding,[],[f1595,f1669,f1672,f1673,f1672,f1673])). 182.17/42.61 thf(f1669,plain,( 182.17/42.61 (d_29_ii = (^[Y0 : $i]: ((^[Y1 : $i]: (l_some @ ((^[Y2 : $i]: ((^[Y3 : $i > $o]: (if @ (?? @ $i @ (^[Y4 : $i]: ((Y3 @ Y4) & (in @ Y4 @ Y2)))) @ (repl @ Y2 @ (^[Y4 : $i]: (if @ (Y3 @ Y4) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ Y2) & (Y3 @ Y5))))))) @ emptyset)))) @ omega @ (^[Y2 : $i]: (~ (emptyset = Y2)))) @ ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (Y6 = Y7)))))) @ ((^[Y5 : $i]: ((^[Y6 : $i > $o]: (if @ (?? @ $i @ (^[Y7 : $i]: ((Y6 @ Y7) & (in @ Y7 @ Y5)))) @ (repl @ Y5 @ (^[Y7 : $i]: (if @ (Y6 @ Y7) @ Y7 @ (eps @ (^[Y8 : $i]: ((in @ Y8 @ Y5) & (Y6 @ Y8))))))) @ emptyset)))) @ omega @ (^[Y5 : $i]: (~ (emptyset = Y5)))) @ Y2 @ (n_pl @ Y3 @ Y4))))))) @ Y0 @ Y1))))))), 182.17/42.61 inference(definition_unfolding,[],[f1640,f1662,f1664])). 182.17/42.61 thf(f1640,plain,( 182.17/42.61 (d_29_ii = (^[Y0 : $i]: ((^[Y1 : $i]: (n_some @ (diffprop @ Y0 @ Y1))))))), 182.17/42.61 inference(cnf_transformation,[],[f1084])). 182.17/42.61 thf(f1084,plain,( 182.17/42.61 (d_29_ii = (^[Y0 : $i]: ((^[Y1 : $i]: (n_some @ (diffprop @ Y0 @ Y1))))))), 182.17/42.61 inference(fool_elimination,[],[f186])). 182.17/42.61 thf(f186,axiom,( 182.17/42.61 (d_29_ii = (^[X0 : $i, X1 : $i] : (n_some @ (diffprop @ X0 @ X1))))), 182.17/42.61 file('/export/starexec/sandbox2/tmp/tmp.Wx2OXKe4bp/E---3.1_26322.p',def_d_29_ii)). 182.17/42.61 thf(f1595,plain,( 182.17/42.61 (moref = (^[Y0 : $i]: ((^[Y1 : $i]: (d_29_ii @ (n_ts @ (num @ Y0) @ (den @ Y1)) @ (n_ts @ (num @ Y1) @ (den @ Y0)))))))), 182.17/42.61 inference(cnf_transformation,[],[f1196])). 182.17/42.61 thf(f1196,plain,( 182.17/42.61 (moref = (^[Y0 : $i]: ((^[Y1 : $i]: (d_29_ii @ (n_ts @ (num @ Y0) @ (den @ Y1)) @ (n_ts @ (num @ Y1) @ (den @ Y0)))))))), 182.17/42.61 inference(fool_elimination,[],[f232])). 182.17/42.61 thf(f232,axiom,( 182.17/42.61 ((^[X0 : $i, X1 : $i] : (d_29_ii @ (n_ts @ (num @ X0) @ (den @ X1)) @ (n_ts @ (num @ X1) @ (den @ X0)))) = moref)), 182.17/42.61 file('/export/starexec/sandbox2/tmp/tmp.Wx2OXKe4bp/E---3.1_26322.p',def_moref)). 182.17/42.61 thf(f1579,plain,( 182.17/42.61 (rt_more = (^[Y0 : $i]: ((^[Y1 : $i]: (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (and3 @ (inf @ Y2 @ (class @ Y0)) @ (inf @ Y3 @ (class @ Y1)) @ (moref @ Y2 @ Y3))))))))))), 182.17/42.61 inference(cnf_transformation,[],[f557])). 182.17/42.61 thf(f557,plain,( 182.17/42.61 (rt_more = (^[Y0 : $i]: ((^[Y1 : $i]: (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (and3 @ (inf @ Y2 @ (class @ Y0)) @ (inf @ Y3 @ (class @ Y1)) @ (moref @ Y2 @ Y3))))))))))), 182.17/42.61 inference(fool_elimination,[],[f480])). 182.17/42.61 thf(f480,axiom,( 182.17/42.61 ((^[X0 : $i, X1 : $i] : (l_some @ frac @ (^[X2 : $i] : (l_some @ frac @ (^[X3 : $i] : (and3 @ (inf @ X2 @ (class @ X0)) @ (inf @ X3 @ (class @ X1)) @ (moref @ X2 @ X3))))))) = rt_more)), 182.17/42.61 file('/export/starexec/sandbox2/tmp/tmp.Wx2OXKe4bp/E---3.1_26322.p',def_rt_more)). 182.17/42.61 thf(f1667,plain,( 182.17/42.61 (d_not = (^[Y0 : $o]: ((^[Y1 : $o]: ((^[Y2 : $o]: (Y1 => Y2)))) @ Y0 @ $false)))), 182.17/42.61 inference(definition_unfolding,[],[f1425,f1648])). 182.17/42.61 thf(f1425,plain,( 182.17/42.61 (d_not = (^[Y0 : $o]: (imp @ Y0 @ $false)))), 182.17/42.61 inference(cnf_transformation,[],[f1125])). 182.17/42.61 thf(f1125,plain,( 182.17/42.61 (d_not = (^[Y0 : $o]: (imp @ Y0 @ $false)))), 182.17/42.61 inference(fool_elimination,[],[f34])). 182.17/42.61 thf(f34,axiom,( 182.17/42.61 (d_not = (^[X0 : $o] : (imp @ X0 @ $false)))), 182.17/42.61 file('/export/starexec/sandbox2/tmp/tmp.Wx2OXKe4bp/E---3.1_26322.p',def_d_not)). 182.17/42.61 thf(f1666,plain,( 182.17/42.61 (all_of = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i > $o]: (Y4 @ Y3)))) @ Y2 @ Y0) => (Y1 @ Y2))))))))), 182.17/42.61 inference(definition_unfolding,[],[f1406,f1318])). 182.17/42.61 thf(f1318,plain,( 182.17/42.61 (is_of = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (Y1 @ Y0)))))), 182.17/42.61 inference(cnf_transformation,[],[f742])). 182.17/42.61 thf(f742,plain,( 182.17/42.61 (is_of = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (Y1 @ Y0)))))), 182.17/42.61 inference(fool_elimination,[],[f1])). 182.17/42.61 thf(f1,axiom,( 182.17/42.61 ((^[X0 : $i, X1 : $i > $o] : (X1 @ X0)) = is_of)), 182.17/42.61 file('/export/starexec/sandbox2/tmp/tmp.Wx2OXKe4bp/E---3.1_26322.p',def_is_of)). 182.17/42.61 thf(f1406,plain,( 182.17/42.61 (all_of = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((is_of @ Y2 @ Y0) => (Y1 @ Y2))))))))), 182.17/42.61 inference(cnf_transformation,[],[f1159])). 182.17/42.61 thf(f1159,plain,( 182.17/42.61 (all_of = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((is_of @ Y2 @ Y0) => (Y1 @ Y2))))))))), 182.17/42.61 inference(fool_elimination,[],[f1158])). 182.17/42.61 thf(f1158,plain,( 182.17/42.61 (all_of = (^[X0 : $i > $o, X1 : $i > $o] : (! [X2] : ((is_of @ X2 @ X0) => (X1 @ X2)))))), 182.17/42.61 inference(rectify,[],[f2])). 182.17/42.61 thf(f2,axiom,( 182.17/42.61 (all_of = (^[X0 : $i > $o, X1 : $i > $o] : (! [X2] : ((is_of @ X2 @ X0) => (X1 @ X2)))))), 182.17/42.61 file('/export/starexec/sandbox2/tmp/tmp.Wx2OXKe4bp/E---3.1_26322.p',def_all_of)). 182.17/42.61 thf(f1392,plain,( 182.17/42.61 ($true != (all_of @ (^[Y0 : $i]: (in @ Y0 @ rat)) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ rat)) @ (^[Y1 : $i]: ((d_not @ (rt_more @ Y0 @ Y1)) => (rt_lessis @ Y0 @ Y1)))))))), 182.17/42.61 inference(cnf_transformation,[],[f1280])). 182.17/42.61 thf(f1280,plain,( 182.17/42.61 ($true != (all_of @ (^[Y0 : $i]: (in @ Y0 @ rat)) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ rat)) @ (^[Y1 : $i]: ((d_not @ (rt_more @ Y0 @ Y1)) => (rt_lessis @ Y0 @ Y1)))))))), 182.17/42.61 inference(flattening,[],[f1252])). 182.17/42.61 thf(f1252,plain,( 182.17/42.61 ~($true = (all_of @ (^[Y0 : $i]: (in @ Y0 @ rat)) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ rat)) @ (^[Y1 : $i]: ((d_not @ (rt_more @ Y0 @ Y1)) => (rt_lessis @ Y0 @ Y1)))))))), 182.17/42.61 inference(fool_elimination,[],[f1251])). 182.17/42.61 thf(f1251,plain,( 182.17/42.61 ~(all_of @ (^[X0 : $i] : (in @ X0 @ rat)) @ (^[X1 : $i] : (all_of @ (^[X2 : $i] : (in @ X2 @ rat)) @ (^[X3 : $i] : ((d_not @ (rt_more @ X1 @ X3)) => (rt_lessis @ X1 @ X3))))))), 182.17/42.61 inference(rectify,[],[f494])). 182.17/42.61 thf(f494,negated_conjecture,( 182.17/42.61 ~(all_of @ (^[X0 : $i] : (in @ X0 @ rat)) @ (^[X0 : $i] : (all_of @ (^[X1 : $i] : (in @ X1 @ rat)) @ (^[X1 : $i] : ((d_not @ (rt_more @ X0 @ X1)) => (rt_lessis @ X0 @ X1))))))), 182.17/42.61 inference(negated_conjecture,[],[f493])). 182.17/42.61 thf(f493,conjecture,( 182.17/42.61 (all_of @ (^[X0 : $i] : (in @ X0 @ rat)) @ (^[X0 : $i] : (all_of @ (^[X1 : $i] : (in @ X1 @ rat)) @ (^[X1 : $i] : ((d_not @ (rt_more @ X0 @ X1)) => (rt_lessis @ X0 @ X1))))))), 182.17/42.61 file('/export/starexec/sandbox2/tmp/tmp.Wx2OXKe4bp/E---3.1_26322.p',satz81e)). 182.17/42.61 thf(f7653,plain,( 182.17/42.61 ($false = (in @ sK11 @ rat)) | ($false = (in @ sK12 @ rat))), 182.17/42.61 inference(trivial_inequality_removal,[],[f7652])). 182.17/42.61 thf(f7652,plain,( 182.17/42.61 ($false = $true) | ($false = (in @ sK11 @ rat)) | ($false = (in @ sK12 @ rat))), 182.17/42.61 inference(forward_demodulation,[],[f7651,f3700])). 182.17/42.61 thf(f3700,plain,( 182.17/42.61 ($false = (l_some @ frac @ (^[Y0 : $i]: (l_some @ frac @ (^[Y1 : $i]: (~ ((in @ Y0 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ sK11)) => ((in @ Y1 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ sK12)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y2 : $i]: ((~ (emptyset = Y2)) & (in @ Y2 @ omega)))) @ (repl @ omega @ (^[Y2 : $i]: (if @ (~ (emptyset = Y2)) @ Y2 @ (eps @ (^[Y3 : $i]: ((in @ Y3 @ omega) & (~ (emptyset = Y3)))))))) @ emptyset) @ (^[Y2 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1)) @ Y2)))))))))))))), 182.17/42.61 inference(not_proxy_clausification,[],[f3699])). 182.17/42.61 thf(f3699,plain,( 182.17/42.61 ($true = (~ (l_some @ frac @ (^[Y0 : $i]: (l_some @ frac @ (^[Y1 : $i]: (~ ((in @ Y0 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ sK11)) => ((in @ Y1 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ sK12)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y2 : $i]: ((~ (emptyset = Y2)) & (in @ Y2 @ omega)))) @ (repl @ omega @ (^[Y2 : $i]: (if @ (~ (emptyset = Y2)) @ Y2 @ (eps @ (^[Y3 : $i]: ((in @ Y3 @ omega) & (~ (emptyset = Y3)))))))) @ emptyset) @ (^[Y2 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1)) @ Y2))))))))))))))), 182.17/42.61 inference(binary_proxy_clausification,[],[f3695])). 182.17/42.61 thf(f3695,plain,( 182.17/42.61 ($false = ((~ (l_some @ frac @ (^[Y0 : $i]: (l_some @ frac @ (^[Y1 : $i]: (~ ((in @ Y0 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ sK11)) => ((in @ Y1 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ sK12)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y2 : $i]: ((~ (emptyset = Y2)) & (in @ Y2 @ omega)))) @ (repl @ omega @ (^[Y2 : $i]: (if @ (~ (emptyset = Y2)) @ Y2 @ (eps @ (^[Y3 : $i]: ((in @ Y3 @ omega) & (~ (emptyset = Y3)))))))) @ emptyset) @ (^[Y2 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1)) @ Y2))))))))))))) => (sK11 = sK12)))), 182.17/42.61 inference(binary_proxy_clausification,[],[f3693])). 182.17/42.61 thf(f3693,plain,( 182.17/42.61 ($false = ((~ (l_some @ frac @ (^[Y0 : $i]: (l_some @ frac @ (^[Y1 : $i]: (~ ((in @ Y0 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ sK11)) => ((in @ Y1 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ sK12)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y2 : $i]: ((~ (emptyset = Y2)) & (in @ Y2 @ omega)))) @ (repl @ omega @ (^[Y2 : $i]: (if @ (~ (emptyset = Y2)) @ Y2 @ (eps @ (^[Y3 : $i]: ((in @ Y3 @ omega) & (~ (emptyset = Y3)))))))) @ emptyset) @ (^[Y2 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0)) @ Y2))))))))))))) => ((~ (l_some @ frac @ (^[Y0 : $i]: (l_some @ frac @ (^[Y1 : $i]: (~ ((in @ Y0 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ sK11)) => ((in @ Y1 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ sK12)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y2 : $i]: ((~ (emptyset = Y2)) & (in @ Y2 @ omega)))) @ (repl @ omega @ (^[Y2 : $i]: (if @ (~ (emptyset = Y2)) @ Y2 @ (eps @ (^[Y3 : $i]: ((in @ Y3 @ omega) & (~ (emptyset = Y3)))))))) @ emptyset) @ (^[Y2 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1)) @ Y2))))))))))))) => (sK11 = sK12))))), 182.17/42.61 inference(binary_proxy_clausification,[],[f3692])). 182.17/42.61 thf(f3692,plain,( 182.17/42.61 ($false = ((in @ sK12 @ rat) => ((~ (l_some @ frac @ (^[Y0 : $i]: (l_some @ frac @ (^[Y1 : $i]: (~ ((in @ Y0 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ sK11)) => ((in @ Y1 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ sK12)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y2 : $i]: ((~ (emptyset = Y2)) & (in @ Y2 @ omega)))) @ (repl @ omega @ (^[Y2 : $i]: (if @ (~ (emptyset = Y2)) @ Y2 @ (eps @ (^[Y3 : $i]: ((in @ Y3 @ omega) & (~ (emptyset = Y3)))))))) @ emptyset) @ (^[Y2 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0)) @ Y2))))))))))))) => ((~ (l_some @ frac @ (^[Y0 : $i]: (l_some @ frac @ (^[Y1 : $i]: (~ ((in @ Y0 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ sK11)) => ((in @ Y1 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ sK12)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y2 : $i]: ((~ (emptyset = Y2)) & (in @ Y2 @ omega)))) @ (repl @ omega @ (^[Y2 : $i]: (if @ (~ (emptyset = Y2)) @ Y2 @ (eps @ (^[Y3 : $i]: ((in @ Y3 @ omega) & (~ (emptyset = Y3)))))))) @ emptyset) @ (^[Y2 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1)) @ Y2))))))))))))) => (sK11 = sK12)))))), 182.17/42.61 inference(beta_eta_normalization,[],[f3691])). 182.17/42.61 thf(f3691,plain,( 182.17/42.61 ($false = ((^[Y0 : $i]: ((in @ Y0 @ rat) => ((~ (l_some @ frac @ (^[Y1 : $i]: (l_some @ frac @ (^[Y2 : $i]: (~ ((in @ Y1 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y3 : $i]: ((^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3))))))) @ sK11)) => ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y3 : $i]: ((^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3))))))) @ Y0)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ (^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y1) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y1)) @ Y3))))))))))))) => ((~ (l_some @ frac @ (^[Y1 : $i]: (l_some @ frac @ (^[Y2 : $i]: (~ ((in @ Y1 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y3 : $i]: ((^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3))))))) @ sK11)) => ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y3 : $i]: ((^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3))))))) @ Y0)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ (^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y1)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y1) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2)) @ Y3))))))))))))) => (sK11 = Y0))))) @ sK12))), 182.17/42.61 inference(sigma_clausification,[],[f3689])). 182.17/42.61 thf(f3689,plain,( 182.17/42.61 ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ rat) => ((~ (l_some @ frac @ (^[Y1 : $i]: (l_some @ frac @ (^[Y2 : $i]: (~ ((in @ Y1 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y3 : $i]: ((^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3))))))) @ sK11)) => ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y3 : $i]: ((^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3))))))) @ Y0)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ (^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y1) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y1)) @ Y3))))))))))))) => ((~ (l_some @ frac @ (^[Y1 : $i]: (l_some @ frac @ (^[Y2 : $i]: (~ ((in @ Y1 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y3 : $i]: ((^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3))))))) @ sK11)) => ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y3 : $i]: ((^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3))))))) @ Y0)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ (^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y1)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y1) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2)) @ Y3))))))))))))) => (sK11 = Y0)))))))), 182.17/42.61 inference(binary_proxy_clausification,[],[f3688])). 182.17/42.61 thf(f7651,plain,( 182.17/42.61 ((l_some @ frac @ (^[Y0 : $i]: (l_some @ frac @ (^[Y1 : $i]: (~ ((in @ Y0 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ sK11)) => ((in @ Y1 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ sK12)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y2 : $i]: ((~ (emptyset = Y2)) & (in @ Y2 @ omega)))) @ (repl @ omega @ (^[Y2 : $i]: (if @ (~ (emptyset = Y2)) @ Y2 @ (eps @ (^[Y3 : $i]: ((in @ Y3 @ omega) & (~ (emptyset = Y3)))))))) @ emptyset) @ (^[Y2 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1)) @ Y2)))))))))))) = $true) | ($false = (in @ sK11 @ rat)) | ($false = (in @ sK12 @ rat))), 182.17/42.61 inference(subsumption_resolution,[],[f7646,f3701])). 182.17/42.61 thf(f3701,plain,( 182.17/42.61 (sK11 != sK12)), 182.17/42.61 inference(equality_proxy_clausification,[],[f3698])). 182.17/42.61 thf(f3698,plain,( 182.17/42.61 ($false = (sK11 = sK12))), 182.17/42.61 inference(binary_proxy_clausification,[],[f3695])). 182.17/42.61 thf(f7646,plain,( 182.17/42.61 ($false = (in @ sK12 @ rat)) | (sK11 = sK12) | ((l_some @ frac @ (^[Y0 : $i]: (l_some @ frac @ (^[Y1 : $i]: (~ ((in @ Y0 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ sK11)) => ((in @ Y1 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ sK12)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y2 : $i]: ((~ (emptyset = Y2)) & (in @ Y2 @ omega)))) @ (repl @ omega @ (^[Y2 : $i]: (if @ (~ (emptyset = Y2)) @ Y2 @ (eps @ (^[Y3 : $i]: ((in @ Y3 @ omega) & (~ (emptyset = Y3)))))))) @ emptyset) @ (^[Y2 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1)) @ Y2)))))))))))) = $true) | ($false = (in @ sK11 @ rat))), 182.17/42.61 inference(trivial_inequality_removal,[],[f7642])). 182.17/42.61 thf(f7642,plain,( 182.17/42.61 ($false = (in @ sK12 @ rat)) | (sK11 = sK12) | ((l_some @ frac @ (^[Y0 : $i]: (l_some @ frac @ (^[Y1 : $i]: (~ ((in @ Y0 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ sK11)) => ((in @ Y1 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ sK12)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y2 : $i]: ((~ (emptyset = Y2)) & (in @ Y2 @ omega)))) @ (repl @ omega @ (^[Y2 : $i]: (if @ (~ (emptyset = Y2)) @ Y2 @ (eps @ (^[Y3 : $i]: ((in @ Y3 @ omega) & (~ (emptyset = Y3)))))))) @ emptyset) @ (^[Y2 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1)) @ Y2)))))))))))) = $true) | ($false = $true) | ($false = (in @ sK11 @ rat))), 182.17/42.61 inference(superposition,[],[f4733,f3697])). 182.17/42.61 thf(f3697,plain,( 182.17/42.61 ($false = (l_some @ frac @ (^[Y0 : $i]: (l_some @ frac @ (^[Y1 : $i]: (~ ((in @ Y0 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ sK11)) => ((in @ Y1 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ sK12)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y2 : $i]: ((~ (emptyset = Y2)) & (in @ Y2 @ omega)))) @ (repl @ omega @ (^[Y2 : $i]: (if @ (~ (emptyset = Y2)) @ Y2 @ (eps @ (^[Y3 : $i]: ((in @ Y3 @ omega) & (~ (emptyset = Y3)))))))) @ emptyset) @ (^[Y2 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0)) @ Y2)))))))))))))), 182.17/42.61 inference(not_proxy_clausification,[],[f3696])). 182.17/42.61 thf(f3696,plain,( 182.17/42.61 ($true = (~ (l_some @ frac @ (^[Y0 : $i]: (l_some @ frac @ (^[Y1 : $i]: (~ ((in @ Y0 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ sK11)) => ((in @ Y1 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? 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[X2 : $i,X1 : $i] : (($true = (l_some @ frac @ (^[Y0 : $i]: (l_some @ frac @ (^[Y1 : $i]: (~ ((in @ Y0 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ X1)) => ((in @ Y1 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? 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@ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ X1)) => ((in @ Y1 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ X2)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y2 : $i]: ((~ (emptyset = Y2)) & (in @ Y2 @ omega)))) @ (repl @ omega @ (^[Y2 : $i]: (if @ (~ (emptyset = Y2)) @ Y2 @ (eps @ (^[Y3 : $i]: ((in @ Y3 @ omega) & (~ (emptyset = Y3)))))))) @ emptyset) @ (^[Y2 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0)) @ Y2)))))))))))))) | ((in @ X2 @ rat) = $false)) )), 182.17/42.61 inference(equality_proxy_clausification,[],[f4731])). 182.17/42.61 thf(f4731,plain,( 182.17/42.61 ( ! [X2 : $i,X1 : $i] : (($true = (l_some @ frac @ (^[Y0 : $i]: (l_some @ frac @ (^[Y1 : $i]: (~ ((in @ Y0 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ X1)) => ((in @ Y1 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ X2)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y2 : $i]: ((~ (emptyset = Y2)) & (in @ Y2 @ omega)))) @ (repl @ omega @ (^[Y2 : $i]: (if @ (~ (emptyset = Y2)) @ Y2 @ (eps @ (^[Y3 : $i]: ((in @ Y3 @ omega) & (~ (emptyset = Y3)))))))) @ emptyset) @ (^[Y2 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1)) @ Y2))))))))))))) | ((X1 = X2) = $true) | ((in @ X2 @ rat) = $false) | ((in @ X1 @ rat) = $false) | ($false = (~ (l_some @ frac @ (^[Y0 : $i]: (l_some @ frac @ (^[Y1 : $i]: (~ ((in @ Y0 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ X1)) => ((in @ Y1 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ X2)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y2 : $i]: ((~ (emptyset = Y2)) & (in @ Y2 @ omega)))) @ (repl @ omega @ (^[Y2 : $i]: (if @ (~ (emptyset = Y2)) @ Y2 @ (eps @ (^[Y3 : $i]: ((in @ Y3 @ omega) & (~ (emptyset = Y3)))))))) @ emptyset) @ (^[Y2 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0)) @ Y2))))))))))))))) )), 182.17/42.61 inference(not_proxy_clausification,[],[f4730])). 182.17/42.61 thf(f4730,plain,( 182.17/42.61 ( ! [X2 : $i,X1 : $i] : (($true = (l_some @ frac @ (^[Y0 : $i]: (l_some @ frac @ (^[Y1 : $i]: (~ ((in @ Y0 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ X1)) => ((in @ Y1 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ X2)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y2 : $i]: ((~ (emptyset = Y2)) & (in @ Y2 @ omega)))) @ (repl @ omega @ (^[Y2 : $i]: (if @ (~ (emptyset = Y2)) @ Y2 @ (eps @ (^[Y3 : $i]: ((in @ Y3 @ omega) & (~ (emptyset = Y3)))))))) @ emptyset) @ (^[Y2 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1)) @ Y2))))))))))))) | ((in @ X1 @ rat) = $false) | ($false = (~ (X1 = X2))) | ((in @ X2 @ rat) = $false) | ($false = (~ (l_some @ frac @ (^[Y0 : $i]: (l_some @ frac @ (^[Y1 : $i]: (~ ((in @ Y0 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ X1)) => ((in @ Y1 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ X2)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y2 : $i]: ((~ (emptyset = Y2)) & (in @ Y2 @ omega)))) @ (repl @ omega @ (^[Y2 : $i]: (if @ (~ (emptyset = Y2)) @ Y2 @ (eps @ (^[Y3 : $i]: ((in @ Y3 @ omega) & (~ (emptyset = Y3)))))))) @ emptyset) @ (^[Y2 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0)) @ Y2))))))))))))))) )), 182.17/42.61 inference(binary_proxy_clausification,[],[f4729])). 182.17/42.61 thf(f4729,plain,( 182.17/42.61 ( ! [X2 : $i,X1 : $i] : (((in @ X1 @ rat) = $false) | ($true = ((~ (l_some @ frac @ (^[Y0 : $i]: (l_some @ frac @ (^[Y1 : $i]: (~ ((in @ Y0 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ X1)) => ((in @ Y1 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ X2)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y2 : $i]: ((~ (emptyset = Y2)) & (in @ Y2 @ omega)))) @ (repl @ omega @ (^[Y2 : $i]: (if @ (~ (emptyset = Y2)) @ Y2 @ (eps @ (^[Y3 : $i]: ((in @ Y3 @ omega) & (~ (emptyset = Y3)))))))) @ emptyset) @ (^[Y2 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0)) @ Y2))))))))))))) => (l_some @ frac @ (^[Y0 : $i]: (l_some @ frac @ (^[Y1 : $i]: (~ ((in @ Y0 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ X1)) => ((in @ Y1 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ X2)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y2 : $i]: ((~ (emptyset = Y2)) & (in @ Y2 @ omega)))) @ (repl @ omega @ (^[Y2 : $i]: (if @ (~ (emptyset = Y2)) @ Y2 @ (eps @ (^[Y3 : $i]: ((in @ Y3 @ omega) & (~ (emptyset = Y3)))))))) @ emptyset) @ (^[Y2 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1)) @ Y2)))))))))))))) | ($false = (~ (X1 = X2))) | ((in @ X2 @ rat) = $false)) )), 182.17/42.61 inference(binary_proxy_clausification,[],[f4728])). 182.17/42.61 thf(f4728,plain,( 182.17/42.61 ( ! [X2 : $i,X1 : $i] : (((in @ X2 @ rat) = $false) | (((~ (X1 = X2)) => ((~ (l_some @ frac @ (^[Y0 : $i]: (l_some @ frac @ (^[Y1 : $i]: (~ ((in @ Y0 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ X1)) => ((in @ Y1 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ X2)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y2 : $i]: ((~ (emptyset = Y2)) & (in @ Y2 @ omega)))) @ (repl @ omega @ (^[Y2 : $i]: (if @ (~ (emptyset = Y2)) @ Y2 @ (eps @ (^[Y3 : $i]: ((in @ Y3 @ omega) & (~ (emptyset = Y3)))))))) @ emptyset) @ (^[Y2 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0)) @ Y2))))))))))))) => (l_some @ frac @ (^[Y0 : $i]: (l_some @ frac @ (^[Y1 : $i]: (~ ((in @ Y0 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ X1)) => ((in @ Y1 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ X2)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y2 : $i]: ((~ (emptyset = Y2)) & (in @ Y2 @ omega)))) @ (repl @ omega @ (^[Y2 : $i]: (if @ (~ (emptyset = Y2)) @ Y2 @ (eps @ (^[Y3 : $i]: ((in @ Y3 @ omega) & (~ (emptyset = Y3)))))))) @ emptyset) @ (^[Y2 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1)) @ Y2)))))))))))))) = $true) | ((in @ X1 @ rat) = $false)) )), 182.17/42.61 inference(binary_proxy_clausification,[],[f4727])). 182.17/42.61 thf(f4727,plain,( 182.17/42.61 ( ! [X2 : $i,X1 : $i] : (($true = ((in @ X2 @ rat) => ((~ (X1 = X2)) => ((~ (l_some @ frac @ (^[Y0 : $i]: (l_some @ frac @ (^[Y1 : $i]: (~ ((in @ Y0 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ X1)) => ((in @ Y1 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ X2)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y2 : $i]: ((~ (emptyset = Y2)) & (in @ Y2 @ omega)))) @ (repl @ omega @ (^[Y2 : $i]: (if @ (~ (emptyset = Y2)) @ Y2 @ (eps @ (^[Y3 : $i]: ((in @ Y3 @ omega) & (~ (emptyset = Y3)))))))) @ emptyset) @ (^[Y2 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0)) @ Y2))))))))))))) => (l_some @ frac @ (^[Y0 : $i]: (l_some @ frac @ (^[Y1 : $i]: (~ ((in @ Y0 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ X1)) => ((in @ Y1 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y2 : $i]: ((^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2))))))) @ X2)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y2 : $i]: ((~ (emptyset = Y2)) & (in @ Y2 @ omega)))) @ (repl @ omega @ (^[Y2 : $i]: (if @ (~ (emptyset = Y2)) @ Y2 @ (eps @ (^[Y3 : $i]: ((in @ Y3 @ omega) & (~ (emptyset = Y3)))))))) @ emptyset) @ (^[Y2 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y0) @ (second1 @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ Y1)) @ Y2)))))))))))))))) | ((in @ X1 @ rat) = $false)) )), 182.17/42.61 inference(beta_eta_normalization,[],[f4726])). 182.17/42.61 thf(f4726,plain,( 182.17/42.61 ( ! [X2 : $i,X1 : $i] : (((in @ X1 @ rat) = $false) | ($true = ((^[Y0 : $i]: ((in @ Y0 @ rat) => ((~ (X1 = Y0)) => ((~ (l_some @ frac @ (^[Y1 : $i]: (l_some @ frac @ (^[Y2 : $i]: (~ ((in @ Y1 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y3 : $i]: ((^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3))))))) @ X1)) => ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y3 : $i]: ((^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3))))))) @ Y0)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ (^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y1) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y1)) @ Y3))))))))))))) => (l_some @ frac @ (^[Y1 : $i]: (l_some @ frac @ (^[Y2 : $i]: (~ ((in @ Y1 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y3 : $i]: ((^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3))))))) @ X1)) => ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y3 : $i]: ((^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3))))))) @ Y0)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ (^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y1)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y1) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2)) @ Y3)))))))))))))))) @ X2))) )), 182.17/42.61 inference(pi_clausification,[],[f4725])). 182.17/42.61 thf(f4725,plain,( 182.17/42.61 ( ! [X1 : $i] : (((in @ X1 @ rat) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ rat) => ((~ (X1 = Y0)) => ((~ (l_some @ frac @ (^[Y1 : $i]: (l_some @ frac @ (^[Y2 : $i]: (~ ((in @ Y1 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y3 : $i]: ((^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3))))))) @ X1)) => ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y3 : $i]: ((^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3))))))) @ Y0)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ (^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y1) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y1)) @ Y3))))))))))))) => (l_some @ frac @ (^[Y1 : $i]: (l_some @ frac @ (^[Y2 : $i]: (~ ((in @ Y1 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y3 : $i]: ((^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3))))))) @ X1)) => ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y3 : $i]: ((^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3))))))) @ Y0)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ (^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y1)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y1) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2)) @ Y3))))))))))))))))))) )), 182.17/42.61 inference(binary_proxy_clausification,[],[f4724])). 182.17/42.61 thf(f4724,plain,( 182.17/42.61 ( ! [X1 : $i] : (($true = ((in @ X1 @ rat) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ rat) => ((~ (X1 = Y0)) => ((~ (l_some @ frac @ (^[Y1 : $i]: (l_some @ frac @ (^[Y2 : $i]: (~ ((in @ Y1 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y3 : $i]: ((^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3))))))) @ X1)) => ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y3 : $i]: ((^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3))))))) @ Y0)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ (^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y1) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y1)) @ Y3))))))))))))) => (l_some @ frac @ (^[Y1 : $i]: (l_some @ frac @ (^[Y2 : $i]: (~ ((in @ Y1 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y3 : $i]: ((^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3))))))) @ X1)) => ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y3 : $i]: ((^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3))))))) @ Y0)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y3 : $i]: ((~ (emptyset = Y3)) & (in @ Y3 @ omega)))) @ (repl @ omega @ (^[Y3 : $i]: (if @ (~ (emptyset = Y3)) @ Y3 @ (eps @ (^[Y4 : $i]: ((in @ Y4 @ omega) & (~ (emptyset = Y4)))))))) @ emptyset) @ (^[Y3 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y1)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y1) @ (second1 @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ Y2)) @ Y3)))))))))))))))))))) )), 182.17/42.61 inference(beta_eta_normalization,[],[f4723])). 182.17/42.61 thf(f4723,plain,( 182.17/42.61 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ rat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ rat) => ((~ (Y0 = Y1)) => ((~ (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (~ ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) @ Y4))))))))))))) => (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (~ ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) @ Y4))))))))))))))))))) @ X1))) )), 182.17/42.61 inference(pi_clausification,[],[f4722])). 182.17/42.61 thf(f4722,plain,( 182.17/42.61 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ rat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ rat) => ((~ (Y0 = Y1)) => ((~ (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (~ ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? 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@ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) @ Y4)))))))))))))))))))))), 182.17/42.61 inference(boolean_simplification,[],[f4721])). 182.17/42.61 thf(f4721,plain,( 182.17/42.61 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ rat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ rat) => (((Y0 = Y1) => $false) => ((~ (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (~ ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) @ Y4))))))))))))) => (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (~ ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) @ Y4)))))))))))))))))))))), 182.17/42.61 inference(boolean_simplification,[],[f4720])). 182.17/42.61 thf(f4720,plain,( 182.17/42.61 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ rat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ rat) => (((Y0 = Y1) => $false) => ((~ (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (~ ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => ((l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) @ Y4)))) => $false))))))))) => (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (~ ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) @ Y4)))))))))))))))))))) = $true)), 182.17/42.61 inference(boolean_simplification,[],[f4719])). 182.17/42.61 thf(f4719,plain,( 182.17/42.61 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ rat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ rat) => (((Y0 = Y1) => $false) => ((~ (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (~ ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => (~ (~ ((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => ((l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) @ Y4)))) => $false))))))))))) => (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (~ ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) @ Y4)))))))))))))))))))))), 182.17/42.61 inference(boolean_simplification,[],[f4718])). 182.17/42.61 thf(f4718,plain,( 182.17/42.61 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ rat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ rat) => (((Y0 = Y1) => $false) => ((~ (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (~ ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => (~ (((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => ((l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) @ Y4)))) => $false)) => $false))))))))) => (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (~ ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) @ Y4)))))))))))))))))))) = $true)), 182.17/42.61 inference(boolean_simplification,[],[f4717])). 182.17/42.61 thf(f4717,plain,( 182.17/42.61 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ rat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ rat) => (((Y0 = Y1) => $false) => ((~ (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (~ ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => ((l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) @ Y4)))) => $false)) => $false) => $false)))))))) => (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (~ ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) @ Y4)))))))))))))))))))))), 182.17/42.61 inference(boolean_simplification,[],[f4716])). 182.17/42.61 thf(f4716,plain,( 182.17/42.61 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ rat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ rat) => (((Y0 = Y1) => $false) => ((~ (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => ((l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) @ Y4)))) => $false)) => $false) => $false)) => $false)))))) => (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (~ ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) @ Y4)))))))))))))))))))) = $true)), 182.17/42.61 inference(boolean_simplification,[],[f4715])). 182.17/42.61 thf(f4715,plain,( 182.17/42.61 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ rat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ rat) => (((Y0 = Y1) => $false) => (((l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => ((l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) @ Y4)))) => $false)) => $false) => $false)) => $false))))) => $false) => (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (~ ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => (~ (l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) @ Y4)))))))))))))))))))))), 182.17/42.62 inference(boolean_simplification,[],[f4714])). 182.17/42.62 thf(f4714,plain,( 182.17/42.62 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ rat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ rat) => (((Y0 = Y1) => $false) => (((l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => ((l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) @ Y4)))) => $false)) => $false) => $false)) => $false))))) => $false) => (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (~ ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => ((l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) @ Y4)))) => $false)))))))))))))))))), 182.17/42.62 inference(boolean_simplification,[],[f4713])). 182.17/42.62 thf(f4713,plain,( 182.17/42.62 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ rat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ rat) => (((Y0 = Y1) => $false) => (((l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? 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@ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) @ Y4)))) => $false)) => $false) => $false)) => $false))))) => $false) => (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (~ ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => (~ (~ ((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => ((l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) @ Y4)))) => $false)))))))))))))))))))), 182.17/42.62 inference(boolean_simplification,[],[f4712])). 182.17/42.62 thf(f4712,plain,( 182.17/42.62 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ rat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ rat) => (((Y0 = Y1) => $false) => (((l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => ((l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) @ Y4)))) => $false)) => $false) => $false)) => $false))))) => $false) => (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (~ ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => (~ (((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => ((l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) @ Y4)))) => $false)) => $false)))))))))))))))) = $true)), 182.17/42.62 inference(boolean_simplification,[],[f4711])). 182.17/42.62 thf(f4711,plain,( 182.17/42.62 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ rat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ rat) => (((Y0 = Y1) => $false) => (((l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => ((l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) @ Y4)))) => $false)) => $false) => $false)) => $false))))) => $false) => (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (~ ((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => ((l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) @ Y4)))) => $false)) => $false) => $false))))))))))))))))), 182.17/42.62 inference(boolean_simplification,[],[f4710])). 182.17/42.62 thf(f4710,plain,( 182.17/42.62 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ rat) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ rat) => (((Y0 = Y1) => $false) => (((l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => ((l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) @ Y4)))) => $false)) => $false) => $false)) => $false))))) => $false) => (l_some @ frac @ (^[Y2 : $i]: (l_some @ frac @ (^[Y3 : $i]: (((in @ Y2 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y0)) => ((((in @ Y3 @ (e_in @ (power @ frac) @ (anec @ frac @ (^[Y4 : $i]: ((^[Y5 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5)) = (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y5) @ (second1 @ (if @ (?? @ $i @ (^[Y6 : $i]: ((~ (emptyset = Y6)) & (in @ Y6 @ omega)))) @ (repl @ omega @ (^[Y6 : $i]: (if @ (~ (emptyset = Y6)) @ Y6 @ (eps @ (^[Y7 : $i]: ((in @ Y7 @ omega) & (~ (emptyset = Y7)))))))) @ emptyset) @ Y4))))))) @ Y1)) => ((l_some @ (if @ (?? @ $i @ (^[Y4 : $i]: ((~ (emptyset = Y4)) & (in @ Y4 @ omega)))) @ (repl @ omega @ (^[Y4 : $i]: (if @ (~ (emptyset = Y4)) @ Y4 @ (eps @ (^[Y5 : $i]: ((in @ Y5 @ omega) & (~ (emptyset = Y5)))))))) @ emptyset) @ (^[Y4 : $i]: ((n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2)) = (n_pl @ (n_ts @ (first1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y2) @ (second1 @ (if @ (?? @ $i @ (^[Y5 : $i]: ((~ (emptyset = Y5)) & (in @ Y5 @ omega)))) @ (repl @ omega @ (^[Y5 : $i]: (if @ (~ (emptyset = Y5)) @ Y5 @ (eps @ (^[Y6 : $i]: ((in @ Y6 @ omega) & (~ (emptyset = Y6)))))))) @ emptyset) @ Y3)) @ Y4)))) => $false)) => $false) => $false)) => $false))))))))))))))), 182.17/42.62 inference(beta_eta_normalization,[],[f1745])). 182.17/42.62 thf(f1745,plain,( 182.17/42.62 ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i > $o]: (Y4 @ Y3)))) @ Y2 @ Y0) => (Y1 @ Y2))))))) @ (^[Y0 : $i]: (in @ Y0 @ rat)) @ (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: (!! @ $i @ (^[Y3 : $i]: (((^[Y4 : $i]: ((^[Y5 : $i > $o]: (Y5 @ Y4)))) @ Y3 @ Y1) => (Y2 @ Y3))))))) @ (^[Y1 : $i]: (in @ Y1 @ rat)) @ (^[Y1 : $i]: ((^[Y2 : $o]: ((^[Y3 : $o]: ((^[Y4 : $o]: ((^[Y5 : $o]: ((^[Y6 : $o]: ((^[Y7 : $o]: (Y6 => Y7)))) @ ((^[Y6 : $o]: ((^[Y7 : $o]: ((^[Y8 : $o]: (Y7 => Y8)))) @ Y6 @ $false)) @ Y5))) @ Y2 @ ((^[Y5 : $o]: ((^[Y6 : $o]: ((^[Y7 : $o]: (Y6 => Y7)))) @ ((^[Y6 : $o]: ((^[Y7 : $o]: ((^[Y8 : $o]: (Y7 => Y8)))) @ Y6 @ $false)) @ Y5))) @ Y3 @ Y4))))))) @ ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (Y3 = Y4)))))) @ rat @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (l_some @ frac @ (^[Y4 : $i]: (l_some @ frac @ (^[Y5 : $i]: ((^[Y6 : $o]: ((^[Y7 : $o]: ((^[Y8 : $o]: ((^[Y9 : $o]: ((^[Y10 : $o]: ((^[Y11 : $o]: ((^[Y12 : $o]: ((^[Y13 : $o]: (Y12 => Y13)))) @ Y11 @ $false)) @ ((^[Y11 : $o]: ((^[Y12 : $o]: ((^[Y13 : $o]: ((^[Y14 : $o]: (Y13 => Y14)))) @ Y11 @ ((^[Y13 : $o]: ((^[Y14 : $o]: ((^[Y15 : $o]: (Y14 => Y15)))) @ Y13 @ $false)) @ Y12))))) @ Y9 @ Y10))))) @ Y6 @ ((^[Y9 : $o]: ((^[Y10 : $o]: ((^[Y11 : $o]: ((^[Y12 : $o]: ((^[Y13 : $o]: (Y12 => Y13)))) @ Y11 @ $false)) @ ((^[Y11 : $o]: ((^[Y12 : $o]: ((^[Y13 : $o]: ((^[Y14 : $o]: (Y13 => Y14)))) @ Y11 @ ((^[Y13 : $o]: ((^[Y14 : $o]: ((^[Y15 : $o]: (Y14 => Y15)))) @ Y13 @ $false)) @ Y12))))) @ Y9 @ Y10))))) @ Y7 @ Y8))))))) @ ((^[Y6 : $i]: (in)) @ frac @ Y4 @ ((^[Y6 : $i]: ((^[Y7 : $i > $i > $o]: (e_in @ (power @ Y6) @ (anec @ Y6 @ Y7))))) @ frac @ (^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (Y9 = Y10)))))) @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ (n_ts @ (first1 @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ Y6) @ (second1 @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ Y7)) @ (n_ts @ (first1 @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ Y7) @ (second1 @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ Y6)))))) @ Y2)) @ ((^[Y6 : $i]: (in)) @ frac @ Y5 @ ((^[Y6 : $i]: ((^[Y7 : $i > $i > $o]: (e_in @ (power @ Y6) @ (anec @ Y6 @ Y7))))) @ frac @ (^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (Y9 = Y10)))))) @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ (n_ts @ (first1 @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ Y6) @ (second1 @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ Y7)) @ (n_ts @ (first1 @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ Y7) @ (second1 @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ Y6)))))) @ Y3)) @ ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: (l_some @ ((^[Y10 : $i]: ((^[Y11 : $i > $o]: (if @ (?? @ $i @ (^[Y12 : $i]: ((Y11 @ Y12) & (in @ Y12 @ Y10)))) @ (repl @ Y10 @ (^[Y12 : $i]: (if @ (Y11 @ Y12) @ Y12 @ (eps @ (^[Y13 : $i]: ((in @ Y13 @ Y10) & (Y11 @ Y13))))))) @ emptyset)))) @ omega @ (^[Y10 : $i]: (~ (emptyset = Y10)))) @ ((^[Y10 : $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: ((^[Y13 : $i]: ((^[Y14 : $i]: ((^[Y15 : $i]: (Y14 = Y15)))))) @ ((^[Y13 : $i]: ((^[Y14 : $i > $o]: (if @ (?? @ $i @ (^[Y15 : $i]: ((Y14 @ Y15) & (in @ Y15 @ Y13)))) @ (repl @ Y13 @ (^[Y15 : $i]: (if @ (Y14 @ Y15) @ Y15 @ (eps @ (^[Y16 : $i]: ((in @ Y16 @ Y13) & (Y14 @ Y16))))))) @ emptyset)))) @ omega @ (^[Y13 : $i]: (~ (emptyset = Y13)))) @ Y10 @ (n_pl @ Y11 @ Y12))))))) @ Y8 @ Y9))))) @ (n_ts @ (first1 @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ Y6) @ (second1 @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ Y7)) @ (n_ts @ (first1 @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ Y7) @ (second1 @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ Y6)))))) @ Y4 @ Y5))))))))) @ Y0 @ Y1) @ ((^[Y2 : $i]: ((^[Y3 : $i]: (l_some @ frac @ (^[Y4 : $i]: (l_some @ frac @ (^[Y5 : $i]: ((^[Y6 : $o]: ((^[Y7 : $o]: ((^[Y8 : $o]: ((^[Y9 : $o]: ((^[Y10 : $o]: ((^[Y11 : $o]: ((^[Y12 : $o]: ((^[Y13 : $o]: (Y12 => Y13)))) @ Y11 @ $false)) @ ((^[Y11 : $o]: ((^[Y12 : $o]: ((^[Y13 : $o]: ((^[Y14 : $o]: (Y13 => Y14)))) @ Y11 @ ((^[Y13 : $o]: ((^[Y14 : $o]: ((^[Y15 : $o]: (Y14 => Y15)))) @ Y13 @ $false)) @ Y12))))) @ Y9 @ Y10))))) @ Y6 @ ((^[Y9 : $o]: ((^[Y10 : $o]: ((^[Y11 : $o]: ((^[Y12 : $o]: ((^[Y13 : $o]: (Y12 => Y13)))) @ Y11 @ $false)) @ ((^[Y11 : $o]: ((^[Y12 : $o]: ((^[Y13 : $o]: ((^[Y14 : $o]: (Y13 => Y14)))) @ Y11 @ ((^[Y13 : $o]: ((^[Y14 : $o]: ((^[Y15 : $o]: (Y14 => Y15)))) @ Y13 @ $false)) @ Y12))))) @ Y9 @ Y10))))) @ Y7 @ Y8))))))) @ ((^[Y6 : $i]: (in)) @ frac @ Y4 @ ((^[Y6 : $i]: ((^[Y7 : $i > $i > $o]: (e_in @ (power @ Y6) @ (anec @ Y6 @ Y7))))) @ frac @ (^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (Y9 = Y10)))))) @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ (n_ts @ (first1 @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ Y6) @ (second1 @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ Y7)) @ (n_ts @ (first1 @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ Y7) @ (second1 @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ Y6)))))) @ Y2)) @ ((^[Y6 : $i]: (in)) @ frac @ Y5 @ ((^[Y6 : $i]: ((^[Y7 : $i > $i > $o]: (e_in @ (power @ Y6) @ (anec @ Y6 @ Y7))))) @ frac @ (^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (Y9 = Y10)))))) @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ (n_ts @ (first1 @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ Y6) @ (second1 @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ Y7)) @ (n_ts @ (first1 @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ Y7) @ (second1 @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ Y6)))))) @ Y3)) @ ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: (l_some @ ((^[Y10 : $i]: ((^[Y11 : $i > $o]: (if @ (?? @ $i @ (^[Y12 : $i]: ((Y11 @ Y12) & (in @ Y12 @ Y10)))) @ (repl @ Y10 @ (^[Y12 : $i]: (if @ (Y11 @ Y12) @ Y12 @ (eps @ (^[Y13 : $i]: ((in @ Y13 @ Y10) & (Y11 @ Y13))))))) @ emptyset)))) @ omega @ (^[Y10 : $i]: (~ (emptyset = Y10)))) @ ((^[Y10 : $i]: ((^[Y11 : $i]: ((^[Y12 : $i]: ((^[Y13 : $i]: ((^[Y14 : $i]: ((^[Y15 : $i]: (Y14 = Y15)))))) @ ((^[Y13 : $i]: ((^[Y14 : $i > $o]: (if @ (?? @ $i @ (^[Y15 : $i]: ((Y14 @ Y15) & (in @ Y15 @ Y13)))) @ (repl @ Y13 @ (^[Y15 : $i]: (if @ (Y14 @ Y15) @ Y15 @ (eps @ (^[Y16 : $i]: ((in @ Y16 @ Y13) & (Y14 @ Y16))))))) @ emptyset)))) @ omega @ (^[Y13 : $i]: (~ (emptyset = Y13)))) @ Y10 @ (n_pl @ Y11 @ Y12))))))) @ Y9 @ Y8))))) @ (n_ts @ (first1 @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ Y6) @ (second1 @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ Y7)) @ (n_ts @ (first1 @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ Y7) @ (second1 @ ((^[Y8 : $i]: ((^[Y9 : $i > $o]: (if @ (?? @ $i @ (^[Y10 : $i]: ((Y9 @ Y10) & (in @ Y10 @ Y8)))) @ (repl @ Y8 @ (^[Y10 : $i]: (if @ (Y9 @ Y10) @ Y10 @ (eps @ (^[Y11 : $i]: ((in @ Y11 @ Y8) & (Y9 @ Y11))))))) @ emptyset)))) @ omega @ (^[Y8 : $i]: (~ (emptyset = Y8)))) @ Y6)))))) @ Y4 @ Y5))))))))) @ Y0 @ Y1)))))))), 182.17/42.62 inference(definition_unfolding,[],[f1356,f1666,f1666,f1690,f1694,f1700,f1702])). 182.17/42.62 thf(f1690,plain,( 182.17/42.62 (or3 = (^[Y0 : $o]: ((^[Y1 : $o]: ((^[Y2 : $o]: ((^[Y3 : $o]: ((^[Y4 : $o]: ((^[Y5 : $o]: (Y4 => Y5)))) @ ((^[Y4 : $o]: ((^[Y5 : $o]: ((^[Y6 : $o]: (Y5 => Y6)))) @ Y4 @ $false)) @ Y3))) @ Y0 @ ((^[Y3 : $o]: ((^[Y4 : $o]: ((^[Y5 : $o]: (Y4 => Y5)))) @ ((^[Y4 : $o]: ((^[Y5 : $o]: ((^[Y6 : $o]: (Y5 => Y6)))) @ Y4 @ $false)) @ Y3))) @ Y1 @ Y2))))))))), 182.17/42.62 inference(definition_unfolding,[],[f1410,f1668,f1668])). 182.17/42.62 thf(f1410,plain,( 182.17/42.62 (or3 = (^[Y0 : $o]: ((^[Y1 : $o]: ((^[Y2 : $o]: (l_or @ Y0 @ (l_or @ Y1 @ Y2))))))))), 182.17/42.62 inference(cnf_transformation,[],[f1130])). 182.17/42.62 thf(f1130,plain,( 182.17/42.62 (or3 = (^[Y0 : $o]: ((^[Y1 : $o]: ((^[Y2 : $o]: (l_or @ Y0 @ (l_or @ Y1 @ Y2))))))))), 182.17/42.62 inference(fool_elimination,[],[f45])). 182.17/42.62 thf(f45,axiom,( 182.17/42.62 (or3 = (^[X0 : $o, X1 : $o, X2 : $o] : (l_or @ X0 @ (l_or @ X1 @ X2))))), 182.17/42.62 file('/export/starexec/sandbox2/tmp/tmp.Wx2OXKe4bp/E---3.1_26322.p',def_or3)). 182.17/42.62 thf(f1356,plain,( 182.17/42.62 ($true = (all_of @ (^[Y0 : $i]: (in @ Y0 @ rat)) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ rat)) @ (^[Y1 : $i]: (or3 @ (rt_is @ Y0 @ Y1) @ (rt_more @ Y0 @ Y1) @ (rt_less @ Y0 @ Y1)))))))), 182.17/42.62 inference(cnf_transformation,[],[f1223])). 182.17/42.62 thf(f1223,plain,( 182.17/42.62 ($true = (all_of @ (^[Y0 : $i]: (in @ Y0 @ rat)) @ (^[Y0 : $i]: (all_of @ (^[Y1 : $i]: (in @ Y1 @ rat)) @ (^[Y1 : $i]: (or3 @ (rt_is @ Y0 @ Y1) @ (rt_more @ Y0 @ Y1) @ (rt_less @ Y0 @ Y1)))))))), 182.17/42.62 inference(fool_elimination,[],[f1222])). 182.17/42.62 thf(f1222,plain,( 182.17/42.62 (all_of @ (^[X0 : $i] : (in @ X0 @ rat)) @ (^[X1 : $i] : (all_of @ (^[X2 : $i] : (in @ X2 @ rat)) @ (^[X3 : $i] : (or3 @ (rt_is @ X1 @ X3) @ (rt_more @ X1 @ X3) @ (rt_less @ X1 @ X3))))))), 182.17/42.62 inference(rectify,[],[f495])). 182.17/42.62 thf(f495,axiom,( 182.17/42.62 (all_of @ (^[X0 : $i] : (in @ X0 @ rat)) @ (^[X0 : $i] : (all_of @ (^[X1 : $i] : (in @ X1 @ rat)) @ (^[X1 : $i] : (or3 @ (rt_is @ X0 @ X1) @ (rt_more @ X0 @ X1) @ (rt_less @ X0 @ X1))))))), 182.17/42.62 file('/export/starexec/sandbox2/tmp/tmp.Wx2OXKe4bp/E---3.1_26322.p',satz81a)). 182.17/42.62 thf(f3694,plain,( 182.17/42.62 ($true = (in @ sK12 @ rat))), 182.17/42.62 inference(binary_proxy_clausification,[],[f3692])). 182.17/42.62 % SZS output end Proof for E---3.1_26322 182.17/42.62 % (26751)------------------------------ 182.17/42.62 % (26751)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 182.17/42.62 % (26751)Termination reason: Refutation 182.17/42.62 182.17/42.62 % (26751)Memory used [KB]: 16886 182.17/42.62 % (26751)Time elapsed: 10.201 s 182.17/42.62 % (26751)Instructions burned: 11074 (million) 182.17/42.62 % (26751)------------------------------ 182.17/42.62 % (26751)------------------------------ 182.17/42.62 % (26428)Success in time 42.193 s 182.17/42.62 EOF